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METAOBJ Manual - (La)TeX Navigator

1. Figure 44 Dismantling a tree The possibilities are endless 121 10 Comparison with other packages 10 1 Compatibility with boxes mp METAOBJ can be used instead of boxes mp but not together with boxes mp It contains most of the functionalities found in John Hobby s boxes and rboxes packages In particular it uses the same syntax for accessing the cardinal points of an object or setting an object position The newBox constructor can be used in place of boxit and we have actu ally redefined boxit to behave like newBox Similarly rboxit and circleit have been redefined to refer to newRBox which is a variant of newBox and to newEllipse However there is one important difference In METAOBJ when an object is created it is rigid Once the newBox constructor has been called it is no longer possible to easily change the values of dx and dy for instance In the boxes package it is possible to define a box with a certain content to put its center somewhere after the call to boxit this is also how it is done in METROBJ and then to set the values of dx and dy In METAOBJ these values must be given when newBox is called Nevertheless it should be possible to reuse most of the figures written for the boxes package with METROBJ 10 2 fancybox package The fancybox package provides several ways to frame a box e Nshadowbox this can be achieved in METAOBJ with a Box and the shadow
2. ncline 0bj t obj Obj t root treeroot Obj t 1 we call ncfan because we draw a non standard fan ncfan Obj t obj Obj t root ntreepos Obj t 2 1 2 Obj t c origin draw_0bj t we call drawfan because we draw a non standard fan drawfan 0bj t ntreepos Obj t 2 102 2 Figure 40 Skipping levels in a tree after page 50 of 16 we take great care to have the circles properly aligned 111 above ove below t 7T Tc TC TC Tc treemode R arrows draw hsep 2cm Obj t c origin ObjLabel Obj t btex below etex labpathid 1 labdir bot ObjLabel 0bj t btex above etex labpathid 2 labdir top ObjLabel 0bj t btex above etex labpathid 3 labdir top draw 0bj t Figure 41 Positionning of labels with the labpathid and labdir options t 7T Tc TC TC Tc treemode R arrows draw hsep 2cm Obj t c origin ObjLabel Obj t btex below etex labpathid 1 labdir bot labangle 0 labpos 0 4 bjLabel 0bj t btex above etex labpathid 2 labdir top labpos 0 6 ObjLabel Obj t btex above etex labpathid 3 labdir top labangle 0 labpos 0 3 draw_0bj t Figure 42 Alignment of labels on paths after page 45 of 16 112 newBox a a newEllipse b b newEllipse c c filled true fillcolor red picturecolor green framecolor blue framewidth 2pt newTree t c a b l
3. _T TCs T_ TCs Tr btex J_1 etex Tr_ btex J 2 etex hsep 3cm T_ TCs Tr btex K 1 etex Tr btex K 2 etex hsep 3cm Dis _T TCs T_ TCs Tr_ btex Y 1 etex Tr btex Y_2 etex hsep 3cm T_ TCs Tr btex X_1 etex Tr btex X 2 etex hsep 3cm Obj t c origin draw_0bj t Figure 28 A complete tree TCs is the default filled disk after page 40 of 16 We don t have a hook for a given level as PSTricks does so we have to give the hsep option several times however we could avoid it by building the tree in a non streamlined way Also the labels are given in the opposite order but the order could be changed with the treeflip option 103 0 6 setObjectDefaultOption Tree treemode R t T new Circle circmargin 3mm Tcircle btex L etex Tcircle btex H etex Tcircle btex K etex Tcircle btex N etex edge ncdiag angleB 0 armA 0 armB 1cm hsep 3 5cm posA e arrows draw Obj t c origin draw_0bj t Figure 29 Illustrating the ncdiag connection in a tree after page 41 of 16 acy A a Nee ee O T lt Y setObjectDefaultOption Tree treemode R setObjectDefaultOption Tree Ralign center t T_ new_Circle_ circmargin 1mm framewidth 1pt Tr btex x lt y etex Tr_ btex z_2 lt yMeq x etex Tr_ btex z_1 lt y leq z 2 etex Tr_ btex z 1Mleq y etex edge ncdiag node
4. framed false Obj t c origin 0 5cm draw_0bj t Figure 18 Forcing the alignment on the bottom with struts and smash after page 34 of 16 98 A LN setCurveDefaultOption arrows draw setCurveDefault ption nodesepA 3pt works setCurveDefault ption nodesepB 3pt works setObjectDefaultOption Tree hideleaves true t _T TCs _T TCs TCs Tn _T TCs TCs _T TCs Tn TCs Obj t c origin draw_0bj t Figure 19 Illustrating the nodesepA option after page 35 of 16 the empty node Tn doesn t have the same size as the black disks and causes the leftmost segment to have a slope slightly different to the two other segments going to the right this could be corrected with the treenodehsize option TCs is the default filled disk 99 0 00 def Tdot expr p new Circle p circmargin 2mm enddef def Toplus Tdot btex 4 etex enddef setCurveDefault ption arrows draw setObjectDefaultOption Tree hideleaves true setCurveDefaultOption nodesepA 3pt setCurveDefaultOption nodesepB 3pt setObjectDefaultOption Tree Ualign center setObjectDefaultOption Tree Lalign center setObjectDefaultOption Tree hbsep 5mm setObjectDefaultOption Tree vbsep 5mm setObjectDefaultOption Tree hsep 2cm setObjectDefaultOption Tree vsep 2cm t T_ Tc_ 1 5mm T
5. 5 7 6 ncangles ncangles is similar to ncangle but the length of arm A measured from the node is fixed by the armA option Arm A is connected to arm B by two line segments that meet arm A and each other at right angles The angle at which they join arm B and the length of the connecting segments depends on the positions of the two arms ncangles generally draws a total of four line segments 46 ncangles a b angleA 0 angleB 50 linecolor blue linewidth 1pt armA 3cm armB 2cm N In the next example the start of the line is offset by 0 1cm ncangles a b angleA 0 angleB 50 linecolor blue linewidth 1pt armA 3cm armB 2cm offsetA 0 1cm ncangles a b angleA 90 angleB 50 linecolor blue linewidth 1pt armA 3cm armB 2cm 5 7 7 ncdiag ncdiag draws an arm at each node joining at angle angleA or angleB and with a length of armA or armB from the centers of the nodes Then the two arms are connected by a straight line so that the whole line has three line segments ncdiag a b angleA 90 angleB 50 linecolor blue linewidth 1pt armA 3cm armB 2cm ncdiag a b angleA 0 angleB 90 linecolor blue linewidth 1pt armA 2cm armB 2cm L 47 5 7 8 ncdiagg ncdiagg is similar to ncdiag but only the arm for node A is drawn The end of this arm is then connected directly to node B armB is not used ene ncdiagg a b
6. If the pointedfan option is set to false the top end of the fan is at the center of the root node The color of a fan can be changed with the fillcolor option its style can be changed with the fanlinestyle option and the rounding of its corners can be modified with the fanlinearc option A root node can also be a fan as demonstrated in the following example also adapted from page 36 of 16 81 t _T new_Circle btex foo etex T new HFan 1cm 0 filled true fillcolor red fanlinearc imm TC new HFan 1cm 0 fanlinestyle dashed evenly gt Obj t c origin draw_0bj t Here the red fan is the root of a subtree The top of the black disk is aligned with the bottom of the fan because descending trees are by default aligned on the top and the fan is considered an horizontal line and its top is the same as its bottom This wouldn t have been the case if the second parameter of new_HFan_ had been different to 0 HFan and VFan options The two classes have exactly the same options Option Type Default filled boolean false fillcolor color black edge string yes pointedfan boolean true fanlinestyle string uL fanlinearc numeric 0 Most of these options have been explained The edge option is a string which by default is yes This means that the fan edges must be drawn There are certain cases where we want fans to skip levels and one way of achieving it is t
7. angleA 90 angleB 50 linecolor blue linewidth 1pt armA 3cm ncdiagg a b angleA 0 angleB 90 linecolor blue linewidth 1pt armA 2cm 5 7 9 ncloop ncloop is also in the same family as ncangle and ncangles but now typically five line segments are drawn Hence ncloop can reach around to opposite sides of the nodes The lengths of the arms from the centers of the nodes are fixed by armA and armB Starting at arm A ncloop makes a 90 degrees turn to the left drawing a segment of length loopsize This segment connects to arm B the way arm A connects to arm B with ncangles that is two more segments are drawn which join the first segment and each other at right angles and then join arm B The next two examples seem buggy but I think I have correctly imple mented the specification from PSTricks In the first case the value given to armB is too large ncloop a b angleA 0 angleB 90 linecolor blue linewidth 1pt armA 2cm armB 2cm 48 ncloop a a angleA 0 angleB 90 linecolor blue linewidth 1pt armA 2cm armB 2cm This is like the first example but the value of armB is smaller ncloop a b angleA 0 angleB 90 linecolor blue linewidth 1pt armA 2cm armB icm b Here are two more examples ncloop a b angleA 0 angleB 180 linecolor blue linewidth 1pt armA 2cm armB icm ncloop a b angleA 0 angl
8. apples oranges vegetables In the next tree the two subtrees overlap because the hideleaves was set to true newBox a btex apples etex newBox b btex oranges etex newBox c btex bananas etex newBox f btex fruits etex newTree fruits f a b c food Dalign bot hideleaves true newBox d btex potatoes etex vegetables newBox e btex peas etex newBox v btex vegetables etex Teas newTree vegetables v d e Dalign center newBox fo btex food etex newTree food fo fruits vegetables hsep 1cm scale0bj food 5 food c origin draw0bj food apples oranges newBox a btex apples etex newBox b btex oranges etex newBox c btex bananas etex newBox f btex fruits etex newTree fruits f a b c Dalign bot hideleaves true newBox d btex potatoes etex newBox e btex peas etex newBox v btex vegetables etex newTree vegetables v d e Dalign center hideleaves true newBox fo btex food etex newTree food fo fruits vegetables hbsep 5cm scale0bj food 5 food c origin draw0bj food apples oranges bananas potatoes peas Two different directions can be mixed In this case we have hidden the fruits 77 food vegetables apples oranges bananas peas potatoes newBox a btex apples etex newBox b btex oranges etex newBo
9. fit false polymargin 5mm newBox b btex Box B etex scaled magstep3 newHRazor ba 1cm Box A Box B newPolygon c btex Box C etex scaled magstep2 11 polymargin 3mm newHBox h a b ba c align center hsep 3mm h c origin draw0bj h 68 nw SW HBox options Option Type Default Description dx numeric 0 horizontal clearance around the object dy numeric 0 vertical clearance around the object hbsep numeric 1mm horizontal separation between elements elementsize numeric 1pt if non negative all the objects are assumed to have this width align string bot top and center are the other possible values framed boolean false true if the object is framed filled boolean false true if the box is filled fillcolor color black filling color framewidth numeric 5bp width of the frame framecolor color black color of the frame framestyle string style of the frame dashed etc flip boolean false if true reverses the order of the components shadow boolean false true if there is a shadow framed too must be true shadowcolor color black shadow color 7 3 2 VBox A VBox is the vertical equivalent of an HBox The boxes are piled up from bottom to top which is unlike the behavior of Nvbox in TEX where the components would start at the top By default the components are aligned to the left as in Wvbox Box C Box B
10. rncarc rncdiag rncdiagg rncbar rncloop rncbox rncarcbox rnczigzag and rnccoil There are no reverse variants of the tree and matrix variants of the con nection commands If needed they can be easily supplied 5 8 Adding labels Labels can be added to an object The main command is ObjLabel This command takes an object as parameter a label and then a list of options Let us first look at a first example also as figure 41 t T Tc TC TC Tc treemode R arrows draw hsep 2cm Obj t c origin ove ObjLabel Obj t btex below etex labpathid 1 labdir bot ObjLabel Obj t btex above etex labpathid 2 labdir top below bjLabel 0bj t btex above etex labpathid 3 labdir top draw 0bj t abov In this example three labels have been added to the tree t This tree is given by a number and the real tree object is obtained when Obj is called on t ObjLabel takes 0bj t as its first suffix parameter and the labels are given as TEX pictures The options decide where the labels will be put It is the labpathid option which decides on which connection the label goes In a tree each standard connection has a number from 1 until n the number of subtrees This value can be given as parameter to labpathid If this had been the only option the labels would have come out over the connections The abdir option 54 is used to shift the label with respect to the normal point where it w
11. 1cm obj subc a obj suba a 7cm 2cm Qitsw xpart obj Gitsuba a ypart obj subb c ne obj G subc a 23 Here we defined the sw point as having the same xpart as point a of subobject suba and the same ypart as point c of subobject subb Incidentally we would have obtained the same result with the function rebindVisible0bj even with an inappropriate definition of the cardinal points This function takes an object and moves the outside cardinal points so that they encloses the visible part tightly However in order for this to work the cardinal points must be attached to the object If we now apply transformations to the object the interface will follow the transformations The previous object rotated clockwise by 30 degrees produces Notice that the scale operation does not apply to the thickness of the lines It would be possible to have the transformation operate on the thickness of the lines but it is not the default behavior We can even reflect it for instance with reflect0bj tta origin 0 1 which is a reflection about a vertical axis 24 Since every linear transformation unties the objet to which it is applied be cause presumably the object is likely to be put elsewhere there is no rotation around a point or a reflection with respect to a certain line There are only absolute rotations and reflections with respect to directions Writing reflect0bj
12. 31 115 ObjPoint command 12 31 59 114 ObjPointArray command 115 ObjString command 115 ObjStringArray command 115 ObjSubArray command 115 ObjTransform command 115 ObjTransformArray command 115 offset connection option 42 offsetA connection option 41 43 56 offsetB connection option 41 43 56 OptionValue command 37 pairarraylist_ attribute 57 pairlist_ attribute 57 pathfillcolor connection option 38 41 pathfilled connection option 38 41 91 picturearraylist_ attribute 57 picturecolor class option 26 62 67 picturelist_ attribute 57 pointarraylist_ attribute 57 pointedfan class option 81 82 pointlist_ attribute 56 57 points in arrayslist_ attribute 57 Polygon class 7 63 116 polymargin class option 63 pos connection option 42 posA connection option 41 43 106 posB connection option 41 43 PTree class 56 82 84 Ralign class option 80 RandomBox class 60 RBox class 119 rbox radius class option 31 62 rdrawarrow command 40 107 rebindObj command 34 rebindrelativeObj command 34 75 76 rebindVisibleObj command 24 27 34 79 RecursiveBox class 28 71 replaceMatrixElement exp command 90 replaceTreeElement exp command 82 rncangle command 54 rncangles command 54 rncarc command 54 rncarcbox command 54 rncbar command 54 rncbox command 54 rnccoil comm
13. 44 5 7 3 ncarc ncarc connects the two nodes with an arc The angle between the arc and the line between the two nodes is arcangleA at the beginning and arcangleB at the end There are default values that draw a curved connection as shown below ncarc a b ncarc a b ncarc b a ncarc a b arcangleA 50 ncarc b a NA 5 7 4 ncbar ncbar draws a line from the first node leaving at angle angleA The line reaches the second node with the same angle angleB is ignored These two lines are connected with a line at right angles and each end line is at least as long as armA or armB the length being counted until the center of the objects In this example we also set the color with linecolor ncbar a b angleA 50 linecolor blue linewidth 1pt armB 2cm a 45 gt ncbar a b angleA 90 linecolor blue linewidth 1pt armB 2cm 5 7 5 ncangle ncangle usually draws three segments but in certain cases there are only two The two extreme segments are at angles defined by the angleA and angleB options The point on the last segment at a distance armB from the node is connected to node A with a right angle armA is not taken into account In the next example the first segment is of length 0 ncangle a b angleA 90 angleB 80 linecolor blue linewidth 1pt armB 2cm ncangle a b angleA 0 angleB 50 linecolor blue linewidth 1pt armA 3cm armB 2cm
14. 54 tccurve command 54 tcdiag command 54 tcdiagg command 54 Tcircle_ command 64 tcline command 40 54 tcloop command 54 TCs command 65 97 99 101 103 Tf command 62 81 Tn command 59 99 109 Toval_ command 64 106 Tr_ command 62 106 109 transformarraylist_ attribute 57 transformObj command 11 Tree class 7 32 36 42 73 79 81 82 90 113 117 118 treeflip class option 76 80 103 treemode class option 36 37 80 83 85 treenodehsize class option 80 99 101 106 treenodehsize command 102 treenodevsize class option 80 101 Ualign class option 80 untieObj command 15 35 valign class option 89 92 vardef command 8 VBox class 67 69 80 vbsep class option 70 80 VFan class 81 visible connection option 41 Von Koch flake 8 VonKochFlake class 72 VRazor class 60 81 vsep class option 66 67 70 80 85 92 whatever command 12 136
15. 72 80 85 92 edge 80 82 104 107 elementsize 69 70 fanlinearc 81 82 fanlinestyle 81 82 fillcolor 34 60 67 69 70 72 80 82 85 92 filled 34 37 60 67 69 70 72 80 82 85 92 117 fit 31 62 64 66 67 flip 69 70 framecolor 34 60 67 69 70 72 80 85 92 framed 31 34 36 59 67 69 70 72 80 85 92 framestyle 34 60 67 69 70 72 80 85 92 framewidth 34 60 67 69 70 72 80 85 92 halign 89 92 hbsep 69 80 hideleaves 77 78 80 81 hsep 66 68 80 85 92 103 Lalign 80 lenddx 84 85 Irsep 85 Istartdx 85 matrixnodehsize 92 matrixnodevsize 92 name 37 40 105 picturecolor 26 62 67 pointedfan 81 82 polymargin 63 Ralign 80 rbox radius 31 62 rotangle 72 rrsep 85 rule 85 shadow 31 34 59 67 69 70 12 B0 85 02 shadowcolor 34 59 67 69 70 72 80 85 92 treeflip 76 80 103 treemode 36 37 80 83 85 treenodehsize 80 99 101 106 treenodevsize 80 101 Ualign 80 valign 89 92 vbsep 70 80 vsep 66 67 70 80 85 92 Classes Assumption 83 Axiom 83 BB 27 34 90 117 Box 7 8 30 31 38 61 62 65 67 81 83 122 Circle 64 81 119 Conclusion 83 DBox 65 66 122 DHllipse 66 Ellipse 63 66 119 120 122 Empty Box 9 27 28 32 60 61 HBox 67 70 80 HFan 81 HRazor 60 81 129 Matrix 89 90 92 Pentagon 116 Polygon 7 62 63 116 PTree 56 73 82 84 PTreeL 83 PTre
16. Box A Box C Box B Box A Box C Box B Box A newBox a btex Box A etex newBox b btex Box B etex scaled magstep3 newBox c btex Box C etex scaled magstep2 newVBox h a b c h c origin draw0bj h The cardinal points are as follows ne se bounding box A right alignment is obtained with the align right option newBox a btex Box A etex newBox b btex Box B etex scaled magstep3 newBox c btex Box C etex scaled magstep2 newVBox h a b c align right h c origin draw0bj h The components can be centered 69 Box C Box B Box A newBox a btex Box A etex newBox b btex Box B etex scaled magstep3 newBox c btex Box C etex scaled magstep2 newVBox h a b c align center h c origin draw0bj h As for HBox the vertical separation between components can be changed with the vsep option Box C Box B newBox a btex Box A etex newBox b btex Box B etex scaled magstep3 newBox c btex Box C etex scaled magstep2 newVBox h a b c align center vsep 3mm h c origin draw0bj h And it is possible to put any kind of object instead of mere boxes Box B Box A VBox options newPolygon a btex Box A etex 5 fit false polymargin 5mm newBox b btex Box B etex scaled magstep3 newVRazor ba 1cm newPolygon c btex
17. Here there is a connection between the two points nw and ne but the first point is left with an angle of 30 degrees with respect to the horizontal This seems fine and one would think that it is sufficient to record the appropriate drawing instruction in the object Unfortunately this is not convenient because the application of linear transformations to the object will produce strange results if the hardwired angle of 30 degrees is kept For instance if we turn this object by 50 degrees counterclockwise we get ne nw One could think of computing the correct angle but even if one does the angle is actually not enough to specify the right path even if METAPOST draws a path it is probably not the one we want This is obvious if one considers the control points of a path A first problem is one similar as with the pictures we cannot have paths connecting undefined points Therefore when an object is floating we could either store a fixed path and move it but this may not always be convenient if we want to change the size of the object as we will see later One way out of this dilemma is to store inside the object all the points defining the path including its control points Then we can forget about the angles and just let the points move according to the transformations that are applied to the objects and then reconstruct the path from its points and control points 10 1 4 6 Subobjects An object can refer to othe
18. T Tc Tr btex j etex Tr btex K 4 etex Tr btex x y etex Obj t c origin draw_0bj t Figure 23 Leaves with different widths after page 38 of 16 K4 is not cen tered 101 j Ka vy setCurveDefaultOption arrows draw t T_ Tc Tr_ btex j etex Tr_ btex K_4 etex Tr_ btex x gt y etex treenodehsize 5mm Obj t c origin draw_0bj t Figure 24 Leaves whose width was set with treenodehsize after page 38 of 16 K4 is now centered setCurveDefaultOption arrows draw t _T TCs Te T TCs _T Te Te Tc Tc TCs TOC TCS2D Obj t c origin draw_0bj t Figure 25 Tree with visible subtrees TCs is the default filled disk after page 39 of 16 setCurveDefault ption arrows draw setObjectDefaultOption Tree hideleaves true t _T TCs Tc _T TCs _T Tc Tc Tc Tc TCs TCs TCs Obj t c origin draw_0bj t Figure 26 Tree with hidden subtrees TCs is the default filled disk after page 39 of 16 102 setCurveDefaultOption arrows draw t T_ TCs _T TCs TCs TCs _T TCSs TCs TCs vsep 5cm hbsep 2cm Obj t c origin draw_0bj t Figure 27 Illustrating different horizontal separations at different levels TCs is the default filled disk after page 39 of 16 X Xi Yo Y K2 Ki Ja J setCurveDefaultOption arrows draw setObjectDefaultOption Tree treemode R t _T Tc
19. Tc 1 5mm Toplus Toplus treemode L Toplus Toplus treemode U 0bj t c origin draw 0bj t Figure 20 A tree with two different directions after page 37 of 16 8 9 A1 A2 setCurveDefault ption arrows draw setObjectDefaultOption Tree hsep 1cm setObjectDefaultOption Tree vsep 1cm 4 we draw two trees which share a root node t T_ new_Circle btex root etex Tr_ btex B etex treemode L Obj t c origin u _T obj Obj t root Tr_ btex A1 etex Tr_ btex A2 etex draw_0bj t draw_0bj u Figure 21 Two trees sharing the same root node after page 37 of 16 there are two draw_0bj commands to draw them and actually the root will be drawn twice The u tree is automatically positionned because its root is already set in the first tree 100 setCurveDefaultOption arrows draw setObjectDefaultOption Tree Dalign center setObjectDefaultOption Tree hbsep 5mm t _T Tc TCs T Tc new_Circle_ filled true circmargin 15pt TCs treenodehsize 1cm TCs Obj t c origin draw_0bj t Figure 22 The large disk does not change the balance because the treenodehsize option pretends all subtrees are 1cm wide it does however enlarge the tree vertically because we didn t use the treenodevsize option TCs is the default filled disk after page 38 of 16 j Ka Ty setCurveDefault ption arrows draw t
20. after page 27 of 16 95 Ya ras N newCircle x btex X etex newCircle y btex Y etex framed false newCircle Z btex Z etex framed false z is reserved newMatrix mat 2 2 nb x y Z hsep icm vsep 2cm mcline mat 1 2 2 1 nodesepA 3pt mcline mat 1 2 2 2 nodesepA 3pt mcline mat 2 1 2 2 linestyle dashed withdots mat c origin draw0bj mat Figure 12 Another matrix after page 28 of 16 gt jv mat new Matrix 2 2 new Box btex A etex framed false new Box btex B etex framed false new Box btex sqrt xty over z etex framed false new Box btex D etex framed false hsep icm vsep icm mcline Obj mat 1 1 1 2 arrows draw mcline Obj mat 1 1 2 1 arrows draw mcline Obj mat 1 2 2 2 arrows draw mcline Obj mat 2 1 2 2 arrows draw Obj mat c origin draw 0bj mat Figure 13 Another matrix after page 122 of 2 96 firstly lastly then setCurveDefault ption linestyle dashed withdots mat new Matrix 2 2 0 new Circle btex A etex new Circle btex B etex new Circle btex Nsqrt x yVover z etex new Circle btex D etex hsep 1cm vsep 1cm mcline 0bj mat 1 1 1 2 name firstly mcline Obj mat 2 1 1 1 name lastly mcline 0bj mat 1 2 2 2 name next mcline 0bj mat 2 2 2 1 name then ObjLabel 0Obj mat btex Nit firstly etex labpathname firstly labdir to
21. boxsize 3mm ncline 0bj t treeroot Obj t 2 treeroot Obj t 4 name N ObjLabel Obj t btex N etex labpathname N labdir top we add labels on edges the standard edges of a tree are numbered 1 2 and we use labpathid we must take care to give the correct objet as first parameter of lObjLabell ObjLabel treepos 0bj t 2 btex L etex labpathid 1 labdir 1ft ObjLabel treepos Obj t 2 btex R etex labpathid 2 labdir rt ObjLabel ntreepos 0bj t 2 1 btex 1 etex labpathid 1 labdir 1ft The previous is a shorthand for ObjLabel treepos treepos Obj t 2 1 btex 1 etex labpathid 1 labdir 1ft ObjLabel ntreepos Obj t 2 1 btex r etex labpathid 2 labdir rt ObjLabel ntreepos Obj t 2 2 btex 1 etex labpathid 1 labdir 1ft ObjLabel ntreepos Obj t 2 2 btex r etex labpathid 2 labdir rt etex labpathid 1 labdir 1ft etex labpathid 2 labdir rt etex labpathid 1 labdir 1ft etex labpathid 2 labdir rt ObjLabel ntreepos Obj t 2 1 2 btex c ObjLabel ntreepos Obj t 2 1 2 btex d ObjLabel ntreepos Obj t 2 2 2 btex c ObjLabel ntreepos Obj t 2 2 2 btex d labels on nodes ObjLabel ntreepos Obj t 2 1 1 btex 10 10 10 etex labcard s 4 the distance between the node and the label is icm as defined in ObjLabel l ObjLabel ntreepos Obj t
22. se sw amp South 5 CHne Cise amp 4 East 5 0 nw sw amp 4 West 5 Cin Ots Center These equations are given as string constants so that they can be used within the ObjCode section of a constructor They define a rectangular shape The standard internal equations are defined with def StandardInnerEquations ine G ne Qtinw Qitnw G isw G sw ise G se amp Qitin Qitn is 0 s Hie C He O iw O W C Hic O c enddef Finally all the standard equations are defined by def StandardEquations PureStandardEquations amp StandardInnerEquations enddef In order to define the newThreeTriangles constructor with both a standard interface and standard equations we can write vardef newThreeTriangles suffix sa sb sc assignObj ThreeTriangles StandardInterface SubObject suba sa SubObject subb sb SubObject subc sc ObjCode StandardEquations obj subb a obj Gitsuba a 4cm 1cm obj subc a obj G suba a 7cm 2cm obj suba a G c StandardTies enddef 22 Here the previous explicit definition of point c is now part of the standard interface and this is now the c to which refers the last equation It is however not sufficient to declare the standard interface and the standard equations They still have to be defined Having undefined points is not a problem per se but because these points may be used by the
23. 34 5 4 Unabt ching an DB cc RR RR Rex 35 5 5 COPA ou sio Rok eee ee dee Ba de bed 4 35 DU BA ok kk me ee Se Ro a OH eB ek 35 Hoo o 22x p Se Soe AR ee GR 36 5 5 3 Option definition casa socor aa ca 544544 nm 37 504 Option names 0 4 24 Roo orem RR E RES 3T 5 6 Adding paths to Objects 222r 37 5 7 A nounou axo os x Res ACER ATE ox e iR 39 Dolo MELIDE s rapona e 09 OX RO see s 42 Meise o 44 Logo oe X ou ur ee ee D d ee Rex 44 Dia c o PT 45 Bd CENA 2290699 cn n ge E ROG S Sod SS A e 45 Boo MOONE cs sos E S Rx Re e o EOS RR RA 46 De DESEES os sous sw PURA E REGE ve deba 46 BOY DOTE baa pan dada ashe bb aa wg we x a 47 e oo o ior 4 4 be ew G ote det Sete oe AS 48 En A 48 ILI il ouod uo ee a ee ar ar ar bo dem e MUS 50 VEG MEn AI ee Ga 50 Dela DESECHOS 22 929 4 3 5 oS oad XE bad a 51 519 nczigzag dud peoill cc cesos 52 5 14 Tree and matrix variants 222229 c 53 5 8 Adding labels 2 222225 93 9 9 ER RR Ro RR 54 6 The object structure 9 7 Standard Library Gallery Ll irc s MM PM CT pEPSNE r6 E EDD C C TT Tl HESSE cocinada Ree eem Rus medie Vole BenomBAx 2 4 4 2 204000444 444448448464 1 2 Basic COR AMIBES Lolo ngo xo xoxo ek SOROR C ME DP E E ee ee ee Fa POO 2 SAA a hee ARA tier BLLPSE ice eka ee ERE Ed ee eRe a d Jod GERD 22 ba ae oso dodo SU ooa eee aan dd To DBGE o3 oo RN JU BELDEBSB os Pe ha 4x eR eim eed es pf Box alignment eonsbrHebots su sse a o RR n JaMlI BO o iia a bos o 4 A qo EORR
24. 6929 S b xpart s b ypart s b As you can see s a is defined with respect to s b Only one point is unknown If we write s a origin we get s a 0 0 s b 28 34645 56 6929 Now we can apply a rotation rotate0bj s 30 and we have s a xpart s a ypart s a s b xpart s a 3 79764 ypart s a 63 27086 Notice that the object is now no longer attached This is a choice we made because you usually seldom want to rotate an object around a point and keep it there You want to rotate an object and build something with it The final location of an object will then depend on the other objects and even if you can fix one object you will not be able to do so with all objects However one could still write a small function doing a rotation and fixing a given point This is left as a trivial exercise When we are done with the transformations of the object we want to draw it We can of course write draw s a s b but for complex objects it would become very cumbersome So whenever an object is defined one also defines a drawing function In this case it is very simple def drawSegment suffix n draw n a n b enddef The initial segment is drawn with 13 drawSegment s and this produces It is also possible to write draw0bj s and draw0bj will call drawSegment It is actually a good idea to always use draw0bj because it makes a program easier to maintain If you wanted to define another kind
25. Box C etex scaled magstep2 11 polymargin 3mm newVBox h a b ba c align center vsep 3mm h c origin draw0bj h Option Type Default Description dx numeric 0 horizontal clearance around the object dy numeric 0 vertical clearance around the object ubsep numeric 1mm vertical separation between elements elementsize numeric 1pt if non negative all the objects are assumed to have this height align string left center and right are the other possible values framed boolean false true if the object is framed filled boolean false true if the box is filled fillcolor color black filling color framewidth numeric 5bp width of the frame framecolor color black color of the frame framestyle string style of the frame dashed etc flip boolean false if true reverses the order of the components shadow boolean false true if there is a shadow framed too must be true shadowcolor color black shadow color 70 7 4 Recursive objects and fractals METROBJ provides several standard objects whose purpose is to show how re cursive objects can be defined 7 4 1 RecursiveBox This is one of the simplest kind of recursive object It is a box which contains a box slightly rotated which itself contains such a box etc The depth of the box is a parameter of the constructor newRecursiveBox a 10 scale0bj a 3 a c origin draw0bj a The bounding
26. a special drawSquare function def drawSquare expr p 1 a draw Square p 1 a draw Square p 5mm dir a 45 1 1mm a enddef If we now want a picture in the middle of the square we can add it as a parameter to drawSquare and so on Objects can be built up for instance using pictures Some of these pictures might have been created with the image function That way one can even use the boxes package to put frames around frames etc The boxes package is interesting because it provides a first step towards structures and each box has a standard interface a bounding path as well as special cardinal points such as n North e East etc There are however problems with the boxes package Assume we want to draw something like where all the rectangles are boxes created with the boxit function from the boxes package and assume we want to connect point e of one subbox to point w of the other and obtain something like We would like to use boxes or something similar because it provides a very simple way to frame a picture We do not want to have to place four corners every time we have to frame something boxes instead provides a functional approach If we decide to make pictures of each subbox and then somehow stuff them inside a boxit we can t achieve our task because the positions of the points of interest to us have been lost We could of course build the c
27. and the cardinal points follow the operations SW ne se DEllipse options newDEllipse a btex some text etex scale0bj a 2 rotate0bj a 45 a c origin draw0bj a Option Type Default circmargin numeric 2bp filled boolean false fillcolor color black framed boolean true fit boolean true framewidth numeric 5bp framecolor color black framestyle string Jen picturecolor color black hsep numeric 1mm usep numeric 1mm shadow boolean false shadowcolor color black 7 3 Box alignment constructors There are two basic box building constructors HBox and VBox Their names have been chosen with analogy to the hbox and vbox primitives of TEX 7 3 1 HBox The newHBox constructor provides an horizontal alignment of objects By de fault the objects are aligned on the bottom and they appear from left to right In the following example we have three boxes created with newBox of differ ent sizes and contents The boxes are put in one larger box which can then be manipulated like a simple object Box A Box B Box C A etex B etex scaled magstep3 C etex scaled magstep2 newBox a btex Box newBox b btex Box newBox c btex Box newHBox h a b c h c origin draw0bj h 67 The cardinal points show the bounding box of the HBox They are not compulsory on an object In the next example they happen to coincide with the bottom lef
28. and will pass them to the non streamlined version When certain arguments are not expressions for instance if they are lists the call to streamline is different For the Tree class it is 32 streamline Tree expr theroot text subtrees suffixpar theroot suffixlist subtrees This means that the streamlined version will receive a root number and a list of subtrees numbers But these parameters can t be passed like that to the non streamlined version The numbers must be converted into suffixes and this is what suffixpar and suffixlist do In addition to the constructors several operations have streamlined versions so that they can operate in a streamlined context For instance the streamlined version of rotateObj is rotate 0bj In order to create a first box with the text abc to rotate it counterclockwise by 24 degrees and to frame it again we can simply write b new Box rotate 0bj new Box btex abc etex 24 If this seems too complex the user is advised to define shortcuts This was done in one of the first examples when we showed that trees could be built The streamlined versions however are incompatible with the options mech anism for non streamlined constructors Therefore we provide two streamlined versions of each constructor the normal one and a streamlined version which supports options This version has a trailing _ This explains why the first polygon was defined with new Polygon The second
29. constructor 36 5 5 3 Option definition Options can be defined easily Here is how the filled and treemode options are defined define_global_boolean_option filled define_local_string_option treemode The first is global because the information is used when the object is drawn and the second is local because it is only used at the time of the object con struction OptionValue t v returns the value of option v of object t For instance in order to find out if an object should be filled or not one could write if OptionValue t filled fis There are many such examples in the METAOBJ source code 5 5 4 Option names All the options recognized by an object are shown in section 7 In addition to the options given there it is possible to use a name option This option makes it possible to provide an explicit name to an object This is of course useful only in case one uses the streamlined version of a constructor The name given to an object can then be used later for instance in connection commands 5 6 Adding paths to objects The easiest way to add some line to an object is to add an instruction such as draw in the function drawing an object In that case the line drawn is not really part of the object but part a command belonging to the class However it is also possible to include lines and more generally paths to the structure representing an object More precisely objects can contain one or more path arr
30. end etex a c origin b c a c 3cm 2cm draw0bj a b Some of the descriptions borrow from the PSTricks documentation 16 5 7 1 ncline ncline is the simplest of all connection commands It connects either two points or two objects by a straight line If two objects are connected the line is cut before the bounding path of the first object and after the bounding path of the second object ncline a b If ncline is used to connect two object points such as a c and b c the bounding paths of the objects are not taken into account ncline a c b c 42 UA The thickness and the style of the line can easily be changed with the linewidth and linestyle options ncline a b linewidth imm linestyle dashed evenly The position where the line starts can be set with the posA option Similarly the position where the line ends can be set with the posD option It must be a point of the object The default positions are the ic points It is important not to use the c point because c is not always at the center of an object in case the bounding box is changed In the next example posA n causes the line to start at a n ncline a b posA n The starting point can also be offset by a vector with the offsetA option There is also a similar offsetB option These options differ from those of PSTricks where offsetA and offsetB are numerical values and not vectors ncline a b offsetA 1cm 0 w A
31. ends with the semi colon When a streamlined constructor is used the same construction cannot be used because the semi colon usually lies beyond the scope of the constructor 35 Therefore there are two versions of the streamlined constructors one with op tions and one with no options For the HBox class the two constructors are new HBox with options and new_HBox no options In addition to the normal parameters of the constructor the option streamlined version has an addition nal parameter which is the list of options Hence the three previous examples would be written new EmptyBox 2cm 1cm framed true new_RandomBox_ 2cm 1cm 2mm 1mm framed true framewidth imm new HBox b a hbsep 1cm framed true align center dx 5mm dy 5mm These streamlined constructors returns numbers and are usually used as parameters to other constructors 5 5 2 Option types A given option such as framed has a type The type is always the same for a given option and it is not possible to have options with the same name but different types in different objects For instance the type of framed is boolean Its value can be true false or some expression returning a boolean Many options have a numerical type and they usually correspond to some dimension in an object In all cases but one the value between parentheses is of the type the option awaits There is one exception when the type of the option is a st
32. l I B C A miz SAO Lal BF A A4 PCFA TEBVC A miz 3 mia 4 ra TP ra T F C A AY A AY ra T CF A A 5 miz Pa I Tra T DAI I A A A AY A A4 contr contrg Ty FA AY Dal PA AY contr contrg DA TA STA IT C A AY A AY A AY 5 mix ra I ra Ir F C A AY A AY DAI CEA AY mia 3 mia 4 Ty4 I BrFA AY oe T CFA I BVC A LBFA TEBVON d PFEOGA DEBOAN II II IIs ITs Pal EH OA T BVCFA v UB CA T BFA T CFA miz 1 Is II IL Figure 7 Proofs in top down and bottom up mode from David Nour Raffalli Introduction la logique Paris Dunod 2001 p 197 The source is given in figures 8 and 9 86 input metaobj verbatimtex newcount pntcnt pntcnt 0 def npoints 1 pntcnt 1 vbox offinterlineskip kern5pt npointsa def npointsa ifnum pntcnt gt 0 hbox kern5pt advance pntcnt 1 expandafter npointsa fi etex setObjectDefaultOption PTree treemode U for bottom up newAssumption pii btex Pi_1 etex newConclusion piici btex npoints3 etex newPTreeR piiproof piici pii rule 0 newConclusion piic2 btex Gamma B vdash Delta etex newPTreeR al pi1c2 pilproof rule 0 newAssumption pi2 btex Pi_2 etex newConclusion pi2ci btex npoints3 etex newPTreeR pi2proof pi2c1 pi2 rule 0 newConclusion pi2c2 btex Gamma C vdash Delta etex newPTreeR a2 pi2c2 pi2proof rule 0
33. line can be doubled with doubleline and the arrow style of the line can be changed with the arrows option This option takes a name of a draw function such as draw drawarrow etc as parameter ncline a b doubleline true arrows draw A gap can be introduced at either ends of the connection with the nodesepA and nodesepB options 43 ncline a b nodesepB 10mm arrows draw 5 7 2 nccurve nccurve draws a Bezier curve between the nodes The default angles at which the curve leaves or reaches the nodes are those obtained when a straight line connects the nodes Hence without options nccurve behaves like ncline The two angles can be changed with the angleA and angleB options nccurve a b angleA 0 More parameters can be modified for instance the linecolor the linewidth the style with linestyle and the fact that the line is drawn double with doubleline end nccurve a b angleA 30 angleB 80 linecolor red linewidth imm doubleline true linestyle dashed withdots The tension of the line in METAPOST s sense can be modified with the linetensionA and linetensionB options or with the linetension shortcut This allows a control similar to the one provided with PSTricks ncurvA and ncurvB parameters The default tensions are 1 nccurve a b angleA 30 angleB 80 e linecolor red linevidth 3pt e linestyle dashed withdots linetension 2 o
34. object had to be available Then trees were implemented Then I had to implement paths especially for trees because many examples of trees I saw had additional paths It seemed then interesting to have ways to add PS Iricks like paths I started to implement functions like ncline ncbar etc corresponding to PS Tricks ncline ncbar etc After some time the aim was to be able to get good approximations of the PSTricks constructions involving node connections trees and matrices METAOBJ does not provide a full compatibility neither in the syntax nor in the output but it tries to get as close as possible One should keep in mind that METRPOST is not TEX and METAPOST does not have the same flexibility in its syntax as TEX It is not possible to change catcodes in METAPOST or to grab characters one by one Therefore the METROBJ code corresponding to the PS Tricks drawings is longer than the PS Tricks one However it should still be high level code and understandable It is high level code written in a syntax less flexible than TEX What should now be done is to write a TEX front end to METAOBJ which would hide the verbosity of METAOBJ and still retain high level code On the following pages we present figures similar to those found in the PSTricks documentation PSTricks and METROBJ s parameters do not always have an exact correspondence and even if so the default values are not always the same We tried to produce figures that we
35. of segment such as vardef newLongSegment assign0bj 0 LongSegment ObjPoint a b ObjCode Otb Ota 2 1cm 2cm enddef you could just replace newSegment s by newLongSegment s and there would be no need to change anything else Of course in this case drawSegment and drawLongSegment are probably identical but usually this is not so 2 2 Connecting two objects Let us now create two new objects each being a triangle vardef newMyTriangle0tt assignObj MyTriangle ObjPoint a b c ObjCode b a 2cm 0cm c b b O a rotated 120 enddef def drawMyTriangle suffix n_ draw n_ a n_ b n_ c n_ a enddef We create two of them and we rotate the second one by 180 degrees 14 newMyTriangle t1 newMyTriangle t2 rotate0bj t2 180 ti a origin t2 a t1 a 4cm 1cm draw0bj t1 t2 This produces The second triangle was positionned with respect to the first one Even though we first positionned t1 we could have written t2 a t1 a 4cm 1cm ti a origin and would have obtained the same result Before any of these two equations are given we have two floating objects If we write t2 a t1 a 4cm 1cm the two objects behave like one object However the bond can be broken if needed using the untie0bj function For instance if we want to detach the second triangle to rotate it 20 degrees more and to place it a bit further to the right and up we can do it with ne
36. on the main object s inner interface One should also notice that equations that are too long to fit on a line can be split like strings are split One should not write two strings separated by a comma because internally a semicolon is added at the end of each string def BpathRecursiveBox suffix n StandardBpath n enddef The drawRecursiveBox function is interesting because it shows that one can check if a given object has some features Here we call draw0bj on a subobject only when there is a subobject We could of course have resorted to other ways like storing the depth of the object within the object This could have been done with an ObjNumeric declaration def drawRecursiveBox suffix n 29 drawFramedOrFilled0bject n if known n sub draw0bj obj n sub fi drawMemorizedPaths_ n enddef The call to drawMemorizedPaths makes it possible to draw additional paths that may have been added to the object by the user Let s now study newBox This object is very similar to the rectangle boxes from the boxes package but it can not only frame a picture but also any other standard object It can also put round corners This explains why the code is somewhat lengthy The v parameter is either a picture or a string or a numeric If it is a numeric the number is the internal number of an object vardef newBox expr v text options Execute0ptions options assignObj Box StandardInterface Standard
37. put at the right we use an empty string for the left rule We could also have used newPTreeR A A B MP newAssumption a btex A etex newAssumption b btex A rightarrow B etex newConclusion c btex B etex newPTree proof c a b btex MP etex proof c origin draw0bj proof The horizontal line is by default built so that it covers the last formula of what is above the line However there may be cases where the automatic 83 computation is not satisfactory and it is then possible to change the length of the line by extending its right or left ends In order to lengthen the right end by 1cm we can pass 1cm to the lenddx option of newPTree or its variants newAssumption a btex A etex newAssumption b btex A rightarrow B etex newConclusion c btex B etex newPTreeR proof c a b btex MP etex lenddx icm proof c origin draw0bj proof Transformations can be applied to a proof as for any other object A ASL LD VY scaleObj proof 2 slantObj proof 1 proof c origin draw0bj proof The next example shows that it is possible to have two overlapping proofs The first two lines are one proof built top down and this proof is also the conclusion of a second proof built bottom two formulas on the last line This is another such example where the the others A AB MP BBBBBBBBBBBBBB D E up and whose assumptions are the newAssumption a b
38. user will have to define new functions to manipulate them When creating an object the implementer should first try to define carac teristic points which will be used to express the equations These points should be given names different from those of the standard interfaces and equations between these points should be given This will be sufficient for most objects with straight lines The constraints on the points should be given as equations never as as signments except for intermediate computations otherwise objects might no longer be floating For certain objects the difficult part is to find the good equations For instance it is not that simple to find good equations for a triangle enclosing a rectangular box such as text However in many cases the equations are simple but there are many different cases to consider depending on the values of parameters and on the presence of certain subobjects Parameters should be introduced when necessary These parameters should be consistant with already existing parameters When in doubt new parameter names should be created Consider for instance the following object abcdefg XXXXXXX Here we want a rectangular box where XXXXXXX an object or a picture is centered In addition we want some label at the top left First we should identify the caracteristic points It is natural to consider that the corners of the outer rectangle are those of the standard interfac
39. w f etf w 0 newTree fruits f a b c Ralign right treemode R newTree vegetables v d e Ralign center treemode R newBox fo btex food etex newTree food fo fruits vegetables hsep icm treemode R Scale0bj food 5 food c origin draw0bj food newBox a btex apples strut etex newBox b btex oranges strut etex newBox c btex bananas strut etex newBox f btex fruits etex newTree fruits f a b c Ualign bot treemode U newBox d btex potatoes etex newBox e btex peas etex newBox v btex vegetables etex newTree vegetables v d e Ualign center treemode U newBox fo btex food etex newTree food fo fruits vegetables hsep icm treemode U scale0bj food 5 food c origin draw0bj food In the following example the treeflip option is set to true and the order of all subtrees is reversed set bjectDefaultOption Tree treeflip true newBox a btex apples strut etex newBox b btex oranges strut etex newBox c btex bananas strut etex newBox f btex fruits etex newTree fruits f a b c Ualign bot treemode U newBox d btex potatoes etex newBox e btex peas etex newBox v btex vegetables etex newTree vegetables v d e Ualign center treemode U newBox fo btex food etex newTree food fo fruits vegetables hsep 1cm treemode U scale0bj food 5 food c origin draw0bj food potatoes bananas peas
40. 0 horizontal clearance around the proof tree dy numeric 0 vertical clearance around the proof tree hsep numeric 3mm horizontal separation between two subtrees vsep numeric 2mm vertical distance between the assumption s and the conclusion the rule is in the middle of this space lrsep numeric 2mm separation between the horizontal line and the left rule rrsep numeric 2mm separation between the horizontal line and the right rule lstartdx numeric 0 how much the horizontal line is reduced if the option value is positive or extended if it is negative on the left side lenddx numeric 0 how much the horizontal line is extended if the option value is positive or reduced if it is negative on the right side rule numeric 5bp rule thickness framed boolean false if true the proof tree is framed this can be useful to frame a part of a proof tree which is also a proof tree filled boolean false if true the proof tree is filled fillcolor color black filling color framewidth numeric 5bp thickness of the frame if applicable framecolor color black frame color framestyle string n frame style shadow boolean false true if there is a shadow framed too must be true shadowcolor color black shadow color Table 6 PTree options 85 II IL I T BHA T CHA T BVCHA Y TEBCNAN miz 1 ra ITF B C AA IIs II ITs Il IY B C A T BEA TEBVOZ A
41. 10 shows a matrix with labels and various connections This figure is adapted from a figure in the PSTricks documentation 7 6 4 Matrix options The table 7 shows all options supported by the Matrix class Option Type Default Description dx numeric 0 horizontal clearance around the matrix dy numeric 0 vertical clearance around the matrix hsep numeric Imm horizontal separation between columns usep numeric Imm vertical separation between rows matrixnodehsize numeric 1pt if non negative all the nodes are assumed to have this width matriznodevsize numeric 1pt if non negative all the nodes are assumed to have this height halign string gn a string where each character corresponds to one column and specifies the horizontal align ment within that column valign string c a string where each character corresponds to one row and specifies the vertical alignment within that row framed boolean false true if the matrix is framed filled boolean false true if the matrix is filled fillcolor color black filling color framewidth numeric 5bp frame thickness framecolor color black frame color framestyle string n frame style shadow boolean false true if there is a shadow framed too must be true shadowcolor color black shadow color Table 7 Matrix options 92 7 7 PSTricks METAOBJ gallery METAOB started as a package implementing objects A basic tenet was that the structure of an
42. 2 3 posA e posB n angleA 0 angleB 90 linecolor red linetension 1 75 The second and third parameters after gt the name of the tree are lists of integers If we had written tccurve gt 2 1 3 2 posA e posB n angleA 0 angleB 90 linecolor red linetension 1 75 53 we would have connected the node at position 2 1 first subtree of second subtree of gt with the node at position 3 2 second subtree of third subtree of gt All other connection commands are similarly adapted tcline tcangle tcangles tcarc tccurve tcdiag tcdiagg tcloop tccircle tcbox and tcarcbox Variants for matrices are also available with the names mcline mcarc mccurve mcangle mcangles mcdiag mcdiagg mcloop mccircle mcbox mcarcbox mczigzag and mccoil Instead of an object identification these commands take a pair of integers representing the position of the object within the matrix For instance a dashed line can be drawn between the objects at positions 1 1 and 2 2 in matrix mat2 with mcline mat2 1 1 2 2 linestyle dashed evenly If a component of a matrix is itself a matrix this notation can not be used and special access commands can be used such as matpos or mpos There are also reverse variants of certain connection commands These reverse variants can be useful for tree connections See for instance figure 35 The reverse connections are rncline rnccurve rncangle rncangles
43. 2 2 1 btex 10 10 0 etex labcard s ObjLabel ntreepos Obj t 2 1 2 1 btex 3 8 4 etex labcard s ObjLabel ntreepos Obj t 2 1 2 2 btex 8 3 4 etex labcard s ObjLabel ntreepos Obj t 2 2 2 1 btex 4 8 3 etex labcard s ObjLabel ntreepos Obj t 2 2 2 2 btex 0 5 0 etex labcard s ObjLabel treepos Obj t 4 btex 0 0 0 etex labcard e 4 4 because the HRazor counts for one subtree draw_0bj t Figure 39 An annotated tree end of the code 110 def TCE rebindrelative_0bj new_Circle_ filled true circmargin 5mm 5mm 5mm 5mm 5mm enddef setCurveDefault ption arrows draw setObjectDefaultOption Tree treemode R setObjectDefaultOption Tree vbsep 5mm setObjectDefaultOption Tree treenodevsize 1 setObjectDefaultOption Tree treenodehsize 5mm t T_ Tc T_ Tc _T Tc TCE TCE T Tn T Tn TCE edge none edge none T_ Tn T Tn _T Tc TCE TCE edge none edge none TCE edge none _T Tn new VFan 2mm 1cm edge none edge none pointedfan false ncline 0bj t treeroot Obj t 1 treeroot 0bj t 1 12 ncline 0bj t treeroot Obj t 1 treeroot Obj t 1 2 1 1 ncline 0bj t treeroot Obj t 1 treeroot Obj t 1 3 1 1 ncline 0bj t treeroot Obj t 1 ntreepos Obj t 1 4
44. 33 duplicateObj 18 19 33 73 115 etex 30 ExecuteOptions 28 114 extendObjDown 34 extendObjLeft 34 75 extendObjRight 34 75 76 extendObjUp 34 find bot most 29 find Ift most 29 find rt most 29 find top most 29 image 5 61 label 55 matpos 54 mcangle 54 mcangles 54 mcarc 54 mcarcbox 54 mcbox 54 mccircle 54 mccoil 54 mccurve 54 mcdiag 54 mcdiagg 54 mcline 40 54 mcloop 54 mczigzag 54 mpos 54 nb 89 ncangle 46 48 ncangles 46 48 130 ncarc 45 51 ncarcbox 41 50 51 108 ncbar 45 93 ncbox 41 50 51 107 nccircle 40 50 nccoil 52 nccurve 38 41 44 106 ncdiag 47 48 104 ncdiagg 48 ncline 38 40 42 44 55 93 105 116 ncloop 41 48 nczigzag 52 new Box 32 new Ellipse 106 new_Polygon_ 33 new Iree 79 new Tree 81 newobjstring 18 28 56 newRBox 62 newTree 79 ntreepos 56 Obj 32 40 54 obj 18 115 ObjBoolean 115 ObjBooleanArray 115 ObjCode 12 22 31 115 ObjColor 115 ObjColorArray 115 ObjLabel 54 55 91 ObjNumeric 29 114 115 ObjNumericArray 115 ObjPair 114 115 ObjPairArray 115 ObjPath 39 115 ObjPicture 25 31 115 ObjPoint 12 31 59 114 ObjPointArray 115 ObjString 115 ObjStringArray 115 ObjSubArray 115 Obj Transform 115 ObjTransformArray 115 OptionValue 37 rdrawarrow 40 107 rebindObj 34 rebindrelativeObj 34 75 76 rebindVisib
45. 50 arcangle connection option 42 arcangleA connection option 41 45 51 arcangleB connection option 41 45 51 arm connection option 42 armA connection option 41 45 48 107 armB connection option 41 45 49 arrows connection option 38 40 41 43 assignObj command 12 22 114 Assumption class 83 Attributes booleanarraylist_ 57 code 57 59 colorarraylist 57 ctransform 57 59 extra code 57 nsubobjties 57 numericarraylist_ 57 numericlist_ 57 pairarraylist_ 57 pairlist_ 57 picturearraylist_ 57 picturelist_ 57 pointarraylist_ 57 pointlist_ 56 57 points_in_arrayslist_ 57 stringarraylist_ 57 subarraylist_ 57 sublist 56 57 subobjties_ 57 58 128 transformarraylist_ 57 Axiom class 83 BB class 27 90 117 booleanarraylist_ attribute 57 border connection option 41 bordercolor connection option 41 Box class 7 61 62 65 83 boxdepth connection option 41 50 boxheight connection option 41 50 boxit command 10 boxsize connection option 41 50 BpathCircle command 39 BpathEmptyBox command 28 BpathObj command 28 bracketit exp command 91 btex command 30 cdraw connection option 41 42 Circle class 81 119 circleit command 10 circmargin class option 64 65 67 Class options align 36 68 70 angle 63 circmargin 64 65 67 Dalign 74 80 dx 62 65 66 69 70 72 80 85 92 dy 62 65 66 69 70
46. Gamma_A NGamma vdash Delta Delta _A Delta Delta _A Delta Delta _A etex newPTreeR proof3d c8 proof5 proof3b btex it mix 5 etex hsep 5mm newConclusion c9 btex Gamma_A Gamma vdash Delta Delta _A etex newPTreeR proof3E c9 proof3d btex contr g contr d etex yscale0bj proof3E 2 reflect0bj proof3E 0 0 0 1 slantObj proof3E 0 2 proof3E c origin draw0bj proof3E Figure 9 Proof tree code for figure 7 end 88 7 6 Matrices A special Matrix class provides a combination of horizontal and vertical boxes A matrix is constructed with newMatrix by specifying a number n of rows and a number m of columns and then a list of n x m objects Here is a first matrix with one row and one column The matrix contains the object mela which is a framed box newBox mela btex A etex A newMatrix mat 1 1 mela mat c origin draw bj mat The second matrix contains two rows and one column newBox melb btex B etex dx 1cm newBox melc btex C etex dy 1cm newMatrix mata 2 1 melb melc C mata c origin draw bj mata The third matrix has three rows and two columns but only five elements The last element of the first line is empty This is shown in the newMatrix call with a nb value This is a special value meaning null box Matrix elements are by default centered both horizontally and vertically I
47. TC is a filled circle of radius 1mm 105 Coot Y setCurveDefaultOption arrows draw setObjectDefaultOption Tree treemode R t T_ Toval_ btex root etex Tr_ btex Z etex Tr btex Y etex Tr btex X etex edge nccurve angleA 0 angleB 0 hsep 3 5cm posA e Obj t c origin draw_0bj t Figure 33 nccurve connections in a tree after page 43 of 16 posA is used to set the starting point on the right of the ellipse Toval is a shortcut so to say for new Ellipse oo gt Xx y Ze setObjectDefaultOption Tree treemode D t T_ new_Polygon_ btex root etex 4 name top new_Box_ btex x etex framed false name 1x new Box btex y etex framed false name ly new Box btex z etex framed false name 1z edge none vsep 1 5cm ncbar 0bj t top 1x angleA 180 armA 1cm ncline 0bj t top ly ncbar 0bj t top 1z angleA 0 armA 1cm Obj t c origin draw_0bj t Figure 34 Different tree connections in a same tree after page 43 of 16 the middle line is not completely vertical because x is slightly larger than z This could be corrected by using the treenodehsize option and forcing all subtrees to a same width 106 Lon setCurveDefault ption nodesepA 2mm setCurveDefaultOption nodesepB 0 setCurveDefault ption arrows rdrawarrow t T new Polygon bt
48. The METAOBJ tutorial and reference manual Denis Roegel LORIA Nancy France roegel loria fr June 14 2001 METAFONT is in some ways an incredible programming language it basically consists of object oriented macros Donald E Knuth Questions and Answers III 1996 reprinted in 10 page 632 Contents 1 Introduction Ll Low level METRPOST 2 2 12 METAOBS requirements scr ow omo m m a a RI ER 1 3 An appetizer oy oaa A RA A a ae a a This document describes METAOBJ version 0 80 1 4 What iso Obl gt e coasa be 9 A REGIE SE 8 LAT AP ELT 8 LES POIS a4 ue ono m dog ORE LSU eR eno dd 9 1 4 3 Eguin os ca eosa a g x rw ooo ERA 9 144 PIQDOR coca A a O33 x3 EA 10 LES Pais 2625s aa da eee BA eee e HS 10 1 46 Dubobjects 2222629 R oad 11 LAY Other components 222 R a a RR RA 11 1 5 Transformations oe 22229989 eee 11 A first object 12 2l UY o A 12 2 2 Connecting two objects o 14 2 3 Creating an object containing objects 16 Interfaces and reusability 21 dl Standard POS a sa a aoa aos meu RR ew ee 21 dud handabrd equations e a uuu xod ROO o e RE e a 22 Real examples 27 Advanced operations 32 5 1 Streamlined constructors aaua wawa 32 5 2 don A a gs A A A A ew 33 5 3 Fiddling with the bounding box 33 5 3 1 BB a new bounding box layer 34 bane Rebinding an object a a eee eae
49. al clearance on each side of the con tent and inside the inner frame dy numeric 3bp vertical clearance on each side of the content and inside the inner frame filled boolean false true if the object is filled in which case the double frame is not very useful fillcolor color black filling color framed boolean true true if the object is framed fit boolean true true if the box fits its content both horizon tally and vertically if false the contents only fits horizontally framewidth numeric 5bp width of the frame framecolor color black color of the frame framestyle string style of the frame dashed etc picturecolor color black color of the picture if there is a picture inside the object hsep numeric Imm horizontal separation between the two frames usep numeric Imm vertical separation between the two frames shadow boolean false true if there is a shadow framed too must be true shadowcolor color black shadow color 7 2 6 DEllipse The newDEllipse constructor is to newEllipse what the newDBox constructor is to newBox nw newDEllipse a btex some text etex a c origin draw0bj a bounding box newDEllipse a btex some text etex fit false a c origin draw0bj a newDEllipse a filled true circmargin 2mm a c origin draw0bj a 66 nw In the following example the double ellipse is scaled and rotated and we can see that the frames the contents
50. align left hideleaves true treemode L vsep 3mm newEllipse d btex potatoes etex newDEllipse e btex peas etex newDBox v btex vegetables etex newTree vegetables v d e Ralign center hideleaves true treemode R newPolygon fo btex food etex 12 newTree food fo fruits vegetables hsep 1icm scale0bj food 5 food c origin draw0bj food When we frame the tree we get a frame that only extends to the root and the two leaves of the root not to the other nodes because the bounding box of the tree was changed when the hideleaves option was given newDEllipse ff food ff c origin drawObj ff In order to frame the whole tree we can change the bounding box and set it to the visible part of the tree with rebindVisible0bj rebindVisible0bj food vegetables newDEllipse ff food draw0bj ff The next example shows that we can build a new tree having as a leaf the object with a double elliptic frame The root of the tree is typeset larger because it is not in the scope of scaleQbj his is a new roo newEllipse xx btex This is a new root etex newTree x xx ff draw0bj x Tree options Table 5 shows which options are supported by a Tree A Tree constructor also accepts connection options see section 5 7 and figure 30 for an example which are useful to modify the way standard tree connections are displayed Other options might be defined
51. an object and it can be done with untie0bj untie0bj a After this operation an object can be put elsewhere The untie0bj is used internally when paths are added to floating objects In that case the object is first fixed the path is added and then the object is again untied If untie0bj is called on an already unattached object the object is not changed 5 5 Options Many of the objects of the standard METAOBJ library are parameterized For instance a Box is parameterized by its content which is an explicit parameter but also by other parameters that can be implicit We call such parameters options An option is therefore an information that can be passed to a con structor but which has a default value otherwise This mechanisme gives us a lot of flexibility and avoids providing a long list of parameters that are mostly not used 5 5 1 Syntax The way an option is provided differs according to whether the constructor is used in its normal or streamlined form When a normal constructor is called the options are given as lists of strings after the constructor Each string has the syntax name value where value does not contain quotes The strings are comma separated Here are a few examples newEmptyBox a 2cm 1cm framed true newRandomBox a 2cm 1cm 2mm 1mm framed true framewidth 1mm newHBox c b a hbsep 1cm framed true align center dx 5mm dy 5mm The list of options
52. anas oranges bananas oranges vegetables newBox a btex apples etex newBox b btex oranges etex newBox c btex bananas etex newBox f btex fruits etex newTree fruits f a b c Lalign left treemode L newBox d btex potatoes etex newBox e btex peas etex newBox v btex vegetables etex newTree vegetables v d e Lalign center treemode L newBox fo btex food etex newTree food fo fruits vegetables hsep icm treemode L scale0bj food 5 food c origin draw0bj food In the next tree all five boxes on the left are extended to the right so that their width is 3cm This is done with extend0bjRight This is not sufficient to get the five boxes aligned We also need to make sure that the fruits are as large as the vegetables Therefore the fruits box was extended to the left so that its width is exactly that of the vegetables box with rebindrelativeObj We might also have called extendObjLeft with the appropriate value vegetables 75 newBox a btex apples etex newBox b btex oranges etex newBox c btex bananas etex newBox d btex potatoes etex newBox e btex peas etex extendObjRight a 3cm extendObjRight b 3cm extendObjRight c 3cm extendObjRight d 3cm extendObjRight e 3cm newBox f btex fruits etex newBox v btex vegetables etex rebindrelative0bj f 0 0 0 xpart v e v w f e f w newTree fruits f a b c Lalign
53. and 54 rnccurve command 54 rncdiag command 54 rncdiagg command 54 rncline command 54 rncloop command 54 rnczigzag command 54 rotangle class option 72 135 rotate Obj command 33 rotateObj command 11 29 33 119 rrsep class option 85 rule class option 85 scaleObj command 24 79 119 setBoolean command 115 setColor command 115 setCurveDefaultOption command 40 42 setNumeric command 114 setObjectDefaultOption command 118 setPair command 114 setPicture command 115 setString command 115 setTransform command 115 setTreeEdge command 105 shadow class option 31 34 59 67 69 70 72 80 85 92 shadowcolor class option 34 59 67 69 70 72 80 85 92 show_empty boxes command 59 showObj command 56 58 StandardEquations command 115 StandardInterface command 114 StandardObjectOrPictureContainerSetup command 30 StandardTies command 17 18 28 115 streamline command 32 116 stringarraylist_ attribute 57 subarraylist_ attribute 57 sublist_ attribute 56 57 SubObject command 17 115 subobjties_ attribute 57 58 suffixlist command 33 suffixpar command 33 T command 79 T_ command 81 TC command 65 105 Tc command 64 TC command 65 Tc command 65 109 tcangle command 54 tcangles command 54 tcarc command 54 tcarcbox command 54 tcbox command 54 tccircle command
54. asses They were borrowed from PS Tricks HFan represents an horizontal fan where one of the fan segments is horizontal VFan represents a vertical fan Both HFan and VFan objects take a width and a height as well as options The height of a HFan and the width of a VFan will usually be small often 0 These two classes are quite similar to HRazor and VRazor but they are classes on their own They differ from ordinary boxes in the way they are connected to the root node The connection takes the appearance of a fan Here is an example inspired by a PS Tricks example page 36 of 16 set bjectDefaultOption Tree hideleaves true foo t T new Circle btex foo etex new HFan 1cm 0 filled true Tf _T new_RBox btex bar etex new HFan 1cm 0 Dalign center Obj t c origin draw 0bj t Here we build a tree with a Circle root node and three subtrees The first subtree is a HFan of width 1cm and height 0 This fan is filled The second subtree is a black square obtained with Tf which is a shortcut for newBox with certain options The third subtree is a tree with a rounded corner box newRBox at its root and with one leaf which is a HFan All the leaves of the main tree are vertically centered and this causes the nice alignment given that the leaf of the third subtree is actually hidden because hideleaves was set to true The two fans are pointed which means that the top end reaches the bounding path
55. ated we will usually provide equations defining it We might have a segment object and define the relations between its points as above More complex objects have more complex equations But in every case the aim is to define all points relative to each other No point should be defined in an absolute way We will see later that it is possible to attach points and detach them later but we consider this a lack of elegance 1 4 4 Pictures An object can naturally contain pictures The boxes package provides two functions boxit and circleit which frame pictures However there is a big difference between points and pictures a point can be floating a picture can not A picture is always at some place and an equation will not move it You can assign it to another place but not just hope it will move alone The boxes package always puts the pictures at the origin and so do we In order to give the feeling of floatness we will have a floating point corresponding to the location of the picture and everytime we need to draw the picture we can merely move it to its location 1 4 5 Paths An object usually contains lines arrows etc in addition to pictures or labels When the lines are straight and connect two or more points of an object the only thing to do is to keep track of the instruction drawing the line Everything else is already there However certain connections are more complex Consider for instance nw ne
56. atrixElement exp matd 2 2 deleteMatrixElement exp matd 4 2 deleteMatrixElement exp matd 3 1 1 d deleteMatrixElement exp matd 3 2 1 22 T deleteMatrixElement exp matd 3 2 deleteMatrixElement exp matd 1 1 matd c origin draw0bj matd 7 6 2 Matrices with brackets experimental METAOBJ contains a very experimental and probably almost useless function to bracket an object This function bracketit exp actually adds two pictures which can be brackets Currently it scales the pictures to the correct size and adds them to the object as labels This function serves mainly as an illustration of the use of ObjLabel Here is an example newBox xa btex A etex newBox xb btex B etex newBox xc btex C etex newBox xd btex D etex PA B newBox xe btex E etex newBox xf btex F etex CID newMatrix mat 3 2 xa xb xc xd xe xf E F halign ee valign sns bracketit exp mat btex etex btex etex mat c origin draw0bj mat The parentheses are very bold because they were enlarged from their 10pt versions We can have lighter parentheses if we start with larger ones but this is cumbersome An interesting solution would be to add a path which is a good approximation of a parenthese or a brace etc and filling it This is currently not implemented but it could for instance use addUserPath with the pathfilled option 91 7 6 3 Matrix with labels Figure
57. ays Each array can contain several paths and each path is stored as an array of points This makes it possible to have floating paths which is not possible when using the path type of METAPOST A path array has a name and must be declared with addPathVariables This function takes two parameters the first being an immediate suffix The first parameter is the object to which the path array is added and the second parameter is the name of the array Currently two names of arrays have a special meaning e spath is the array of standard paths of an object standard paths rep resent paths that normally come with the object for instance in the case of trees the node connections from a node to its children are considered standard e upath is the array of user paths this array is for paths added by the user but which could not be devised automatically 37 Each path array keeps track of many parameters and options and the ap propriate structures are defined with addPathVariables As an example the newBox constructor does is the box object addPathVariables _spath_ when there are round corners In this case the newBox constructor will memorize the frame as a path because it is not a simple path made of straight lines The path is then memorized with addPath newBox does the following addPathG _spath_ 1 nnw left down wnw wsw down right ssw sse right up ese G ene up left nne cy
58. bj a 5 a c origin 0 6cm draw0bj a A simplified version of addStandardPath can also be used in constructors ObjPath see section 8 1 1 A path can be added to an object at the time an object is created i e in the constructor or afterwards In any case the object is first attached in case it was floating and the path is dismantled and all its points including the control points are stored Most of the standard classes do not store paths because the paths are very simple and can be reconstructed easily from a few points For instance when a box is not rounded no path is stored because the corners of the box are sufficient to draw it Sometimes a path can be obtained by taking advantage of the current transformation of an object This is for instance the case for a circle where the circle path BpathCircle which is used by drawCircle is defined as follows vardef circle expr a_ b_ c_ d_ fullcircle scaled 2 a cdx transformed ctransform_ shifted a_ c_ 2 enddef def BpathCircle suffix n circle n n isw n ise n ine n inw enddef The circle is drawn from a fullcircle which is scaled to the initial size of the circle before any transformation and then transformed with the current transformation ctransform_ which may turn the circle into an ellipse and finally shifted to the center of the transformed circle In this case the path was not memorized in the object but object points the i
59. bject n drawMemorizedPaths n enddef This function specifies that in order to draw a Polygon the frame should be drawn first possibly filled then the contents then additional memorized paths Memorized paths are typically paths added with the connection com mands ncline etc 8 1 5 Alternate constructors Certain objects have alternate constructors for instance for compatibility rea sons with other packages METAOBJ defines the newPentagon constructor as a variant of newPolygon vardef newPentagon expr v text options newPolygon v 5 options enddef 116 8 1 6 Additional functions A class can have associated functions which make its code simpler These func tions can use all the functions defined in METAOBJ One interesting function that can be used is the is C function which tests whether a given object be longs to a class or not For instance one of the internal functions associated to the Tree class is the following def TreeRoot bj suffix sb if isBB sb TreeRoot0bj obj sb sub elseif isTree sb TreeRoot0bj_ obj sb root else sb fi enddef Given an object this function unwraps all BB layers it may contain and when it reaches a Tree object it calls itself on its root which can itself be a Tree and so on Only when the object is neither a Tree nor a BB wrap does the function return the object itself These is C functions are defined automatically and do not need to be
60. bjectOrPictureContainerSetup v if OptionValue rbox_radius gt 0 bjPoint ene ese sse ssw WSW Wnw nnw nne we use paths for the rounded corners if necessary addPathVariables _spath_ fi if not OptionValue fit Cita max Cita b Q b G a square fi ObjCode StandardEquations if numeric v 5 isw ine 5 obj sub ne obj sub sw object elseif picture v or string v 5 isw Q ine p off picture offset fi if OptionValueG rbox_radius gt 0 Qitine Qitnne Qitise Qitsse Qitnnw QOftinw QOstssw Oftisw amp decimal OptionValue rbox_radius amp 0 Q ine O ene O ese O ise O inw O wnw O wsw O isw 0 amp decimal OptionValue rbox_radius amp fi Ottise Otisw amp decimal 2 a 2 OptionValue dx 0 ine Q ise 0 amp decimal 20 b 2 OptionValue dy StandardTies if OptionValue rbox_radius gt 0 addPath _spath_ 1 nnw left down wnw wsw down right ssw sse right up ese ene up left nne cycle E def ineBox_pathparameters 0t fi enddef Figure 2 Box constructor Let us first see what happens when v is a TEX picture entered with btex etex The call to Standard0bjectOrPictureContainerSetup defines the 30 picture as a part of the object with ObjPicture it defines a point p off which is used in one of the equations and it computes the half diagonal of the obje
61. bjects are shared between two objects So whenever changes are made to one object it will result in changes for the other object This may or may not be the desired behavior If one wishes to have two independent objects one should either use different parameters in the constructors or merely duplicate an object with duplicate0bj This function makes a deep copy of an object If we want now a rotated copy of the three triangles by 90 degrees we can simply write duplicate0bj ttb tta rotate0bj ttb 90 obj tta suba a origin obj ttb suba a origin 10cm 2cm draw0bj tta ttb The result is shown here 19 The previous coding is still unsatisfactory in the way we have to access sub object points such as obj tta suba a This is so because our group of three triangles does not have a point with significance besides those of the subobjects The c point is not used except internally when memorizing equations and remains undefined What we could do is to decide that the c point is one of the three triangle s points In order to say that c is the point a of the first triangle it is sufficient to add the string obj suba a c to the equations of newThreeTriangles ObjCode obj subb a obj suba a 4cm 1cm obj subc a obj suba a 7cm 2cm obj suba a G c Then the objects tta and ttb can be simply positionned with tta c origin ttb c origin 10cm 2cm T
62. body can convince him or herself you can t just write the previous equation after the first one to get the right result because n b n a has two different values and we are using only equations And we can also not write n b n a 1cm 2cm rotated 30 for it is not a correct assignment So how does rotate0bj achieve the desired result It actually first memo rizes all relative positions of the points For instance it would first do something like pair p pi n a p2 n b n a 11 then it would refresh n a and n b METAPOST makes it possible to refresh variables using the whatever construct whatever is a new yet undefined and unnamed numerical variable It is unnamed because whatever is not the name of a variable but it expands into a variable Basically we now refresh the variables with n a whatever n b whatever Then it is possible to achieve the result by merely saying n b n a p2 p1 rotated 30 It is along this scheme that all linear transformations are applied on floating objects Of course we might have positionned the object at a fixed location and then done assignments and finally untied the object but this would nt have been simpler 2 A first object 2 1 A segment We are now ready to create our first object We will start with the Segment object This object will contain two points a and b and they will be located as in the initial example vardef newSegme
63. box has no surprises nw ne bounding box RecursiveBox options The options recognized by the RecursiveBox objects are shown in table 4 71 Option Type Default Description filled boolean false true if the object is filled fillcolor color black filling color framed boolean true true if the object is framed framewidth numeric 5bp thickness of the frame framecolor color black frame color framestyle string n frame style dx numeric 5cm object width dy numeric 5cm object height rotangle numeric 10 angle by which an internal object is rotated before inserting it into an outer object shadow boolean false true if there is a shadow framed too must be true shadowcolor color black shadow color 7 4 2 VonKochFlake Table 4 RecursiveBox options A Von Koch flake of a given depth can easily be obtained with the VonKochFlake object newVonKochFlake a 3 scale0bj a 5 a c origin draw0bj a We can produce some technicolor effects if we assign random colors to all the sides We modify the drawVonKochSide function which is used to draw four segments 72 def randomcolor withcolor uniformedviate 1 uniformedviate 1 e NA uniformedviate 1 enddef a def drawVonKochSide suffix n B if known n suba draw0bj obj n suba Ne else draw n A n B randomcolor fi if known n subb draw bj obj n subb else draw n B n C randomcolor fi 7 if known n s
64. c where the connection ends name string connection name linestyle string n connection style this should be an accept able value such as dashed evenly dashed withdots etc linewidth numeric 5bp line thickness linecolor color black line color arrows string drawarrow name of a draw command such as draw drawarrow etc or the shortcut of such a com mand angleA numeric angle angleB numeric angle arcangleA numeric 10 angle arcangleB numeric 10 angle border boolean Opt true if there is a border around the connection bordercolor color white color of the border nodesepA numeric Opt node separation at start nodesepB numeric Opt node separation at end loopsize numeric 0 25cm parameter for ncloop boxrsize numeric 5mm parameter for ncbox and ncarcbox borheight numeric lpt parameter for ncbox and ncarcbox boxdepth numeric lpt parameter for ncbox and ncarcbox linearc numeric Ocm rounding of corners in connections linetensionA numeric 1 line tension used by nccurve linetensionB numeric 1 line tension used by nccurve armA numeric 5mm connection arm at start armB numeric 5mm connection arm at end doubleline boolean false true if the line is doubled doublesep numeric 1pt separation between the two lines if doubleline is true visible boolean true true if the connection is visible offsetA pair 0 0 offset at the start of a connection offsetB pair 0 0 offset at the end of a
65. change the spacing between leaves of a tree when the spacings are not all identical The constructor looks like 27 vardef newEmptyBox expr dx dy text options Execute ptions options assignObj EmptyBox StandardInterface ObjCode StandardEquations Otise Otisw amp decimal dx amp 0 Ottine Ottise 0 amp decimal dy amp enddef It is called with two dimensions which are the sides of the rectangle It should be noticed that the values of dx and dy can be negative and this makes up for some special effects as we will see later This function also exhibits some features related to the options mecha nism Every constructor can have options modifying its behavior The options are given as the last parameters of the constructor and are used in a call to ExecuteOptions Each object decides which option it honors and how The EmptyBox doesn t have many options but it is still possible to draw its frame with a different thickness or even to fill the box Therefore the drawEmptyBox function actually is with slight simplifications def drawEmptyBox suffix n if show empty boxes drawFramedOrFilledObject n fi drawMemorizedPaths n enddef This function is simple depending on the global variable show empty boxes often used for debugging the empty boxes are shown or not If they are shown they are either filled or merely drawn The drawFramedOrFilledObject_ takes care of the various case
66. cle This means that the path nnw left cycle is stored at index 1 of the _spath_ array in the current box object In addition to storing the path various options are also recorded after the addPath call For instance the number of stored paths has to be incremented The memorized path is drawn in the drawBox function when the function drawMemorizedPaths is called Usually the user does not need to use addPath directly because there are higher level functions such as ncline nccurve adapted from PS Tricks These functions take various parameters and feed them into addPath However there are also higher level functions which make it easy to add stan dard or user paths These functions are addStandardPath and addUserPath and take an object as suffix a path and options We give here two examples many details of which will only be explained in section 5 7 newBox a dx 5cm dy 2cm framecolor blue addUserPath a a nw a se addUserPath a a nw right a se linecolor red arrows arrows pathfilled true pathfillcolor 1 0 1 arrows linecolor 1 0 1 a c origin draw0bj a The paths that have been added follow all linear transformations 38 addUserPath a fullcircle scaled icm shifted a c addUserPath a fullcircle scaled 1cm shifted a ne addUserPath a fullcircle scaled 1cm shifted a sw pathfilled true pathfillcolor 1 0 1 xscale0
67. connection coilarmA numeric 5mm parameter for coils and zigzags coilarmB numeric 5mm parameter for coils and zigzags coilwidth numeric lcm parameter for coils and zigzags coilheight numeric 1 parameter for coils and zigzags coilaspect numeric 45 parameter for coils and zigzags coilinc numeric 90 parameter for coils and zigzags pathfilled boolean false true if the path must be filled none of the standard connections uses this option pathfillcolor color black path filling color cdraw string cdraw default metaoption Table 1 Connection options shortcuts are not shown 41 on An unsupported sequence of symbols will be equivalent to the value The cdraw option defines how the other options are used This option is very seldom used and is not described in this manual Several of the options come in two flavors one for each end of the connection This is for instance the case for posA and posB In this case special shortcuts are provided pos is a shortcut option setting both posA and posB For instance ncline a b pos s is equivalent to ncline a b posA s posB s These shortcuts can also be used with setCurveDefaultOption and when passed to a Tree constructor The shortcuts currently supported are pos coilarm linetension offset arm angle arcangle and nodesep In all the examples below the two circled objects are produced with newCircle a btex start etex newCircle b btex
68. context of the object It is therefore the responsibility of the constructor to attach the points so that all points and subobjects are tied together However the attachment must only be relative Tf it were not we would have the light burden to have to unattach the object after it is created The definition of the points involves additional equations which tie the interface to the subobjects The new equations must take care not to violate the standard equations That means that the standard equations must be a rectangle One possible solution is to add ne obj subc a This is sufficient to define all the points of the interface because of the constraints of the standard equations We can now draw the interface by adding a suitable draw function to the drawThreeTriangles definition This may not be what we want for a bounding box but it is what we asked for Point c is the middle of sw ne as a consequence of the standard equations It is the responsibility of the constructor to define the standard interface so that the content of the object is inside In certain cases one may want to have objects protrude or take only some of the space to achieve special effects The current interface will have the effect that the object will behave at least with the standard library as if it were larger than it really is We can get a better result with different equations ObjCode StandardEquations obj subb a obj suba a 4cm
69. ct as vector stored into a_ b_ When v is a string the text is set in the current font without calling TEX When v is an object this vector is computed too Afterwards we work with this vector and this simplifies the equations The constructor then modifies the vector in case the rectangle must not fit If it fits its size adapts to the size of the object Otherwise the rectangle is a square Therefore if the fit option is not set to true a_ and b_ are defined to be equal to their maximum The newBox constructor distinguishes one special case if the corners are rounded rbor_radius gt 0 eight new points are defined with ObjPoint the rounded frame will pass through these eight points this frame is defined at the end of the constructor with a call to addPath All the points are linked through the equations defined with ObjCode A first part of the code defines either the relative position of the contained object or the picture offset if it is a picture which is boxed A second part of the code defines the additional points depending on the values of the options The last two equations involve two dimensions dx and dy which have default values but can be given different values as options They represent a clearance between the picture or the object and the frame The frame is only memorized in the case of round corners Otherwise it is sufficient to use the corner points in order to draw the frame with drawBox This function see belo
70. d ObjLabel mat btex q etex labpathname d labdir 1ft mcline mat 3 2 3 3 name e ObjLabel mat btex g etex labpathname e labdir bot mcline mat 2 3 3 3 name f ObjLabel mat btex f etex labpathname f labdir rt draw0bj mat Figure 10 Matrix example with labels after page 26 of 16 94 newCircle newCircle newCircle d btex newCircle newCircle a btex b btex c btex e btex A etex B etex C etex D etex E etex verbatimtex small etex newMatrix mat 3 3 nb a nb b e c nb d nb hsep 2cm vsep 2cm mcline mat 2 2 2 3 name a ObjLabel mat btex a etex labpathname a labpos 0 75 labdir top mcline mat 2 2 2 1 name b ObjLabel mat btex b etex labpathname b labdir bot mcline mat 3 2 2 1 name c ObjLabel mat btex c etex labpathname c labdir 1lft mcarc mat 3 2 1 2 arcangleA 40 arcangleB 40 border 3pt name d ObjLabel mat btex d etex labpathname d labdir lrt labpos 0 3 ObjLabel mat btex e etex labpathname d labdir 1lft labpos 0 7 mcarc mat 1 2 2 1 arcangleA 12 arcangleB 12 name f ObjLabel mat btex f etex labpathname f labdir lrt mcarc mat 2 1 1 2 arcangleA 12 arcangleB 12 name g ObjLabel mat btex g etex labpathname g labdir ulft mat c origin draw bj mat Figure 11 A complex matrix with connections and labels
71. d Tox AA mtmsbos Qe ud e Ped bh TA Recursive objects and fractals aaa aaa TAAl dBecursivsBbN cocida a x ok EX RR REG 742 YonKochFlake 2222549 9 RR ade 4 ne ilc AMETE 3nd e uve eO de as Tod EEG uo 96 hoo osos o S n n REGERE ES 13 BEAMER o s sosai a XE Bo OR OR OR er kc E A 7 6 1 Experimental constructions 7 6 2 Matrices with brackets experimental 106 3 Matriz with labels oa 2292 94 36 Res Toe Matrix ophons Loo aad ee A ee ee ee ie PSTricks METAOBJ gallery o Class builder manual 8 1 Components Of a Olde cc a RR Boll E 2 55293 ROIG 4OROROR ee a 8 1 2 Streamlined constructor gt lt e sc na rara m m s e La BOMBAS DAR x 954a a 8 1 8 Drawing funci oros errada eee 8 1 5 Alternate constructors lle 51 0 Additional fumetions o e se k ia sa ee eed 8 1 7 Option declarations sn 8 L8 Detault values for options 2 2452 Rm 8 2 DeseuqubB 2222212939339 eR Ea Non linear transformations on objects 9 1 Simple transformations which do not change the layout 9 1 1 Example 1 changing the frame color 9 1 2 Example 2 changing the content of a label 9 2 Transformations that change the layout 10 Comparison with other packages 10 1 Compatibility with boxes mp 10 2 fancybox package cocog iadaaa Wina 103 PREFIERES 2229223 8 RR REX oo Ro 11 Memory requirements METAPOST bug 12 Using METAOBJ from w
72. d objects may or may not be completely defined just like points e in order to achieve the above considering only the points constituting an object we have to define equations between these points e the objects should by default be rigid with only two degrees of freedom as in boxes in the sense that the position of one point will determine all the other ones e it is interesting to have a boxes mp like interface where an object o can be positionned with something like o c origin e the objects should accept all linear transformations by default that is we must be able to move rotate slant etc our objects and yet keep the equations defining the objects so that after any such linear transforma tion the object can still be put anywhere with a mere o c e we must have composition that is it must be possible to put objects inside objects e paths and pictures must be able to be part of an object e when an object contains another object the subobject should be repla cable by any other object that is the class of an object should not if possible influence its use e all constituents should be reachable e the objects should be customizable for instance through options e a library of classes should be provided and the creation of new classes should be made simple The METAOBJ package addresses all these issues and many others 1 3 An appetizer Before going in the details of the machinery let us give a
73. d_bot_most command 29 find Ift most command 29 find rt most command 29 find top most command 29 fit class option 31 62 64 66 67 flip class option 69 70 framecolor class option 34 60 67 69 70 72 80 85 92 framecolor connection option 38 framed class option 31 34 36 59 67 69 70 72 80 85 92 framestyle class option 34 60 67 69 70 72 80 85 92 framewidth class option 34 60 67 69 70 72 80 85 92 halign class option 89 92 HBox class 67 70 80 hbsep class option 69 80 HFan class 81 hideleaves class option 77 78 80 81 Hobby John 5 HRazor class 60 81 hsep class option 66 68 80 85 92 103 image command 5 61 is 117 Knuth Donald 5 labangle label option 55 labcard label option 55 labcolor label option 55 56 133 labdir label option 54 55 112 label command 55 Label options labangle 55 labcard 55 labcolor 55 56 labdir 54 55 112 laberase 55 56 labpathid 54 55 112 labpathname 55 labpoint 55 labpos 55 labrotate 55 56 labshift 55 56 laberase label option 55 56 labpathid label option 54 55 112 labpathname label option 55 labpoint label option 55 labpos label option 55 labrotate label option 55 56 labshift label option 55 56 Lalign class option 80 lenddx class option 84 85 linearc connection option 41 51 52 li
74. defined by the user 8 1 7 Option declarations If the C class uses options that are not yet part of METAOBJ they should be defined with one of the following commands e define local numeric option e define local pair option e define local string option e define local color option e define local boolean option e define global numeric option e define global pair option e define global string option e define global color option e define global boolean option The first five functions define local options that is options that are used only at the time of the constructor The last functions define global options that is options that are used beyond the constructor for instance when the object is drawn filled is such an option define global boolean option filled This option is used by many objects to decide whether the frame should be filled or not 117 8 1 8 Default values for options All the options should have a default value This default value depends on the class It can be set with setObjectDefaultOption For instance here is how the Tree class defines the default orientation of trees setO0bjectDefaultOption Tree treemode D 8 2 Design rules Several METAOBJ functions assume that objects are rigid Such objects can be floating but the position of all the points should be determined by setting just one point It is of course possible to define objects with less constraints but then the
75. do not have that interface but then the user may have more work to do when plugging objects into one another However this is not the whole story The previous nine points are actually only the external standard interface There is also an internal standard interface made of the nine points in is ie iw ine inw ise isw and ic Initially the internal interface is identical to the external one that is for each object points n and in points s and is etc are at the same location But certain operations to the objects can break these identities as we will see later The external interface is what should be used from outside the object The internal interface is what should be used from the inside This distinction does prove quite useful in certain cases In order to declare an object with a standard interface it is sufficient to write StandardInterface 21 as part of the constructor right after the assign0bj call 3 2 Standard equations The standard points are initially connected according to equations that are called the standard equations These equations are divided in the pure standard equations and the inner standard equations The METAOBJ package defines the pure standard equations with def PureStandardEquations se 0 sw 0 ne 0 nw amp 4 parallelogram equation xpart se G ne 0 Y ypart se sw 0 amp n s e Qiw c enddef 5 0 ne nw amp 4 North 5
76. e and we need no more points for those The corners of the inner XXXXXXX box are also those of its standard interface For the top left label we add three points 1sw lse and 118 lne The top label and the main XXXXXXX box will be parameters to the new constructor Now we have to decide the layout Will XXXXXXX be centered no matter the size of the top left label or will it take the top left label into account These are design decisions that must be taken Let s assume the top left label doesn t influence the position of XXXXXXX Let s also assume that the size of the top left rectangle is exactly that of the label Finally let s assume there is a DX and DY clearance inside the box This gives us the following equations in plain language let L topleftlabel X center box M main box xpart M e X e xpart X w M w DX ypart M n X n xpart X s M s DY M nw L nw M 1sw L sw M lse L se M lne L ne and that s it Actually we might even discard 1sw 1se and 1ne since they are given by L s cardinal points Things get more complex when the object contains lines that are not straight There are two cases either it is easy to compute the line from certain points this is done with the Circle and Ellipse constructors for instance or it is easier to memorize the line as a path This is what is done for round boxes RBox 9 Non linear transformations on objects The whole structure of an object is available and it is therefore po
77. eB 100 linecolor blue linewidth 1pt armA 2cm armB icm ely and two last ones with only one node ncloop a a angleA 0 angleB 0 linecolor blue linewidth 1pt armA 1cm armB 1cm loopsize 1cm 49 ncloop a a angleA 0 angleB 0 linecolor blue linewidth 1pt armA 1cm armB 1cm loopsize 1cm offsetA 0 2mm offsetB 0 3mm 5 7 10 nccircle nccircle draws a circle or part of a circle that if complete would pass through the center of the node counterclockwise at an angle of angleA The angleB option is not used nccircle a angleA 0 linecolor blue linewidth 1pt 5 7 11 ncbox ncbox and ncarcbox do not connect the nodes with an open curve but they enclose the nodes in a box or curved box The half of the width of the box is boxsize The dimensions of the box can also be given with the boxheight and boxdepth options The ends of the boxes extend beyond the nodes by nodesepA and nodesepB This hence gives two different meanings to these two options Two of the sides of the ncbox box are parallel to the line connecting the two node centers No angle is taken into account by ncbox ncbox a b linecolor blue linewidth 1pt nodesepA 1cm nodesepB 1cm 50 ncbox a b linecolor blue linewidth 1pt nodesepA 1cm nodesepB 1cm boxsize icm The corners can be rounded with the linearc option ncbox a b li
78. eR 83 RandomBox 60 RBox 81 119 122 RecursiveBox 28 29 71 Tree 7 8 32 36 42 73 79 81 82 90 113 117 118 VBox 67 69 80 VFan 81 VonKochFlake 8 72 VRazor 60 81 clearObj command 18 code attribute 57 59 coilarm connection option 42 coilarmA connection option 41 52 coilarmB connection option 41 52 coilaspect connection option 41 D2 coilheight connection option 41 pe coilinc connection option 41 52 coilwidth connection option 41 52 colorarraylist_ attribute 57 Commands JT 79 addPath 31 38 addPathVariables 37 38 addStandardPath 38 39 addUserPath 38 91 assignObj 12 22 114 boxit 10 BpathCircle 39 BpathEmptyBox 28 BpathObj 28 bracketit exp 91 btex 30 circleit 10 clearObj 18 define_global_boolean_option 117 define_global_color_option 117 define_global_numeric_option 117 define_global_pair_option 117 define global string option 117 define local boolean option 117 define local color option 117 define_local_numeric_option 117 define_local_pair_option 117 define local string option 117 deleteMatrixElement exp 90 delete TreeElement exp 82 draw 16 23 40 43 draw_Obj 32 100 drawarrow 40 43 107 drawBox 31 38 drawCircle 39 drawEmptyBox 28 drawFramedOrFilledObject_ 28 31 drawMemorizedPaths_ 30 31 38 drawObj 14 16 20 28 29 32 drawPicture 26 drawRecursiveBox 29 drawVonKochSide 72 duplicate_Obj
79. e_ se G sw ne Q nw xpart Gitse Qitne 0 ypart se sw 0 n 5 G ne Qitnw s 5 C se O sw Q e 5 Q ne O se Citw 5 Oitnw Ottsw c 5 C n Qits C Hine G ne O inw O nw O isw G sw C ise G se C in G n G is OG s C ie O e C iw O wW ic 0 c xpart 5 obj Citconc ledge obj conc redge 5 xpart obj subt s 62 07625 xpart obj subt s 55 40683 ypart obj Gitsubt s obj conc n 5 66928 ypart n obj subt n 0 ypart obj conc s s 0 Ottledge 0bj conc sw Ottredge 0bj conc se ypart 1lstart ypart lend ypart obj conc n 2 83464 xpart 1start xpart obj subt c 62 07625 0 xpart lend xpart obj subt c 55 40683 0 xpart e xpart obj subt e 0 xpart obj subt w xpart w 20 33072 1start rdistl 0 obj 1r e Figure 6 Object structure cont d equations show0bj ptre but this does not show the structure of all subobjects We could define a function showing recursively the whole structure of an object but currently the user must call show0bj on each subobject _______ It is possible to go to great depth in an object Even when there are pictures we can find what is inside using the for within construct Each subobject has an associated tying function We have therefore four such functions subobjties_1 subobjties_2 subobjties_3 and subobjties_4 Each object can store
80. ect has been built its structure is still easily accessible and open to introspection This is an important feature which has almost been left aside in this manual It is of course easy to add new objects and we have only provided a few It is also easy for the programmer to write special packages manipulating special graphical formalisms such as UML etc It should also be possible to extend the concept of interface to other kinds of interfaces and to introduce objects that are not completely rigid We have already mentionned that it is possible to use the complete object structure to implement tree layout algorithms We could also have objects whose shape depends on parameters and on their location in a drawing More elaborate operations could also be implemented if the history of an object was known his is currently not the case and causes limitations in certain experimental features such as the reset feature METROBJ can be used as a replacement to boxes mp and rboxes mp to fancybox sty and to many features found in PS Tricks Several features of METAOBJ for instance connections can be used without a reference to objects METAOBJ was especially influenced by my earlier work on animations 14 where an object notion was introduced The 3D objects were very primitive but they provided many useful ideas Several objects have been influenced from their counterparts in various packages This is especially true for rectangular and elliptic boxe
81. ection which is memorized in an object and drawn later The syntax for both cases is the same except that the ob ject name when present is given as a suffix to the connection command For instance ncline A a b is a deferred connection command connecting the objects a and b assuming these are objects and the connection is memorized within the object A If we write ncline a b we get an immediate connection between a and b Each of the connection commands has many options These options make it possible to change the style of the connection the thickness of the line where the line starts etc The options have types and default values but the default values are not bound to a class The complete set of options is the following The types and default values of the options are summarized in table 1 The default values can be changed with setCurveDefaultOption For in stance the default value for arrows is drawarrow and it can be changed to draw with setCurveDefault ption arrows draw Incidentally we might also have written setCurveDefault ption arrows because METAOBJ provides several shortcuts for the kind of arrows Currently the following shortcuts are implemented but others will probably be added Shortcut Full function name draw gt drawarrow lt rdrawarrow 40 Option Type Default Description posA string yc where the connection starts posB string i
82. ed with 56 Attribute Type Default Description pointlist_ string a list of points pairlist string VN list of pairs non movable points pointarraylist string n list of arrays of points subarraylist string n list of arrays of subobjects stringarraylist string n list of arrays of strings colorarraylist string n list of arrays of colors picturearraylist_ string m list of arrays of pictures transformarraylist string nu list of arrays of transforms booleanarraylist string list of arrays of booleans numericarraylist string na list of arrays of numerics pairarraylist_ string UM list of arrays of pairs non movable points points in arrayslist string n enumeration of all movable points of all ar rays of movable points picturelist string n list of pictures numericlist string n list of numerics sublist string m list of subobjects subobjties string array subobj tying equations 1 string subobject nsubobjties numeric 0 number of subobjties code string me code of an object extra_code_ string n extra code of an object ctransform transform identity current transform of that object Table 3 Standard attributes of an object ptre ptre ptre ptre ptre ptre ptre ptre pointlist_ ne nw sw se n s e w C ptre n 0 312 73784 ptre ptre w 95 02467 287 17845 ne 95 02467 312 73784 se 95 02467 261 61906 nw 95 02467 312 73784 ptre p
83. eight 41 50 boxsize 41 50 cdraw 41 42 coilarm 42 coilarmA 41 52 coilarmB 41 52 coilaspect 41 52 coilheight 41 52 coilinc 41 52 coilwidth 41 52 doubleline 41 43 44 doublesep 41 framecolor 38 linearc 41 51 52 linecolor 38 41 44 45 linestyle 41 43 44 linetension 42 44 linetensionA 41 44 linetensionB 41 44 linewidth 41 43 44 loopsize 41 48 name 41 55 nodesep 42 nodesepA 41 43 50 99 nodesepB 41 43 50 offset 42 offset A 41 43 56 offsetB 41 43 56 pathfillcolor 38 41 pathfilled 38 41 91 pos 42 posA 41 43 106 posB 41 43 visible 41 Constructors new_Box 7 8 new_Tree 8 newAssumption 83 newAxiom 83 newBB 34 newBox 30 31 38 66 67 81 122 newCircle 64 newConclusion 83 newDBox 66 newDEllipse 66 newEllipse 63 66 122 newHBox 67 newMatrix 89 newPentagon 116 newPolygon 62 116 newPolygon 8 newP Tree 73 83 84 newPTreeL 83 newPTreeR 83 newRBox 81 122 newRecursiveBox 29 new Tree 36 73 newVonKochFlake 8 newVRazor 60 ctransform attribute 57 59 Dalign class option 74 80 DBox class 65 122 define_global_boolean_option command 117 define global color option command 117 define global numeric option com mand 117 132 define global pair option command II define global string option command 117 define local boolean option command 117 define local_color_option com
84. erarchy 7 1 1 EmptyBox An empty box is a rectangle with a given size It can be framed or not However the frame is only visible when show_empty boxes is set to true An empty box cannot contain something It is only a frame Show empty boxes true newEmptyBox a 2cm 1cm framed true a c origin draw0bj a ne bounding box se METAOBJ defines Tn as a shortcut for new_EmptyBox 0 0 for compatibility with PSTricks EmptyBox options 59 Option Type Default filled boolean false fillcolor color black framed boolean false framewidth numeric 5bp framecolor color black framestyle string ma shadow boolean false shadowcolor color black 7 1 2 HRazor An HRazor object is a degenerated empty box where the height is 0 There is therefore only one size parameter An HRazor is really an EmptyBox The object can be framed or not and the frame is only visible when show_empty_boxes is set to true When not visible an HRazor can be used as an horizontal strut in a variety of contexts The width can also be negative newHRazor a 3cm framed true nw SW a c origin draw0bj a le nw SW ae bounding box There is also a similar newVRazor constructor A VRazor is also a EmptyBox 7 1 3 RandomBox A RandomBox is also an empty object but the frame is slightly random There are four parameters The first two are the normal frame and are
85. ex root etex 3 angle 90 polymargin 4mm TCs TCs TCs TCs edge rncangle angleA 90 angleB 90 armB icm vsep 2 5cm Obj t c origin draw 0bj t Figure 35 Illustrating reverse connections in a tree after page 43 of 16 in all trees the parameter to edge or its default value represents a connection from the root to the subtrees this example shows that it is possible to pass a connection which goes from the subtrees to the root and angleA arma etc then represent parameters for the start of the connections at the bottom the arrow style has to be changed so that the arrow appears at the beginning of the line rdrawarrow is a variant of drawarrow where the two ends are exchanged newBox a btex Ideal etex newBox b btex Idea2 etex b c a c 5cm 3cm a c origin ncbox a b linearc imm linestyle dashed evenly boxsize 1cm nodesepA 1cm nodesepB 1cm draw0bj a b Figure 36 Illustrating ncbox after page 16 of 16 107 H Idea2 H l 4 4 4 4 7 4 1 4 Y Y P 4 2 4 ae p Y PERSAS P ft E T Y FS n Z7 4 MARA Y LU d DN 2 N Ideal 2f 2 Tl 2 E 2 Tu 227 newBox a btex Ideal etex newBox b btex Idea2 etex b c a c 5cm 3cm a c origin ncarcbox a b doubleline true linestyle dashed evenly boxsize 7mm nodesepA 1cm nodesepB 1cm arcangleA 50 draw0bj a b Figure 37 Illustrating ncarcbox afte
86. ey can be drawn using their draw functions through draw0bj or by additional draw instructions For instance if one wants to connect point b of the first triangle with point b of the second triangle it is sufficient to write draw ti b t2 b giving 2 3 Creating an object containing objects Let us consider the previous drawing and assume we somehow need two copies of it one being rotated by 90 degrees This looks more tricky because what we really have are three objects and we do not have a means to move them in a whole We could of course rotate each object but then they would have to be placed again at the right positions This is rather cumbersome The solution is to create a new object containing the three previous ones One trivial way is to write 16 vardef newThreeTriangles0t assignObj ThreeTriangles newMyTriangle ti newMyTriangle t2 rotate0bj t2 180 duplicate0bj t3 t2 rotate0bj t3 20 ObjCode t2 a t1 a 4cm 1cm t3 a t1 a 7cm 2cm enddef def drawThreeTriangles suffix n draw0bj t1 t2 t3 drawarrow t1 b t2 b enddef newThreeTriangles tt ti a origin draw0bj tt This does indeed produce the expected drawing but there are problems with what we have done The objects t1 t2 and t3 are not really marked as subobjects of tt and it won t be possible to rotate tt The object tt is virtually empty It contains nothing As a general rule all objects should contai
87. form of streamlined con structors has a mandatory additional parameter which is a list of options The list can be empty but the opening and closing parentheses must be there In the tree example the option given to the polygon was fit false meaning that the polygon must not fit 5 2 Cloning Objects can be cloned with duplicate0bj or duplicate Obj which is its streamlined version This creates a deep copy which is completely indepen dant of the original object A duplicated object is not attached whether the original object was attached or not because most likely the copy will be put elsewhere than the original object 5 3 Fiddling with the bounding box The bounding box of an object is its outer interface It is what is used by other METAOB functions and especially those honoring the standard interfaces in order to decide how an object is positionned There are however cases where the automatic computation is inadequate For instance certain functions only function appropriately when the bounding boxes are rectangles with horizontal and vertical sides and with the cardinal points nw ne etc located where one expects them This alas is not always the case when transformations are applied There are two major remedies to that e an additionnal layer can be added to an object hiding the idiosyncrasies of the object and making sure the object behaves correctly e an object can be coerced to have a normal interface withou
88. function must be augmented with a call to drawPicture This function automatically uses the location of the picture def drawThreeTriangles suffix n draw0bj obj n suba obj n subb obj n subc drawarrow obj n suba b obj n subb b drawPicture n pic enddef And since drawPicture uses the picturecolor option to find out which color it should use we have to specify a default picture color for the ThreeTriangles class set bjectDefaultOption ThreeTriangles picturecolor black Finally the constructor is merely called with an additional parameter for instance newThreeTriangles tta t1 t2 t3 btex pic etex The result then is and this can be transformed say by a reflection and the picture follows the transformation 26 We can also slant it Now the ne point is actually on the North West and the new bounding box is cumbersome We have already mentionned one way of providing a standard tight bounding box with rebindVisible0bj In this case it would produce se We will see later that there is also a special object BB which encapsulates an object in a bounding box object 4 Real examples We are now ready to look at some real albeit simple examples from the library of objects provided by METAOBJ The simplest of all classes is the EmptyBox An EmptyBox is an empty rect angle normally with no frame Its only purpose is to take some space For instance it is useful to
89. his is about the simplest we can get We now have a complex construction with two objects tta and ttb each being made of three subobjects Each of these eight objects are accessible in isolation They all have names The three triangles of the first object are t1 t2 and t3 The big objects are tta and ttb And the three other triangles have names that were generated automatically at the time of the duplication It is possible to get these names but we can also reach these objects logically For instance the second triangle of ttb is the object obj ttb subb If we desire it we can draw this object by calling draw0bj obj ttb subb This shows that it is better to use draw0bj instead of drawMyTriangle even though the latter will eventually be called All the objects are accessible and so are the points of these objects We can connect point a of subobject subb of object tta to point c of subobject suba of object ttb by writing 20 draw obj tta subb a obj ttb suba c More complex structures can be built and we will still be able to access the complete internal structure 3 Interfaces and reusability As long as objects are built in isolation for a unique use there are few con straints on their construction But when one builds a library of objects there are important issues which must be addressed The main issue is the reusabil ity It is desirable to have objects that can be used like blac
90. if the proof is displayed in a bottom up style an Axiom is built with newAxiom this is actually a specialized version of newPTree e Conclusion is an object which ends a proof it is also a Box object with no frame and can be created with newConclusion e when a proof has only a right rule newPTreeR can be used instead of newPTree similarly there is a newPTreeL constructor for a proof which has only a left rule The first example shows the modus ponens rule of classical logic A AB newAssumption a btex A etex newAssumption b btex A rightarrow B etex newConclusion c btex B etex newPTree proof c a b proof c origin draw0bj proof The default is to build a proof from the top to the bottom This means that a conclusion is below the assumptions It is also possible to do it the other way when the treemode option is used Only two values are recognized U up and D down A A B Rule names can be given left rule right rule newAssumption a btex A etex newAssumption b btex A rightarrow B etex newConclusion c btex B etex newPTree proof c a b treemode U proof c origin draw0bj proof newAssumption a btex A etex newAssumption b btex A rightarrow B etex newConclusion c btex B etex newPTree proof c a b btex left rule etex btex right rule etex proof c origin draw0bj proof If the rule is only
91. illed boolean false true of the tree is filled fillcolor color black filling color framewidth numeric 5bp thickness of the frame framecolor color black color of the frame framestyle string n style of the frame Dalign string top vertical alignment of subtrees for trees that go down the root on the top the other possible values are center and bot Ualign string bot vertical alignment of subtrees for trees that go up the root on the bottom the other possible values are center and top Lalign string right horizontal alignment of subtrees for trees that go left the root on the right the other pos sible values are center and left Ralign string left horizontal alignment of subtrees for trees that go right the root on the left the other pos sible values are center and right shadow boolean false true if there is a shadow framed too must be true shadowcolor color black shadow color Table 5 Tree options 80 e T_ for new_Tree Several examples of their use can be found in section 7 7 HFan and VFan components When we introduced the Tree class we said that the root and the subtrees can be any objects Most of these objects can also be used in a non tree context For instance we can use a circle as a leaf of a tree but also elsewhere outside a tree There are however two objects that are meant to be used only as part of a Tree structure These classes are the HFan and VFan cl
92. in the future Tree shortcuts METAOBJ defines a few useful shortcuts e _T for new_Tree e T for newTree 79 Option Type Default Description treemode string p direction in which the tree develops there are four different possible values D default U L and R treeflip boolean false if true reverses the order of the subtrees treenodehsize numeric 1pt if non negative all the nodes are assumed to have this width treenodevsize numeric 1pt if non negative all the nodes are assumed to have this height dx numeric 0 horizontal clearance around the tree dy numeric 0 vertical clearance around the tree hsep numeric lcm for a horizontal tree this is the separation be tween the root and the subtrees usep numeric lcm for a vertical tree this is the separation be tween the root and the subtrees hbsep numeric lcm for a vertical tree this is the horizontal separa tion between subtrees the subtrees are actu ally put in a HBox and the value of this option is passed to the HBox constructor ubsep numeric lcm for an horizontal tree this is the vertical sepa ration between subtrees the subtrees are actu ally put in a VBox and the value of this option is passed to the VBox constructor hideleaves boolean false if true the subtrees are not taken into account in the bounding box edge string ncline name of a connection command framed boolean false true if the tree is framed f
93. inecolor 1 1 0 newBox aa t filled true fillcolor 0 1 1 rbox radius 2mm aa c origin newHexagon xa hexagon fit false filled true fillcolor 1 0 1 newEllipse xc c filled true fillcolor red picturecolor green framecolor blue framewidth 2pt newTree xt xc xa aa linecolor 1 1 0 newCircle xaa xt filled true fillcolor 6 8 5 newDBox db btex Double box with green shadow etex shadow true shadowcolor green filled true fillcolor blue picturecolor 1 1 0 newTree nt xaa db draw0bj nt nccoil xc db angleA 0 angleB 180 coilwidth 5mm linetension 0 8 linecolor red doubleline true posB e duplicate0bj dt aa reflect bj dt origin up slantObj dt 5 rotate0bj dt 30 dt c nt c 6cm 1cm draw0bj dt nczigzag a treepos obj dt sub 1 angleA 120 coilwidth 7mm linecolor 5green linearc imm border 2pt Figure 43 Cover example The standard Tree class draws the paths before the components because the junction with objects are then better in case the node frames are of a different color than the paths This is why we drew the coil after the main object As a consequence the coil is not part of the object and won t move with it It is possible to see the path and still attach it to the object by modifying the draw function of the object 113 8 Class builder manual 8 1 Component
94. ions Experimental commands on matrices are provided deleteMatrixElement exp and replaceMatrixElement exp These commands are not supported With replaceMatrixElement exp it is possible to replace a matrix element by an other and have the matrix adapt its size to the contents It is also possible to build a Matrix incrementally starting with a 1 x 1 matrix and adding elements in the same row or in a new row These two commands have the same problem than the analog commands for the Tree class The next two figures show various replacements w we IM Bb pf dx 0 an 90 newBox rep btex Very Long Replacement etex replaceMatrixElement exp matd 1 1 rep newBox repc btex court etex replaceMatrixElement exp matd 1 1 repc newBox repd btex D etex yscaled 3 rotated 30 replaceMatrixElement exp matd 3 2 repd newBox repe btex 00000000000000000 etex yscaled 3 rotated 30 replaceMatrixElement exp matd 1 1 repe newBox repf btex new line etex replaceMatrixElement exp matd 4 2 repf matd c origin draw0bj matd newBox repg btex new corner etex replaceMatrixElement exp matd 4 3 repg pf 1 as Bb matd c origin 0 1422 draw0bj matd an new line new corner The last figure shows that elements of a matrix can be deleted and that lines or columns vanish if they contain no elements deleteM
95. ipse The newEllipse constructor builds an ellipse which is a container The ellipse can contain text and by default it fits the text The following ellipse newEllipse a btex some text etex draw0bj a bounding box 63 When the option fit false is given the ellipse doesn t fit the contents vertically but only horizontally and we get a circle newEllipse a btex some text etex fit false a c origin draw0bj a It is possible to build an ellipse with no content and to specify a mar gin with the circmargin option Moreover the ellipse can be filled with the filled true option The following example shows a disk with a 2mm radius newEllipse a filled true circmargin 2mm a c origin draw0bj a METAOB provides Toval_ p as a shortcut for new_Ellipse p for compat ibility with PSTricks Ellipse options Option Type Default circmargin numeric 2bp filled boolean false fillcolor color black framed boolean true fit boolean true framewidth numeric 5bp framecolor color black framestyle string mete picturecolor color black shadow boolean false shadowcolor color black 7 2 4 Circle The newCircle constructor produces a circle The circmargin option can also be used to change its size newCircle a btex some text etex a c origin draw0bj a Circle shortcuts The following shortcuts to streamlined objects are pro vided partly for some com
96. ithin TEX Conclusion Acknowledgments References Index 122 122 122 122 123 124 124 125 126 128 1 Introduction This manual describes METAOBJ a system for high level object oriented draw ing based on METAPOST The name METAOBJ is short for METAPOST Ob jects METAPOST 5 6 2 is a programming language for drawings It was created by John Hobby as an adaptation of Donald Knuth s METAFONT system 9 This manual is not an introduction to METAPOST and some familiarity with METAPOST is assumed This section gives a general introduction to METAOBJ and to the motivations that led us to create it We will first try to show that METAOBJ is a useful approach for complex structural drawing 1 1 Low level METAPOST In low level METAPOST complex drawings can be simplified by well chosen definitions and definitions that are well parameterized For instance a general square can be defined with def Square expr p l a p p 1 dir a p l dir a 1 dir a 90 p l dir a 90 cycle enddef and it can then be drawn with draw Square origin 1cm 50 This definition introduces an important constraint Square returns a path because draw expects a path If we now want to draw a double framed square we can not merely modify Square because the double frame is not a simple path and draw can only draw simple paths The double framed square must be drawn in more than one stroke One way out is to define
97. k boxes When an object contains a subobject this subobject should be replaceable by any other object meeting certain standards This will make the construction of objects much easier since an object will not have to know the inside of the objects it contains 3 1 Standard points In order to achieve such a modularity we take as a convention that all objects have a minimal set of points that can be used from the outside Two objects may have different points but they will at least have this minimal set This minimal set is called the standard interface of an object It is what an object of the library can assume of a subobject This of course is only a convention of our library and the objects we have created so far didn t have this standard interface and they were anyway quite usable The purpose of the standard interface is to help plug in the object in a variety of contexts It won t work for all contexts and sometimes it will be necessary to use more information than the mere standard interface but such an interface provides already quite interesting facilities The standard interface should also serve to define the bounding box of an object We therefore decided to take as the standard interface points all the points defined in boxes such as those provided by boxes mp All the objects of our library will contain the points n s e w ne nw se sw and c We stress that this is only a convention and that one can define objects that
98. leObj 24 27 34 79 replaceMatrixElement exp 90 replace TreeElement exp 82 rncangle 54 rncangles 54 rncarc 54 rncarcbox 54 rncbar 54 rncbox 54 rnccoil 54 rnccurve 54 rncdiag 54 rncdiagg 54 rncline 54 rncloop 54 rnczigzag 94 rotate Obj 33 rotateObj 11 29 33 119 scaleObj 24 79 119 setBoolean 115 setColor 115 setCurveDefaultOption 40 42 setNumeric 114 setObjectDefaultOption 118 setPair 114 setPicture 115 setString 115 set Transform 115 set TreeEdge 105 show_empty_boxes 59 showObj 56 58 StandardEquations 115 StandardInterface 114 StandardObjectOrPictureContain erSetup 30 StandardTies 17 18 28 115 streamline 32 116 SubObject 17 115 suffixlist 33 suffixpar 33 T 79 T 81 TC 65 105 Tc 64 TC_ 65 Tc_ 65 109 tcangle 54 tcangles 54 tcarc 54 tcarcbox 54 tcbox 54 tecircle 54 tccurve 54 131 tediag 54 tcdiagg 54 Tcircle_ 64 tcline 40 54 tcloop 54 TCs 65 97 99 101 103 Tf 62 81 Tn 59 99 109 Toval_ 64 106 Tr_ 62 106 109 transformObj 11 treenodehsize 102 untieObj 15 35 vardef 8 whatever 12 Conclusion class 83 Connection options angle 42 angleA 41 44 47 50 107 angleB 41 44 47 50 arcangle 42 arcangleA 41 45 51 arcangleB 41 45 51 arm 42 armA 41 45 48 107 armB 41 45 49 arrows 38 40 41 43 border 41 bordercolor 41 boxdepth 41 50 boxh
99. left treemode L newTree vegetables v d e Lalign center treemode L newBox fo btex food etex newTree food fo fruits vegetables hsep 1cm treemode L scale0bj food 5 food c origin draw0bj food vegetables bananas oranges apples newBox a btex apples etex newBox b btex oranges etex newBox c btex bananas etex newBox f btex fruits etex newTree fruits f a b c Ralign right treemode R newBox d btex potatoes etex newBox e btex peas etex newBox v btex vegetables etex newTree vegetables v d e Ralign center treemode R newBox fo btex food etex newTree food fo fruits vegetables hsep 1cm treemode R scale0bj food 5 food c origin draw0bj food For the next tree the fruits box was extended to the right with rebindrelative0bj and its width now matches the width of the vegetables box We could also have used extend0bjRight This is sufficient to align the five leaves on the left vegetables potatoes bananas oranges apples apples bananas oranges potatoes peas vegetables newBox a btex apples etex newBox b btex oranges etex newBox c btex bananas etex newBox f btex fruits etex newBox d btex potatoes etex newBox e btex peas etex newBox v btex vegetables etex rebindrelative0bj f 0 0 xpart v e v
100. m 2cm StandardTies enddef The clear0bj function can currently only be applied to isolated objects which are not part of arrays or arrays but not to individual objects in an array t1 t2 and t3 are three objects in the t array and they are all undefined by the clear0bj t call 18 With the current definition the constructor can be used several times and we can also duplicate the objects that were created apply transformations etc An alternative to the previous definition can be a parameterized definition where the three objects are passed to the constructors as parameters In this case the objects must have been created beforehand The definition is now vardef newThreeTriangles suffix sa sb sc assign0bj 0 ThreeTriangles ObjPoint c SubObject suba sa SubObject subb sb SubObject subc sc ObjCode obj G subb a obj suba a 4cm 1cm obj subc a obj G suba a 7cm 2cm StandardTies enddef This shows that objects are normally manipulated as suffixes However we will see later that there is a special way to use numbers for objects when the objects are streamlined The newThreeTriangles constructor is called with newMyTriangle t1 newMyTriangle t2 rotate0bj t2 180 duplicate0bj t3 t2 rotate0bj t3 20 newThreeTriangles tta ti t2 t3 The constructor newThreeTriangles can be called several times with the same objects That means actually that the subo
101. mand IIT define local numeric option command 117 define local_pair option command 117 define local string option command 117 deleteMatrixElement exp command 90 deleteTreeElement exp command 82 doubleline connection option 41 43 44 doublesep connection option 41 draw command 16 23 40 43 draw_Obj command 32 100 drawarrow command 40 43 107 drawBox command 31 38 drawCircle command 39 drawEmptyBox command 28 drawFramedOrFilledObject_ command 28 31 drawMemorizedPaths command 30 31 38 drawObj command 14 16 20 28 29 32 drawPicture command 26 drawRecursiveBox command 29 drawVonKochSide command 72 duplicate Obj command 33 duplicateObj command 18 19 33 73 115 dx class option 62 65 66 69 70 72 80 85 92 dy class option 62 65 66 69 70 72 80 85 92 edge class option 80 82 104 107 elementsize class option 69 70 Ellipse class 119 120 EmptyBox class 9 27 28 32 60 61 etex command 30 ExecuteOptions command 28 114 extendObjDown command 34 extendObjLeft command 34 75 extendObjRight command 34 75 76 extendObjUp command 34 extra_code_ attribute 57 fanlinearc class option 81 82 fanlinestyle class option 81 82 fillcolor class option 34 60 67 69 70 72 80 82 85 92 filled class option 34 37 60 67 69 70 72 80 82 85 92 117 fin
102. med false name 1x Box y framed false name 1y MBox z framed false name 1z edge none vsep 1 5cm ncbar t top 1x angleA 180 armA 1cm ncline t top ly ncbar t top 1z angleA 0 armA 1cm pos t c origin draw t end metaobj Figure 45 Example of possible embedding of METAOBJ in IATEX above a typical METAOBJ code below a possible TEX representation The TEX front end does not yet exist and the commands shown here are imaginary 123 12 Using METAOBJ from within TpX METAPOST code can be embedded in TAT X with the emp sty package on CTAN 13 It should therefore be possible to embed METAOBJ code though this was not tested It should also be possible to use METROBJ within ConTEXt 3 4 where METAPOST code is naturally included in the main TEX file However if METAOBJ benefits from being embedded in TeX or Con TEXt code it would benefit even more if a TEX layer were hiding the verbose syntax of METROBJ No syntax for a TEX front end to METAOBJ has been defined so far but an example of a possible syntax is the one provided by PSTricks It is possible to have both concise code and to use METAOBJ behind the scenes For instance in the future we might input METAOBJ code as shown on figure 45 Conclusion METROBJ makes it possible to define and manipulate objects The standard functions consider that the objects are rigid and can be combined in various ways No matter how an obj
103. n ObjPath command which defines standard paths However they must be defined in the standardpaths section once all equations are defined It is also possible to declare arrays with ObjColorArray ObjBooleanArray ObjNumericArray ObjPointArray ObjPairArray ObjStringArray ObjTransformArray and ObjSubArray These commands all have the same syntax They take two parameters The first is the name of the array and the second is its size The size of the array is stored in the subcomponent n_ of the array For instance ObjSubArray sb Nx Ny declares the array sb of size NxxNy as part of the current object and the size is recorded in sb n This array is an array of subobject names that is an array of strings Arrays are numbered from 1 This is a convention in the duplicate0bj function and if you go beyond the boundaries or use non integer indices the duplication will forget things The METAOBJ source code has many examples of these commands code is actually a list of strings representing equations They are declared with ObjCode These strings can be constructed using other variables or options It is possible to embed low level METAPOST code in these strings and not only equations The concatenation of these strings is executed when the object is created and also when the object is reset but this is an experimental and unsupported function Usually one of the strings is StandardEquations The equations must represent linear c
104. n at least one point All the objects provided in the standard library have at least the cardinal points which are useful to make use of the object in other contexts A better construction could be the following where we add one point c and three subobjects vardef newThreeTriangles assign0bj ThreeTriangles ObjPoint c newMyTriangle ti newMyTriangle t2 rotate0bj t2 180 duplicate0bj t3 t2 rotate0bj t3 20 SubObject suba t1 SubObject subb t2 SubObject subc t3 ObjCode obj G subb a obj suba a 4cm 1cm obj subc a obj Gitsuba a 7cm 2cm StandardTies enddef The three subobjects are here called suba subb and subc The SubObject function marks an object as a subobject of the current object In the equations subobjects are shown with constructions like obj suba the constructor is the command StandardTies This command memorizes the connection between one point of the object hence the need to have at least 17 The last line of one point and a point of each subobject It indicates how a subobject must be transformed when a transformation is applied to the object Usually the same transformation is applied to both but the user could provide his or her own version of StandardTies and achieve other effects With the previous definition we can apply various transformations to the object However if we want to make a copy we must use duplicate0bj We can t jus
105. n example of the capabilities of METAOBJ The package provides a library of objects which can be composed very easily For instance the following tree is obtained with the code on the right def G new Tree enddef def B new Box enddef def P new Polygon enddef tree G P btex root etex 7 fit false B btex leaf 1 etex B btex leaf 2 etex leaf 1 leaf 2 Obj tree c origin draw_0bj tree In this example there are a total of four objects and three different kinds of objects are used a rectangular box Box class here called with new_Box a heptagon Polygon class here called with newPolygon and a tree Tree class called with new_Tree We have defined a few shortcuts G_ B_ and P_ and the tree was built recursively new Box newPolygon the fact that this one has a trailing _ and not the others will be explained later and new Tree are constructors The new Box constructor takes a picture and frames it The new Tree constructor takes a root object and a list of leaves In this case we added an option to the root node in order to have a regular heptagon The default is to have these objects fit the picture and this is the case with the boxes They appear as rectangles not squares Another example is the Von Koch flake newVonKochFlake flake 3 scale0bj flake 0 5 1 3 flake A flake B flake C origin flake c origin draw0bj flake The newVonKochFlake construc
106. necolor connection option 38 41 44 45 linestyle connection option 41 43 44 linetension connection option 42 44 linetensionA connection option 41 44 linetensionB connection option 41 44 linewidth connection option 41 43 44 loopsize connection option 41 48 lrsep class option 85 lstartdx class option 85 matpos command 54 Matrix class 89 90 92 matrixnodehsize class option 92 matrixnodevsize class option 92 mcangle command 54 mcangles command 54 mcarc command 54 mcarcbox command 54 mcbox command 54 mccircle command 54 mccoil command 54 mccurve command 54 mcdiag command 54 mcdiagg command 54 mcline command 40 54 mcloop command 54 mczigzag command 54 mpos command 54 name class option 37 40 105 name connection option 41 55 nb command 89 ncangle command 46 48 ncangles command 46 48 ncarc command 45 51 ncarcbox command 41 50 51 108 ncbar command 45 93 ncbox command 41 50 51 107 nccircle command 40 50 nccoil command 52 nccurve command 38 41 44 106 ncdiag command 47 48 104 ncdiagg command 48 ncline command 38 40 42 44 55 93 105 116 ncloop command 41 48 nczigzag command 52 new Box command 32 new Box constructor 7 8 new Ellipse command 106 new Polygon command 33 new Iree command 79 new_Tree constructo
107. necolor blue linewidth 1pt nodesepA 1cm nodesepB 1cm boxsize icm linearc 3mm 5 7 12 ncarcbox ncarcbox is similar to ncbox It encloses the nodes in a curved box that is arcangleA away from the line connecting the two nodes PSTricks seems to count that angle clockwise whereas it is counted counterclockwise in ncarc We decided for consistency to count the angle counterclockwise in both cases The arcangleB option is not used ncarcbox a b arcangleA 0 linecolor blue linewidth 1pt nodesepA 1cm nodesepB 1cm 51 ncarcbox a b arcangleA 30 linecolor blue linewidth 1pt nodesepA 1cm nodesepB 1cm boxsize 1cm 5 7 13 nczigzag and nccoil All coil and zigzag connections draw a coil or zigzag whose width diameter is coilwidth and with the distance along the axes for each period 360 degrees equal to coilheight x coilwidth nccoil draws a 3D coil projected onto the xz axes The center of the 3D coil lies on the yz plane at angle cotlaspect to the z axis The coil is drawn by joining points that lie at angle coilinc from each other along the coil The coil is drawn as a Bezier curve and not as a succession of segments as PSTricks does and it should always be smooth However decreasing coilinc may produce a better looking coil especially when coilaspect is near 0 nczigzag does not use the coilaspect and coilinc parameters nczigzag and nccoil connect t
108. nents as it is done in boxes 1 4 2 Points The main components of an object are its points An object can be seen as a set of points For instance one of the simplest object is EmptyBox and when we draw its bounding box which normally is not visible it looks like It would seem then that such an object is made of only four points Even though it seems unnecessary there are actually more points First we have exactly the same points as those provided in the boxes package for a rectangle nw n ne SW S se Having all these points is useful because one can use them for connections with other objects without having to recompute them all the time This simple box still contains more points and we will see them in a moment The points of an object can be accessed with the standard boxes notation n c n sw etc These points are pairs and can be used like any other pair 1 4 8 Equations An object need not be fixed in the plane It can be floating For instance if we had an object n representing a segment with two points a and b such that n b n a 1cm 2cm it would be floating The segment cannot be drawn yet Larger sets of points can also be floating At a first sight equations hence belong to the points The value of a point can be an equation or a dependency linking it to other points of that object or even to points that are not part of that object But when an object is cre
109. newConclusion ci btex Gamma B lor C vdash Delta etex newPTreeR proofi ci ai a2 btex lor_g etex newAssumption pi3 btex Pi_3 etex newConclusion pi3ci btex npoints3 etex newPTreeR pi3proof pi3c1 pi3 rule 0 newConclusion pi3c2 btex Gamma vdash B C Delta etex newPTreeR a3 pi3c2 pi3proof rule 0 newConclusion c2 btex NGamma A NGamma Nvdash B C Delta Delta _A etex newPTreeR proof2 c2 proof1 a3 btex Mit mix 1 etex newConclusion c2points btex npoints 12 etex newPTreeR proof2a c2points proof2 rule 0 duplicate0bj a4 al duplicate0bj a5 a3 newConclusion c3 btex Gamma vdash B lor C Delta etex newPTreeR proof3 c3 a5 btex lor_d etex newConclusion c4 btex Gamma_A Gamma B vdash Delta Delta _A etex newPTreeR proof4 c4 a4 proof3 btex Mit mix 2 etex newConclusion c5 btex Gamma_A Gamma Gamma_A Gamma vdash C Delta Delta _A Delta Delta _A etex newHRazor hri 4cm newPTreeR proof5 c5 proof2a hri proof4 btex Nit mix 3 etex Figure 8 Proof tree code for figure 7 beginning 87 duplicate0bj a6 a2 duplicate0bj proof3a proof3 newConclusion c7 btex Gamma_A Gamma C vdash Delta Delta _A etex newPTreeR proof3b c7 a6 proof3a btex Mit mix 4 etex newConclusion c8 btex Gamma_A Gamma Gamma_A Gamma
110. nitial size and the current transformation were used In certain cases it is easier to add a path with addPath 5 7 Connections A connection is a high level means to connect several objects or points of an object METAOBJ implements all the connections available in PSTricks and 39 our description borrows a lot from PSTricks There is not however an identity of behaviors and sometimes METAOBJ interprets a parameter in a way differ ent to the one used by PSTricks because it suits better the METAOBJ model The PSTricks connection commands are ncline nccurve etc and META OBJ uses exactly the same names In addition to these standard connection commands METAOBJ provides special variants such as tcline and mcline for ncline etc All the connection commands except nccircle connect two points or two objects They can therefore take as parameters either objects or points Points must be given as pair variables Objects can be given by their name or by a shortcut given to an object with the name option If an object is given by its number and not its name the Obj command can be used to produce the object name from the object number For instance if a and b are objects we can write either ncline a b or an a bn b ncline 0bj an Obj bn Moreover a connection is either immediate or deferred An immediate con nection is a connection which is not part of an object and is drawn immedi ately A deferred connection is a conn
111. ntOtt assignObj Segment ObjPoint a b ObjCode b Q a 1cm 2cm enddef The definition of the segment is pretty straightforward Everytime we want to create such a segment we write something like newSegment s meaning that s is a new object of class Segment The is the definition represents the name of the object newSegment is the constructor of the Segment class and all constructors have a name like new class though this is only a METAOBJ convention The first instruction of the class assign0bj 0tt Segment memorizes that the object belongs to the Segment class and does various other initializa tions Points are declared with ObjPoint This instruction defines Cita and b as pairs but it also does more as we will see later The last instruction declares the equation of the segment This equation is given as a string because it makes it easier to store it for later use ObjCode not only applies the equations it also memorizes them Several equations can be given as a list of strings where the name of the object is always represented by This is done for convenience and we might have represented the object 12 in the string by something else even though can be used elsewhere in the constructor When an object is created we can display all its points as well as other informations that we do not describe here with show0bj s This produces s a xpart s b 28 34645 ypart s b 56
112. numerical values There are three here but only one is defined It is nst which is the number of subtrees 58 nw Sw ctransform records the current transform of the object And finally all the equations defining the initial state of the object are stored in the code string An object can contain more information but every time there is some vari able the name of this variable must also appear in some list because this is the only way to achieve duplication We can only know what is inside an object if we constantly keep track of it This also explains why special functions should be used to define variables pair would not be enough to record the name of a pair Instead ObjPoint should be used 7 Standard Library Gallery This section shows all the objects contained in the standard METAOBJ library Many options are common to all the objects for instance framed shadow etc The shadow of an object is actually the shadow of its frame It can t be drawn when the object is not framed Shadows will have the color shadowcolor It should also be noted that transformations do not apply to shadows since shadows are not built from additional points in an object If one wishes shadows that follow the object and recognize the various transformations a special object with new points should be created 7 1 Basic objects We call basic objects objects that are not containers and appear at the leaves of a structure hi
113. o set edge to none A more elaborate example is given in figure 40 Incremental construction of trees Two commands make it possible to build a Tree incrementally and even to replace a subtree by another and have the tree adjust automatically These commands are replaceTreeElement exp and deleteTreeElement exp They are experimental commands and are not supported They only work in certain cases and have side effects The side effect of the two experimental commands is that they reset the tree This means that if the tree had been transformed rotated scaled it will be reset to a non transformed stage Moreover all its components will have the same fate and this may reset the tree in a state different from the initial state METAOBJ currently doesn t store enough information to properly reset an object in all cases and all the commands using the reset operation such as replaceTreeElement exp and deleteTreeElement exp can have unexpected results 7 5 2 PTree The PTree object is designed for proof trees It provides for either top down trees or bottom up trees Several other objects are associated to the PTree object 3 All the experimental commands have a name ending in exp 82 e an Assumption is an object which starts a proof it can be created with newAssumption it is actually a Box object with no frame e an Axiomis a proof tree with an empty assumption it appears as a formula with a line on the top or the bottom
114. onnection first and put everything inside the larger box That would work but only because there is no connection from a subbox to another box outside our big box So no matter what we are doing merely making a picture out of something freezes and anonymizes what is inside Achieving the previous drawing with the boxes package is as a matter of fact tricky One would like to use this package but it doesn t suit the task well With boxes mp we can put frames rectangular or elliptic around a picture but we can t go further without losing the structure 1 2 METAOBJ requirements The motivation that led to our work was exactly this when we have several objects such as boxes and certain objects are inside others we still want to have access to the individual structures we want to be able to reach any point anything that s inside Rather quickly this apparently simple task became a more ambitious one where we set ourselves to provide means to manipulate general structures in the plane At the same time we want to keep the declarative features of the language as well as the functional approach of the boxes package After many experiments we found it desirable to meet the following requirements e our system should provide a notion of object and objects should be in stances of classes so that several identical objects can easily be created e an object should be similar in behavior to a point in that an object can be put anywhere an
115. onstraints For instance it is not possible to specify a rotation by an unknown angle In the standardpaths section paths can be defined with ObjPath This command takes a path and can be followed by options Here is an example ObjPath obj suba b dir 60 obj subb b linecolor green Finally StandardTies ties the subobjects to the main object 115 8 1 2 Streamlined constructor In order to be able to chain the objects one should use streamlined versions of the constructors They can be created with appropriate calls to the streamline command For instance the streamlined versions of newPolygon are obtained with streamline Polygon expr v nsides v nsides The parameters of streamline are explained in section 5 1 8 1 3 Bounding path Each class C should have a Bpath C function defining the bounding path This path is used for instance when connections are drawn between two objects The function takes the name of the object as a parameter This name can be used to access points or options etc Here is the corresponding function for the Polygon class def BpathPolygon suffix n for i 1 upto n po n n po i endfor cycle enddef 8 1 4 Drawing function Each class C should also define a draw C function defining the way a C object is drawn The corresponding function for the Polygon class is def drawPolygon suffix n drawFramedOrFilled0bject n drawPictureOrO0
116. option e Novalbox Ovalbox these two frames can be achieved with a Box or RBox and the appropriate values for the corner radius and the thickness of the lines e Ndoublebox this command puts a double rectangular frame around an object it can be achieved in METAOBJ with a DBox object except for the fact that the two frames have the same thickness in METAOBJ in fancybox they have different thicknesses DBox could easily be extended to take this into account 10 3 PSTricks METAOB is not compatible with PSTricks but it includes many functionali ties that are similar to those provided by PSTricks Many option names were borrowed from PSTricks and all the node connections were implemented in METROBJ Section 7 7 shows how many examples from the PS Tricks documentation can be rendered in METAOBJ The METAOB code is lengthier than the correspond ing PS Iricks code but one should really compare a high level TEX description of a METAOBJ graphics with PSTricks code and both would be very similar 122 11 Memory requirements METAPOST bug The METAOBJ package is very large It uses a lot of strings and causes many string compactions in METAPOST When I started to write it I quickly ran into a strange error which didn t appear as a standard array overflow None of the numbers output when tracingstats is set to 1 had reached their limits and none was near its limits However the strange errors vanished when increasing the
117. ould have been positionned labdir takes options similar to those taken by the standard METAPOST label command The table 2 shows the list of all options recognized by the ObjLabel com mand Option name Type Default labpathid numeric labdir string labrotate numeric 0 labangle numeric labpos numeric 0 5 labshift pair 0 0 labcolor color black laberase boolean false labpoint string ic labcard string labpathname string Table 2 Label options means that there are no default values ObjLabel puts a label either somewhere along a path or somewhere near a point of an object Two options help specifying the relevant path e labpathid this option takes a path number as parameter it is seldom used except in cases where the path numbers are well known for instance in the example given previously or in figure 39 e labpathname when a path is created with a connection command such as ncline the path can be given a name with the name option this name can be given as parameter to labpathname examples are given in figure 10 On a given path a position can be specified with labpos This option is a numerical value between 0 and 1 0 represents the beginning of the path if the path starts at the bounding path of an object this is also the 0 position and 1 the end of the path The default value is 0 5 By default a label is set horizontally no matter what is the slo
118. p O0bjLabel 0bj mat btex Nit next etex labpathname next labdir rt O0bjLabel 0bj mat btex Nit then etex labpathname then labdir bot ObjLabel 0bj mat btex Nit lastly etex labpathname lastly labdir 1ft mccurve 0bj mat 1 1 2 2 angleA 90 angleB 180 linestyle linetension 1 5 Obj mat c origin draw 0bj mat Figure 14 Another matrix after page 123 of 2 Goo setCurveDefaultOption arrows draw t _T new_Ellipse btex root etex TCs TCs TCs TCs Obj t c origin draw 0bj t Figure 15 A tree TCs is the default filled disk after page 33 of 16 97 setCurveDefaultOption arrows draw u T_ Tn TCs T Tc TCs TCs hbsep 5mm hideleaves true TCs hbsep 5mm Obj u c origin 0 5cm draw_0bj u Figure 16 TCs is the default filled disk after page 33 of 16 x E setCurveDefault ption arrows draw t T new Circle btex X etex new Box btex tilde tilde X etex framed false new Box btex x etex framed false new Box btex y etex framed false Obj t c origin draw 0bj t Figure 17 Labels aligned on the top after page 35 of 16 X x y setCurveDefaultOption arrows draw t _T new_Circle btex X etex new_Box_ btex strut smash tilde tilde X etex framed false new Box btex strut x etex framed false new_Box_ btex strut y etex
119. patibility with PSTricks e Tcircle p is equivalent to new Circle p e Tc is an empty circle with a radius of 1mm 64 Tc_ r is an empty circle with a radius of r TC is an filled circle with a radius of 1mm TC_ r is an filled circle with a radius of r TCs is a filled circle of the default size Circle options Option Type Default circmargin numeric 2bp filled boolean false fillcolor color black framed boolean true framewidth numeric 5bp framecolor color black framestyle string nat picturecolor color black shadow boolean false shadowcolor color black 7 2 5 DBox A DBox is similar to a Box but the frame is doubled By default it fits its contents For instance newDBox a btex some text etex some text a c origin draw0bj a The cardinal points are located on the outside frame nw ne bounding box SW se We get the next figure when we ask the box not to fit its contents newDBox a btex some text etex fit false a c origin draw0bj a some text Empty double boxes can also be defined and the dimensions can be specified with the dx and dy options In order to have a 2cmx2cm internal box we can for example write newDBox a dx 1cm dy 1cm a c origin draw0bj a 65 DBox options Option Type Default Description dx numeric 3bp horizont
120. pe of the path at the label position The label can be set parallel to the path direction by specifying the labangle option with the value 0 Other values rotate the label with respect to the path tangent A label can also be set with respect to an object point with the labpoint option For instance ObjLabel g btex hello etex labpoint po1 writes hello over point po1 of object g A label can also be set in an object with respect to a cardinal point with the labcard option Like labpoint labcard takes an object point as parameter but the label is not put over the point but beyond the label point in a direction 55 determined by the line joining the center of the object and the point For instance in order to put the label 10 10 10 below south of the object at position 2 1 1 of the tree Obj t we can write O0bjLabel ntreepos 0bj t 2 1 1 btex 10 10 10 etex labcard s ntreepos is a command taking an object and a tree position as parameters and returning the node at that position There are four additional options which apply in both cases labels on a path or next to a point e labrotate with this option a label can be rotated with respect to its normal position e labshift with this option a label can be shifted in a way similar to the offsetA and offsetB connection options e labcolor this option determines the color of the label e laberase this option determines if
121. positive when the top corners must be extended to the top and negative otherwise dys is positive when the bottom corners must be extended to the top and negative otherwise dre is positive when the right corners must be extended to the right and negative otherwise and dxw is positive when the left corners must be extended to the right and negative otherwise that way one can obtain any rectangular bounding box with horizontal and vertical sides one may wish extend bjRight n wd specializes rebindrelative0bj and moves the bounding box of n on the right side so that its width is wd similarly extendObjLeft extend0bjUp and extend0bjDown adjust the bounding box on the other sides e the rebindVisible0bj also moves the corner points of an object but it takes into account all visible parts of an object this function is useful in order to ensure that no part of an object protrudes its bounding box an example of its use is given in section 7 5 1 34 5 4 Unattaching an object When an object is created with a constructor it is floating For instance newBox a btex hello etex is a box which is not located at a precise point and an attempt to draw it would produce an error Before drawing an object it must be attached We could write for instance a c origin Now the object can be drawn but it can no longer be used at other locations because it is attached In certain cases it is useful to be able to unattach
122. r 8 new_Tree_ command 81 newAssumption constructor 83 newAxiom constructor 83 newBB constructor 34 newBox constructor 30 31 38 66 67 81 122 newCircle constructor 64 newConclusion constructor 83 newDBox constructor 66 newDEllipse constructor 66 newEllipse constructor 63 66 122 newHBox constructor 67 newMatrix constructor 89 newobjstring command 18 28 56 newPentagon constructor 116 134 newPolygon constructor 62 116 newPolygon constructor 8 newP Iree constructor 73 83 84 newPTreeL constructor 83 newPTreeR constructor 83 newRBox command 62 newRBox constructor 81 122 newRecursiveBox constructor 29 newTree command 79 newTree constructor 36 73 newVonKochFlake constructor 8 newVRazor constructor 60 nodesep connection option 42 nodesepA connection option 41 43 50 99 nodesepB connection option 41 43 50 nsubobjties_ attribute 57 ntreepos command 56 numericarraylist_ attribute 57 numericlist_ attribute 57 Obj command 32 40 54 obj command 18 115 ObjBoolean command 115 ObjBooleanArray command 115 ObjCode command 12 22 31 115 ObjColor command 115 ObjColorArray command 115 ObjLabel command 54 55 91 ObjNumeric command 29 114 115 ObjNumericArray command 115 ObjPair command 114 115 ObjPairArray command 115 ObjPath command 39 115 ObjPicture command 25
123. r objects that are its constituents Each object will have the names of the objects it contains but those objects will be usable outside the main object The constituents could either be objects created beforehand or objects created by the object which will contain them Among the equations defining an object there will be equations defining how a given subobject is positionned with respect to the main object 1 4 7 Other components In addition to points pictures paths and subobjects objects can contain other common types such as numerics strings etc as well as arrays of such types They are described in section 8 1 1 1 5 Transformations METROBJ provides functions to apply linear transformations to objects The basic function is transform0bj which takes an object and a transformation transform0bj n t Usually however one uses the more familiar versions for rotations scales slants or reflections There is of course no translation because translating a floating object does not make sense If for some reason one wants to translate a fixed object we will see later that it is possible but this facility is seldom needed For instance rotate0bj n 30 rotates the object n by an angle of 30 degrees It is equivalent to transform0bj n identity rotated 30 Assuming n has the two points given above see page 9 this operation would result in the new equation n b n a 1cm 2cm rotated 30 However as any
124. r page 16 of 16 108 Player 1 Player 2 Player 3 10 10 10 3 8 4 8 3 4 4 8 3 0 5 0 4 the black disk is small but its bounding box is extended so that we get a good alignment with the empty circles 4 TCE TC Extended def TCE rebindrelative 0bj new Circle filled true circmargin bmm 1 5mm 1 5mm 1 5mm 1 5mm enddef setCurveDefault ption arrows draw set bjectDefault ption Tree vsep 2cm set bjectDefaultOption Tree hbsep 2cm setObjectDefaultOption Tree treenodevsize 5mm t T_ Tn T_ Tr_ btex Player 1 etex T_ Tr_ btex Player 2 etex Tr_ btex Player 3 etex edge none edge none T Tc 2mm _T Tc_ 2mm TCE T Tc 2mm TCE TCE hideleaves true _T Tc_ 2mm TCE T Tc 2mm TCE TCE hideleaves true hbsep 2cm new HRazor 5cm TCE edge none Obj t c origin Figure 38 An annotated tree beginning of the code after page 51 of 16 Tc builds a circle of a given radius Tr_ builds an unframed box The root of the main tree is an empty node Tn 109 ncbox 0bj t treeroot Obj t 2 1 treeroot Obj t 2 2 linestyle dashed evenly boxsize 3mm nodesepA 5mm nodesepB 5mm linearc 3mm ncarcbox bj t treeroot 0bj t 2 1 2 treeroot Obj t 2 2 2 linestyle dashed evenly arcangleA 30 nodesepA 5mm nodesepB 5mm
125. re close to those produced by PS Iricks but it would be possible to get even better results by better values of the parameters Producing exactly the same result is however not the aim of this section Our purpose is to show that most features concerning objects and connections found in PSTricks can be reproduced in METAOBJ When the METROBJ project started its purpose was not to mimic PSTricks and PS Iricks like functionalities were only added at a later stage METAOBJ has some default way of constructing objects and PS Iricks has another Getting the exact PS Tricks output is possible but it may need a lot of fiddling And this would certainly be the same if one wanted to mimic METAOBJ from PSTricks 93 setObjectDefaultOption Matrix hsep 1cm setObjectDefaultOption Matrix vsep 1cm newBox a btex U etex framed false newBox b btex X times_Z Y etex framed false newBox c btex X etex framed false newBox d btex Y etex framed false newBox e btex Z etex framed false newMatrix mat 3 3 a nb nb nb b c nb d e mat c origin mcline mat 1 1 2 2 name a ObjLabel mat btex y etex labpathname a labdir 1lft mcline mat 1 1 2 3 doubleline true arrows draw linestyle dashed evenly name b ObjLabel mat btex x etex labpathname b labdir urt mcline mat 2 2 2 3 name c ObjLabel mat btex p etex labpathname c labdir bot mcline mat 2 2 3 2 name
126. ring In this case quotes are implicitely added to the value between paren theses For instance the align option takes a string as parameter and somehow align center should be understood as align center The standard li brary reference section 7 gives the list of all options of all objects as well as their type Moreover options can be either local or global Local and global options are used with exactly the same syntax but in the first case the option can only be used within the constructor of the object and therefore doesn t need to be stored inside the object whereas in the second case the option value may be used beyond the constructor for instance when the object is drawn An option of a given name is either local or global but can t be local to one object and global to another Finally each option has a default value This default value depends on the class and can be changed by the user with setObjectDefaultOption For instance the treemode default value for a Tree object is D which means that by default a tree is drawn with the root at the top and the leaves going down This is declared in METAOBJ with setObjectDefaultOption Tree treemode D The value can be changed at any time and it will affect all future calls to the newTree constructor Of course the same effect can be obtained by passing an option such as treemode U to a constructor but in the latter case it needs to be done for all calls to the
127. s newEllipse a btex bananas etex a c origin draw0bj a duplicate0bj b a b p btex apples etex b p b p shifted 5 urcorner b p llcorner b p b c origin 0 2cm draw0bj b 9 2 Transformations that change the layout It is also possible to change the layout of an object for instance by dismantling it Let s for instance build a tree newBox r btex root etex newBox 11 btex leaf 1 etex newBox 12 btex leaf 2 etex newBox 13 btex leaf 3 etex newTree t r 11 12 13 edge nccoil coilarm 2mm coilwidth 3mm t c origin draw0bj t One way to dismantle it is to make independant copies of each subobject duplicate0bj r2 0bj t root duplicate0bj 111 ntreepos t 1 duplicate0bj 112 ntreepos t 2 duplicateDbj 113 ntreepos t 3 These objects can then be used to build a new tree newTree t2 r2 113 112 111 t2 c origin 0 4cm draw bj t2 120 Another possibility is to untie the four components untie0bj obj t root untie0bj ntreepos t 1 untie0bj ntreepos t 2 untie0bj ntreepos t 3 The main object is now a wreck But the components can be reused in a new tree newTree t3 obj t root ntreepos t 1 ntreepos t 2 ntreepos t 3 edge nccoil coilarm 2mm coilwidth 5mm vsep 2cm t3 c origin 0 7cm draw0bj t3 The three trees are shown in figure 44 The second and third trees were obtained from the first tree
128. s If they are filled they are filled with a color that can be given as an option If the object is filled the bounding path of the object is used and it is given by the function BpathEmptyBox Like draw0bj which calls drawEmptyBox Bpath0bj calls BpathEmptyBox Each object must declare its bounding path function For EmptyBox we have def BpathEmptyBox suffix n StandardBpath n enddef The standard bouding path provided by StandardBpath is merely the path n inw n isw n ise n ine cycle This path uses the inner interface so that the drawing of the object does not depend on artificial changes to its bounding box A more elaborate class is the RecursiveBox An object of this class con tains either no object or one object and in this case the subobject is also a RecursiveBox As can be seen a constructor can call another constructor We need to give a fresh name to the subobject and we call newobjstring And we also call StandardTies in order to ensure that the whole structure can be manipulated easily This function memorizes a connection between the main object and the subobjects 28 vardef newRecursiveBox expr n text options Execute0ptions options assignObj RecursiveBox StandardInterface 4 we create a subobject only when n gt 0 if mo we find a name for the subobject Sub bject sub obj newobjstring and we continue to create the hierarchy newRecursiveBox obj sub n 1 ro
129. s PS Iricks provided many ideas and the connection func tions are entirely borrowed from that package However only PS Iricks s user documentation was used not the details of its implementation 18 though sim ilarities can be observed There has also been some work by Denis Girou on high level objects in PS Tricks 1 but this work is not really relevant to what we have done Another work we didn t use was Kristoffer Rose s work on high level 2 dimensional graphics 15 The proof tree class was influenced by a ETEX package I wrote in 1993 and which was never released There are several systems which share ideas with METAOBJ though they didn t influence it One is Functional METAPOST 11 12 a system which 124 provides a Haskell layer to specify drawings more abstractly The drawback of that approach is that one needs a Haskell compiler and of course one needs to learn some of this language Nevertheless this work shares many ideas with METAOBJ in that objects are built by applying functions to already existing structures Another functional approach to picture drawing is FPIC 7 which uses the ML language A very popular system with many similar ideas is the Java2D API 8 It provides graphical objects which can be manipulated by various transformations and modified in various ways The syntax of METROBJ is admittedly verbose but it is hoped that a TEX interface will be provided and that it will alleviate a lot of the user s b
130. s of a class A class C has a name which can t begin or end with _ An object of such a class is defined by a constructor and various other functions are associated to it 8 1 1 Constructor The definition of a class C is vardef new C parameters text options ExecuteOptions options assign0bj C StandardInterface variables code standard paths StandardTies enddef This constructor takes parameters for instance a list of objects It also takes an optional list of options The options are evaluated by ExecuteOptions and some bookkeeping is done when assign0bj is called StandardInterface defines the points and equations corresponding to the standard interface variables is a list of declarations of variables These variables can be or dinary METAPOST variables and save should be used to keep them local to the constructor or object attributes The following simple object attribute declarations are recognized e ObjNumeric numlist declares each element of numlist as a numeric for the current object for instance ObjNumeric a b These values do not change when a linear transformation is applied to the object A nu merical value can be set in a constructor with setNumeric which takes an ObjNumeric name and a numerical value as parameters for instance setNumeric num n These numerical values can be used in the object equations by prefixing them with Qt ObjPoint pointlis
131. sepA 2mm angleB 0 armA 0 armB 3cm hsep 3 5cm arrows draw vbsep 5mm linewidth 1pt Obj t c origin draw_0bj t Figure 30 Illustrating the ncdiag connection in a tree all the options except edge passed to the tree are connection options which will be used by ncdiag after page 42 of 16 104 setObjectDefaultOption Tree treemode U setObjectDefaultOption Tree hbsep 5mm setObjectDefaultOption Tree hideleaves true setCurveDefaultOption arrows draw t _T Tc TCs _T Tc TCs TCs TCs changes to the edges setTreeEdge Obj t 1 linestyle dashed evenly setTreeEdge treepos Obj t 2 1 linestyle dashed evenly Obj t c origin draw_0bj t Figure 31 Changing the style of connections with setTreeEdge after page 42 of 16 setCurveDefault ption arrows draw setCurveDefault ption nodesepA 2mm setCurveDefaultOption nodesepB 2mm t _T Toval_ btex nature etex _T mew_Circle_ circmargin 1mm name top TCs TCs _T new_Circle_ circmargin 1imm name bot TCs TCs Obj t c origin ncline 0bj t top bot nodesepA 0 nodesepB 0 linestyle dashed evenly draw_0bj t Figure 32 Connecting two named nodes in a tree after page 43 of 16 the name option is used to give names to streamlined objects and these names are then used in the ncline connection command
132. similar to the parameters of EmptyBox The last two parameters are maximum horizontal and vertical deviations The deviations are computed randomly using a uniform random generator show_empty_boxes true newRandomBox a 2cm 1cm 2mm 1mm framed true a c origin draw0bj a The cardinal points are now no longer identical to a rectangular bounding box ne bounding box se The thickness of the frame can be modified as shown in newRandomBox a 2cm 1cm 2mm 1mm framed true linewidth imm a c origin draw0bj a 60 A random box can also be filled with a given color newRandomBox a 1cm 5mm 2mm 1mm framed true filled true fillcolor red framewidth imm framecolor green a c origin draw0bj a RandomBox options Option Type Default filled boolean false fillcolor color black framed boolean true framewidth numeric 5bp framecolor color black framestyle string n shadow boolean false shadowcolor color black 7 2 Basic containers All the basic containers take a picture or an object and provide a frame for it A picture can be one given in the TEX notation btex etex or a picture obtained in other ways for instance with the image command of METRPOST 7 2 1 Box Box is the simplest of the containers It is similar to EmptyBox but it is a container and by default the frame is visible The size of the box is adapted to its contents ne
133. ssible to apply various transformations to an object METAOBJ provides the standard METR POST linear transformations but on objects rotate0bj scale0bj etc There are however many other possible transformations We will give a few examples here by distinguishing two kinds of transformations 9 1 Simple transformations which do not change the lay out The first kind of transformation does not change the positions of the points These transformations only change various attributes For instance we might want to change the color of a frame when an object is duplicated or maybe change some of the labels without changing the layout 9 1 1 Example 1 changing the frame color Several attributes of an object are stored in fields that can easily be changed This is for instance the case for the color of the frame It is stored in the option framecolor field and it can be changed as shown here 119 newEllipse a btex a framed text etex framecolor red a c origin draw0bj a duplicate0bj b a b option_framecolor_ blue b c origin 0 2cm draw0bj b 9 1 2 Example 2 changing the content of a label The label of a object such as an Ellipse is stored in its p field We can give a new value to this field and the next time the object is drawn the new value will be used We have to be careful to center the label around the origin The frame of the object is unchanged and therefore it may be smaller or larger than lts content
134. t declares each element of pointlist as a point for the current object for instance ObjPoint a b These points move when the object is transformed They can be used in the object equations by prefixing them with ObjPair pairlist declares each element of pairlist as a pair for the current object for instance ObjPair a b A pair value can be set with setPair which takes an ObjPair name and a pair value as parameters setPair p v These pairs do not move when the object is transformed They are like constant points They can be used in the object equations by prefixing them with 114 e ObjPicture piclist declares each element of piclist as a picture for the current object for instance ObjPicture a b A picture can be set with setPicture which takes an ObjPicture name and a picture as parame ters setPicture pic p To each picture p ObjPicture associates a point p off which is the picture offset The pictures can be used in the object equations by prefixing them with e ObjColor ObjBoolean 0bjString and ObjTransform are commands sim ilar to ObjNumeric and ObjPair and they also have associated setColor setBoolean setString and setTransform commands e Sub bject name object declares name as a string containing the name of object object for instance Sub0bject root theroot These objects can be referred to in the equations by calling obj on their name prefixed with There is also a
135. t is possible to specify different alignments for each column and each line with the halign and valign options In this example halign has a string of two letters as argument and specifies that the left column is align to the right e east and the right column is aligned to the left w west valign has a string of three Gu letters as parameters The first and third letters are s south and mean that 9 the first top and last lines are aligned to the bottom the second letter is n north and means that the second line is aligned to the top newBox melba btex melba etex newBox melda btex D NdisplaystyleMint O Minfty melba i over 1 x 2 dx etex newBox melbb btex Bb etex D 1 d Bb newBox melcb btex C etex 1 72 e newBox meldb btex D etex newMatrix matc 3 2 CIID melba nb melda melbb melcb meldb halign ew valign sns matc c origin 0 10cm draw0bj matc The whole matrix can be duplicated and we can see that the empty slot is duplicated too The matrix object can be scaled as well 89 melba SE m d o bspw Bb T D duplicate0bj matd matc scale0bj matd 2 matd c origin 0 15cm draw0bj matd Multispan columns are not implemented However it is possible to obtain multispan like results by changing the bounding box of a component with the BB wrapper 7 6 1 Experimental construct
136. t and right corners of two boxes but that is only because the boxes are aligned on the bottom and because the component objects are rectangular boxes nw ne Box A Box B Box C bounding box SW se In order to change the alignment the align option can be given with either bot top or center Here is an alignment at the top with the same objects newBox a btex Box A etex newBox b btex Box B etex scaled magstep3 Box A B B B C newBox c btex Box C etex scaled magstep2 OX OX newHBox h a b c align top h c origin draw0bj h The next example shows objects that are centered vertically newBox a btex Box A etex newBox b btex Box B etex scaled magstep3 newBox c btex Box C etex scaled magstep2 Box A Box B Box C newHBox h a b c align center h c origin draw0bj h There is a default horizontal separation between objects but it can be changed with the hsep option newBox a btex Box A etex newBox b btex Box B etex scaled magstep3 newBox c btex Box C etex scaled magstep2 Box A Box B Box C newHBox h a b c align center hsep 3mm h c origin draw0bj h In the following example the components are now not all boxes but poly gons a box and a razor The razor s function is to create a wide horizontal gap It is similar to a kern in TEX newPolygon a btex Box A etex 5
137. t call the constructor twice like in newThreeTriangles ttl newThreeTriangles tt2 The reason is that each call tries to define the three objects t1 t2 and t3 But all the constructors only work if the object to define is currently undefined This can be enforced with clear0bj and one should therefore write newThreeTriangles ttl clearObj t newThreeTriangles tt2 The previous procedure is of course not acceptable because it means one has to know what is inside the object A solution is to create fresh names within the newThreeTriangles function We can do that with the function newobjstring This function returns a string representing a new object name It constructs the string using a prefix that should not be used by the user This prefix can be changed by the user if needed but it is his or her responsibility to ensure that it does not conflict with other variables In order to access the object corresponding to the string one uses the obj function vardef newThreeTriangles assign0bj 0 ThreeTriangles ObjPoint c save sa sb sc string sa sb sc sa newobjstring_ sb newobjstring_ sc newobjstring_ newMyTriangle obj sa newMyTriangle obj sb rotate0bj obj sb 180 duplicate0bj obj sc obj sb rotate0bj obj sc 20 Sub0bject suba obj sa SubObject subb obj sb SubObject subc obj sc ObjCode obj G subb a obj suba a 4cm 1cm obj subc a obj suba a 7c
138. t the intro duction of an additional layer 33 5 3 1 BB a new bounding box layer A new layer can be added to an object with the newBB constructor This is a class taking an object and enclosing it in a standard interface The standard interface tightly encloses the four corners of the object newBB only looks at the four corners and there is no guarantee that the enclosed object lies entirely inside the new object interface Rebinding the object next section may be more appropriate in certain cases newBB is similar to rebind0bj but the latter function doesn t add a layer BB options Option Type Default filled boolean false fillcolor color black framed boolean false framewidth numeric 5bp framecolor color black framestyle string nM shadow boolean false shadowcolor color black 5 3 2 Rebinding an object METAOBJ provides two ways to rebind an object without adding a layer e the rebind0bj and its variants move the corner points of an object in such a way that they are arranged according to a standard initial interface the points are only moved with respect to their former positions and not with respect to other components of the object rebind0bj n is the basic call it rebinds the object n rebindrelative0bj dyn dys dxe dxw this function is called by the rebind0bj function with the four parameters equal to 0 and rebinds and adds shifts in the four directions dyn is
139. tate0bj obj sub OptionValue rotangle the equations are slightly adapted from newBB ObjCode StandardEquations save lftmost rtmost topmost botmost string lftmost rtmost topmost botmost lftmost find lft most obj Qisub rtmost find_rt_most obj sub topmost find_top_most obj sub botmost find_bot_most obj sub xpart inw xpart obj sub obj 1ftmost xpart Cttine xpart obj sub obj rtmost ypart inw ypart obj sub obj topmost ypart isw ypart obj sub obj botmost else ObjCode StandardEquations ise Q isw amp decimal OptionValue dx amp 0 Ottine Cttise 0 amp decimal OptionValue dy amp fi StandardTies enddef Figure 1 RecursiveBox constructor The equations are not the same whether there is a subobject or not If there is no subobject the object is actually quite similar to an empty box When there is a subobject this one is created with newRecursiveBox It is then rotated with rotate0bj The equations handle the positionning of the subobject with respect to the main object First the bounds of the subobject are computed Since the subobject has been rotated we can t be sure that the nw point is really the left and top most point The extreme values are computed with the find lft most find rt most find_top_most and find bot most functions They are used to specify the constraints
140. tex A etex newAssumption b btex A rightarrow B etex newConclusion c btex B etex newAssumption d btex D etex newAssumption e btex E etex newPTreeR proofi c a b btex MP etex newPTreeR proof2 proofi d e treemode U proof2 c origin draw0bj proof2 intermediate formula is wider than newAssumption a btex A etex newAssumption b btex A rightarrow B etex newConclusion c btex BBBBBBBBBBBBBB etex newAssumption d btex D etex newAssumption e btex E etex newPTreeR proof1 c a b btex MP etex newPTreeR proof2 proofi d e treemode U proof2 c origin draw0bj proof 2 A more elaborate proof tree is given in figure 7 The source file defines a TEX command to obtain a column of n dots The top down proof is the default and the bottom up proof is obtained by specifying setObjectDefaultOption PTree treemode U Though the result is quite acceptable one must admit that writing such a proof in METAOBJ directly is not that practical In this case a TEX interface for METAOBJ would prove very useful and would allow a comparison with other packages for proof trees PTree options Table 6 shows the options supported by the PTree class 84 Option Type Default Description treemode string p this option specifies whether the proof tree is top down default or bottom up The two corresponding option values are D and U da numeric
141. the label erases what lies beneath it or not 6 The object structure Figures 3 4 5 and 6 are the result of show0bj on a PTree object called ptre slightly rearranged and simplified to make it more readable An object has a name and all its direct components form a tree of variables all starting with the object name There is unfortunately no easy way to traverse such a tree of variables in METRPOST and there are therefore special variables which keep track of what is in an object We call these variables attributes of an object The complete list of attributes is given in table 3 ptre 100 ptre numericlist dx dy nst ptre nst 2 ptre ctransform 0 0 1 0 0 1 Figure 3 Object structure general data As shown in the first figure an object has a number Here it is 100 It has points the list of which is given in the string pointlist which is a standard attribute of the object It has a list of subobject references the list of which is given as a string sublist Each subobject is actually only given as a string The subobject is not really part of the object and as we said earlier an object can be part of several other objects The ptre object belongs to the PTree class and it contains four subobjects Each subobject has a corresponding string conc conclusion subt subtrees lr left rule rr right rule The value of the string was generated automati cally by newobjstring The structure of ptre was obtain
142. tor takes an integer which represents the depth of the flake This constructor starts by building a triangle and then calls another constructor to make the sides There are therefore two different kinds of objects After the object was built we scale it to half its size This can be done with any object 1 4 What is an object We provide here a first overview of what can be found inside an object 1 4 1 A name First an object is something that has a name and belongs to a certain category When an object is created we need at least to give it a name and we ought to say of which kind the object is The names that can be used for an object are exactly those that are acceptable in the boxes package That is we can use almost any suffix that is almost any name which would be acceptable for a variable For instance an object can be named n or b2 or my object3 or even 4 amp 0 4 etc It is better to stick to simple names though The INames that are forbidden are names of macros including z which is a vardef as well as names of components of boxes for instance aic cannot be used if al is an object with a standard interface because it represents point c of object ai in that case aid or even aici works Which names can or cannot be accepted actually depends on the features of the objects precise rules for suffixes are given in the METAFONTbook 9 The name of an object is used to access its compo
143. tre ptre ptre ptre ptre ine 98 02467 308 30998 ptre inw 98 02469 308 30998 ptre ptre ptre ptre ptre ine inw isw ise in is ie iw ic ledge redge lstart lend c 0 287 17845 s 0 261 61906 e 95 02467 287 17845 sw 95 02467 261 61906 ic 0 283 46451 in 0 308 30998 is 0 258 61905 ie 98 02467 283 46451 iw 98 02469 283 46451 ise 98 02467 258 61905 isw 98 02469 258 61905 ledge 72 57094 258 61905 redge 92 90178 258 61905 lstart 51 91089 292 35118 lend 65 57219 292 35118 Figure 4 Object structure cont d points 57 ptre sublist subt lr rr conc ptre conc _______ zu ptre subt _______ zh ptre lr _______ zs ptre rr _______ zt ptre nsubobjties_ 4 ptre subobjties_1 vardef tie_function_ expr q_1 obj subt ne transform0bj obj subt Qitne obj subt ne p_1 q_1 transformed enddef ptre subobjties_2 vardef tie_function_ expr q_2 obj 1r ne transform0bj obj 1r ne obj 1r ne p_1 q_2 transformed enddef ptre subobjties_3 vardef tie_function_ expr q_3 obj rr ne transform0bj obj rr ne obj rr ne p_1 q_3 transformed enddef ptre subobjties_4 vardef tie_function_ expr q_4 obj conc ne transform0bj obj conc ne obj conc ne p_1 q_4 transformed enddef Figure 5 Object structure cont d subobjects ptre cod
144. tta origin 0 1 or reflect0bj tta origin 3cm 2cm 0 1 3cm 2cm amounts to the same result Now that we have an object with a good interface we can try to add a picture inside This can be done by declaring an ObjPicture variable and defining it We will center the picture in the middle of the second triangle This is done as follows vardef newThreeTriangles0t suffix sa sb sc expr p assignObj ThreeTriangles StandardInterface ObjPoint pic off ObjPicture pic setPicture pic p SubObject suba sa SubObject subb sb SubObject subc sc ObjCode StandardEquations obj Gitsubb a obj Gitsuba a 4cm 1cm obj subc a obj suba a 7cm 2cm Qitsw xpart obj suba a ypart obj subb c ne obj subc a pic off 1 3 obj CHsubb atobj G subb b obj subb c StandardTies enddef The picture is the p parameter and it is stored in the pic variable of the object Each picture variable must also have an associated point called picture off hence the line ObjPoint pic off As we said earlier a picture cannot be floating and instead we move the point where the picture will be centered The boxes package does the same We add therefore the equation pic off 1 3 obj G subb atobj subb b obj subb c 25 which defines the center of the picture as the center of the second triangle In order to draw the picture the drawThreeTriangles
145. ubc draw0bj obj n subc IN else draw n C n D randomcolor fi if known n subd draw0bj obj n subd else draw n D n E randomcolor fi m MN drawMemorizedPaths n enddef v newVonKochFlake a 3 p scale0bj a 5 a c origin draw0bj a This class has currently no options 7 5 Trees The standard library provides a general tree constructor newTree and a more specialized one for proof trees newPTree 7 5 1 Tree Trees are generic and the constructor takes a root and a list of subtrees The root and the subtrees can be any objects having a standard interface The tree is built recursively so that the root and the subtrees given as arguments are no longer changed They are only assembled by the Tree constructor This of course is not always adequate and can leave a lot of unnecessary blank space but it is the default behavior Since the whole Tree object is memorized and can be traversed it is actually possible to reformat such an object completely and implement any tree layout algorithm The reader who is interested in pursuing such an endeavor is encouraged to study the structure of an object section 6 functions such as duplicate0bj that do a complete traversal of an object as well as special transformation functions section 9 Here is a first tree By default a tree is constructed with the root at the top 73 newBox a btex apples etex newBox b btex oranges etex newBox c btex bananas etex newBo
146. ume 78 of CSLI Lecture Notes CSLI 1999 Joachim Korittky Functional METRPOST Eine Beschreibungsspra che f r Grafiken 1998 Diplomarbeit an der Rheinischen Friedrich WilhelmsUniversit t Bonn http tex loria fr Marco Kuhlmann Functional METRPOST for IATEX 2001 http tex lords ifr Thorsten Ohl EMP Encapsulated METAPOST for ATEX 1997 Technische Hochschule Darmstadt http tex loria fr Denis Roegel Creating 3D animations with METAPOST TUG boat 18 4 274 283 1997 ftp ftp loria fr pub ctan graphics metapost macros 3d tugboat tb57roeg pdf Kristoffer H gsbro Rose Very High Level 2 dimensional Graphics with TEX and Xypic TUGboat 18 3 151 158 1997 http www tug org TUGboat Articles tb18 3 tb56rose pdf Timothy van Zandt PSTree user s guide 1993 ftp ftp loria fr pub ctan obsolete pstricks beta 126 17 Timothy van Zandt PSTricks PostScript macros for Generic TEX User s Guide 1993 http tex loria fr 18 Timothy van Zandt and Denis Girou Inside PSTricks TUGboat 15 3 239 248 1994 http www tug org TUGboat Articles tb15 3 tb44tvz p 127 Index T command 79 addPath command 31 38 addPathVariables command 37 38 addStandardPath command 38 39 addUserPath command 38 91 align class option 36 68 70 angle class option 63 angle connection option 42 angleA connection option 41 44 4T 50 107 angleB connection option 41 44 47
147. umeric 0 We might add more options for the shadows in the future Box shortcuts METAOBJ defines a few shortcuts for PSTricks compatibility e Tr p is equivalent to new Box p framed false e Tf is equivalent to new Box filled true 7 2 2 Polygon The newPolygon constructor builds polygons Polygons are containers The number of sides can be specified and we can decide if the polygon fits the contents By default it does Here is a pentagon newPolygon a btex some text etex 5 a c origin draw0bj a 62 Some clearance can be added by changing the polymargin option newPolygon a btex some text etex 5 polymargin 3mm a c origin draw0bj a The cardinal points are those of the rectangle bounding the ellipse on which the vertices are located The cardinal points of the previous example are nw ne bounding box SW se A heptagon which does not fit its contents is newPolygon a btex some text etex 7 fit false polymargin 3mm a c origin draw0bj a A Polygon can also be rotated See for instance figure 35 Polygon options Option Type Default polymargin numeric 2mm angle numeric 0 filled boolean false fillcolor color black framed boolean true fit boolean true framewidth numeric 5bp framecolor color black picturecolor color black framestyle string M shadow boolean false shadowcolor color black 7 2 3 Ell
148. urden Acknowledgments I thank Denis Girou for some explanations on PSTricks ncdiag ncdiagg and ncloop commands Bogustaw Jackowski for helping me to find again the quote on the first page and Damien Wyart for some comments 125 References 1 Denis Girou Building high level objects in PSTricks 1995 Slides 12 13 14 15 16 presented at TUG 95 St Petersburg Florida http www tug org applications PSTricks TUG95 PSTricks_4 ps gz Michel Goossens Sebastian Rahtz and Frank Mittelbach The TpX Graphics Companion Illustrating documents with TEX and PostScript Reading MA Addison Wesley 1997 Hans Hagen ConT Xt the manual 2000 http www pragma ade com Hans Hagen MetaFun 2000 http www pragma ade com John D Hobby A User s manual for MetaPost Technical report AT amp T Bell Laboratories Murray Hill New Jersey 1992 Computing Science Tech nical Report 162 Alan Hoenig TEX Unbound TEX amp TEX Strategies for Fonts Graphics amp More New York Oxford University Press 1998 Samuel N Kamin and David Hyatt A Special Purpose Language for Picture Drawing In USENIX Conf on Domain specific Languages Santa Barbara pages 297 310 October 1997 http www sal cs uiuc edu kamin fpic Jonathan Knudsen Java 2D Graphics O Reilly amp Associates 1999 Donald E Knuth The METAFONTbook Reading MA Addison Wesley 1986 Donald E Knuth Digital Typography vol
149. value of pool size The error was observed on linux with a Web2C 7 3 1 installation and METAPOST 0 641 and on Solaris with the TpEXlive 5 setup It is likely that the bug is still around in the TpXlive 6 setup So far I was unable to get a small file demonstrating the bug which might have something to do with the string compactions Increasing pool size should be attempted only when the limit is explicitely reached or it is not reached but you are sure your source is correct and still have a strange error Other values may also need to be increased but the bug I suspect seems related with poo1 size If you increase pool size you are on your own I have no idea how much it should be increased to avoid the bug If you can get a small file demonstrating the bug let me know setObjectDefaultOption Tree treemode D setCurveDefault ption arrows drawarrow t T new Polygon btex root etex 4 name top new Box btex x etex framed false name 1x new Box btex y etex framed false name ly new Box btex z etex framed false name 1z edge none vsep 1 5cm ncbar 0bj t top 1x angleA 180 armA 1cm ncline 0bj t top ly ncbar 0bj t top 1z angleA 0 armA 1cm Obj t c origin draw_0bj t begin metaobj moset0 Tree treemode D mosetC arrows drawarrow NsetObj t HNTree NPolygon root H 4 name top Box x fra
150. w calls drawFramedOrFilledObject if the corners are not rounded If they are rounded the frame is drawn with drawMemorizedPaths A shadow is drawn when the shadow and framed options are true the shadow being the shadow of the frame drawFramed0OrFilledObject_ does also check if a shadow needs to be drawn def drawBox suffix n if OptionValue n rbox_radius 0 drawFramedOrFilled0bject n else if OptionValue n framed if OptionValue n shadow fill BpathObj n shifted 1mm 1mm withcolor OptionValue n shadowcolor fi unfill BpathObj n fi if OptionValue n filled fill BpathObj n withcolor OptionValue n fillcolor fi fui drawPictureOr0bject n drawMemorizedPaths n enddef We won t study in detail the other objects but the interested reader should study the code which is extensively commented 31 5 Advanced operations 5 1 Streamlined constructors There are two ways to build an object with METROBJ The object can be built by calls to the various constructors and all the objects involved can get a name This forces the user to devise names Of course arrays of names can be used in order to overcome this burden But sometimes we may wish a more structural construction of an object where an object is built and immediately plugged into another one which is built and so on This requires a change in the constructors For instance in order to create a box b one can write newBo
151. wBox a btex some text etex some text a c origin draw0bj a nw ne bounding box SW se By default the frame fits the contents With the fit false option it no longer does The frame is then a square newBox a btex some text etex fit false a c origin draw0bj a some text In addition it is possible to specify horizontal and vertical margins to the contents with the dx and dy options If the contents is empty and we want a 4mmx4mm square and if that square must be filled we can write 61 newBox a filled true 8 dx 2mm dy 2mm a c origin draw0bj a Round corners can be obtained by specifying a radius If the radius is too large the clearance dx and dy may have to be increased newBox a btex This is an ovalbox etex rbox_radius 2mm a c origin draw0bj a This is an ovalbox It is also possible to call the newRBox constructor which is a Box with a default value of 1mm for rboz radius newBox a btex This is a shadowbox etex R 9 h d t e This is a shadowbox s adaw puer a c origin draw0bj a Box options Option Type Default dx numeric 3bp dy numeric 3bp filled boolean false fillcolor color black framed boolean true shadow boolean false shadowcolor color black fit boolean true framewidth numeric 5bp framecolor color black framestyle string n picturecolor color black rbox radius n
152. wMyTriangle t1 newMyTriangle t2 rotate0bj t2 180 t2 a t1 a 4cm 1cm ti a origin draw0bj t1 t2 untie0bj t2 rotate0bj t2 20 t2 a t1 a 7cm 2cm draw bj t2 and the result is 15 The second triangle appears twice because we have drawn it at its first position and at its second position This feature can be convenient when it is necessary to use a same component in several places in a figure It is also possible to define several objects or even to clone an existing object We could have written duplicate0bj t3 t2 rotate0bj t3 20 t3 a t1 a 7cm 2cm draw0bj t3 and the result would still had been the same because the duplication implicitely unties an object It is important to realize that if one wants to have two identical drawings at two different places it is either necessary to draw an object at a first position and then move it or have two different objects But a given object can t be located at more than one place at a given time The previous example showed how to create several objects and to tie them together But something like t3 a t1 a 7cm 2cm can be accepted only when at least one of the two objects is floating Otherwise there will be an error most likely about an inconsistent equation because you are trying to move something that can t be moved by a mere equation In this case untying or duplicating are options to consider Once a number of objects are at precise locations th
153. wo points or two objects starting and ending with straight line segments of length coilarmA and coilarmB All the usual connection modifiers can be used on coils or zigzags However in certain cases strange effects can be produced for instance if coilwidth is too small with respect to linearc It should be emphasized that the path size parameter of METAPOST might overflow if coilinc is small and the coils have many turns In that case you should increase coilinc or enlarge the dimensions of the coil nczigzag a b 52 nczigzag a b angleA 90 angleB 120 linetension 0 8 coilwidth 2mm linearc imm nccoil a b The next example shows various combinations of options including the use of symbolic shortcuts for the kind of arrow nccoil a b doubleline true coilwidth 2mm angleA 0 arrows linewidth 1pt 5 7 14 Tree and matrix variants When tree nodes or matrix nodes have to be connected it is cumbersome to access the nodes even though they are accessible Therefore we provide variants of all the connection commands for trees and matrices The variants have a t and a m instead of the leading n in the names of the connection commands Instead of an object they take as parameters the position of the object within the tree or within the matrix For instance a curve connection between the roots of the second an third subtrees of tree gt can be drawn with tccurve gt
154. x b btex a test box etex This is a function call which returns no value It only modifies the box to which b refers Since this call does not return a value it is not well suited for a plugin For instance we can t write newBox b2 newBox bi btex an inner box etex In order to overcome this problem we can use a streamlined constructor and use streamlined constructions T he streamlined version of the previous failed attempt is b new Box new Box btex an inner box etex Here new Box returns an integer corresponding to a box which was created new Box can also take a object as parameter when the number of the object is passed The outer call to new Box returns a value which must be stored Then a special version of draw0bj called draw 0bj must be used to draw the construction draw 0bj b This can of course be done only after b has been positionned This however can t be done by simply writing b c because b is not the name of an object The real object name can be obtained with a call to the Obj function One should therefore write 0bj b cs in order to define point c of the object represented by the integer b All the standard objects have a streamlined version This version was defined with a call to streamline Here is the call for the EmptyBox class streamline EmptyBox expr dx dy dx dy What this says is that the streamlined version will take two parameters which are expressions
155. x c btex bananas etex newBox f btex fruits etex newTree fruits f a b c Dalign bot hideleaves true newBox d btex potatoes etex newBox e btex peas etex newBox v btex vegetables etex newTree vegetables v d e Ralign center hideleaves true treemode R newBox fo btex food etex newTree food fo fruits vegetables hbsep 1cm scale0bj food 5 food c origin draw0bj food We can of course mix three different directions bananas food oranges vegetables newBox a btex apples etex newBox b btex oranges etex newBox c btex bananas etex newBox f btex fruits etex newTree fruits f a b c Lalign left hideleaves true treemode L vsep 3mm newBox d btex potatoes etex newBox e btex peas etex newBox v btex vegetables etex newTree vegetables v d e Ralign center hideleaves true treemode R newBox fo btex food etex newTree food fo fruits vegetables hbsep 1cm Scale0bj food 5 food c origin draw0bj food The same construction can be made with different objects The fact that we use standard interfaces allows us to plug in any other object in place of a standard rectangular box We don t have to worry about what might happen vegetables newPolygon a btex apples etex 5 newPolygon b btex oranges etex 6 newPolygon c btex bananas etex 7 newPolygon f btex fruits etex 8 newTree fruits f a b c L
156. x f btex fruits etex newTree fruits f a b c newBox d btex potatoes etex newBox e btex peas etex newBox v btex vegetables etex newTree vegetables v d e food vegetables nw oranges bananas newBox fo btex food etex newTree food fo fruits vegetables scale0bj food 5 food c origin draw0bj food ne vegetables bounding box SW oranges bananas potatoes se In the previous example the leaves are aligned on the top and the baselines of the labels are not aligned because the labels have different heights In the next example the left subtree is aligned on the bottom with the Dalign op tion but this was not sufficient to align all the baselines for bananas has no descenders That is why we added a strut in the TEX part of the labels newBox a btex apples strut etex newBox b btex oranges strut etex newBox c btex bananas strut etex newBox f btex fruits etex newTree fruits f a b c Dalign bot newBox d btex potatoes etex newBox e btex peas etex newBox v btex vegetables etex newTree vegetables v d e Dalign center food vegetables apples bananas potatoes peas oranges newBox fo btex food etex newTree food fo fruits vegetables hbsep 1cm scale0bj food 5 food c origin draw0bj food 74 ban

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