The MaLT manual
Contents
1. rt 18 cupk f dp 180 2 arccos 0 5 sin 72 rt 18 rr 180 to dodecahedron a theta cup 3 rt theta gt end Teup 2a et 18 up 2 arccos 0 5 sin 7 a E kiodecahedron 0 fd a 14 Lelie Ge a AA ee we j ee i ee FTES OSES OT RAT TO GT ENTE TON ETE at Ml 1 le 1 8037d9 PENTAGONE at ML lle 1da037 9 init ML 1 le 1d at g talent machinelablogorunti at g talent machinelab logorunti at threelnwact base Threeimpad at g talent machinelab MLEGtor Machinelab 3D Figure 16 Running lines 17 21 theta 0 a 3 Try to run the procedure attributing an arithmetical value to the a and theta variable and observe the graphical result in the Turtle Scene Notice that the sixth pentagon on the upper base of the figure is not logo constructed but shaped by sides of the other ones 3D MODELER MATHS Logo Editor Property Editor File Edit Search Logo Help rr 2 arccos 0 5 sin 7 2 pentagone a llr 2 arccos 0 5 sin 72 fd a xt 72 rt 18 up Z arccos 0 5 sin 7Z 1t 18 fd sa ile 18 dp 180 2 arccos 0 5 sain 72 1t 18 rt 108 fd a lt 72 fd a rt 18 dp 180 2 arccos 0 5 sin 72 rt 18 rr 180 cup a end is dodecahedron 3 0 Figure 17 Running the dodecahedron procedure theta 0 a 3 4 Perspectives 4 1 In terms of developments The idea was to employ new technologies emerging for 3d animations2. to develop a mathematical microworlds environment integrating the two most prominent technologies for engagement with geometry turtle geometry based programming and dynamic manipulation Both of these perspectives are part of the theoretical te EDUCATIONAL TECHNOLOGY LAB ETL NKUA 16 MaLT Manual perspective developed at ETL to engage in design research involving interventions in classrooms aiming to immerse students in constructionist mathematics including the use of formalism to generate mathematical meanings The main problems met in the process of developing the software were due to the need to connect 3d engines to java based programming and develop a logo language with java to construct and manipulate models The best available 3d engine originally was 3impact which we had identified before the beginning of the project and ported a Delphi programming language to build custom 3d models In ReMath we thus needed to change the language to java so as to have multiple windows and dynamic manipulation The manipulation however was very slow due to fragmentation in the design of the different compartments of the software We thus identified a recently available new 3d engine and ported the java logo components on to that with highly improved results We also created a better GUI to make the software more stable The prospect is to use this in the future as a base for a larger variety of programmable mathematical and scientific models an
3. 17 rt 18 up 2 arccos 0 5 sin 72 It 18 line 18 fd a line 19 lt 18 dp 180 2 arccos 0 5 sin 72 It 18 line 20 rt 108 fd a It 72 fd a line 21 rt 18 dp 180 2 arccos 0 5 sin 72 rt 18 rr 180 line 22 cup a line 23 end line 24 line 25 dodecahedron 3 0 The point at which the construction of the dodecahedron will begin is defined in line 10 The turtle will turn right clockwise by a number of degrees that will be defined by the theta variable At that point the construction of a cup will begin However regardless the value of the theta variable the turtle will finish the construction of the cup at the bottom of the figure To move upwards and find the right node so as to start the construction of the upper cup the turtle will need to move according to lines 17 21 To avoid creating unnecessary lines it will have to move on the bottom cup s existing lines d EDUCATIONAL TECHNOLOGY LAB ETL NKUA 15 MaLT Manual Logo Edtor Property Editor Lego LGtor Property Editor File Edit Search Logo Help File Edt Search Logo Help rou dwdexde H feden yavia to pentagone 4 to dodecahedron a theta wepeat 5 fd a rt 72 rt 0 end cup 3 rt 18 pentagone 3 up 2 arccos 0 5 sin 72 Lt 18 to cup a fa 3 repeat 5 it 18 rr 2 arccos 0 5 sin 72 dp 180 2 arccos 0 pentagone 3 Le 18 Jr 2 arceos 0 5 31in 72 rt 108 fd a rt 72 d 3 Lt 72 end fa 3 A
4. The MaLT manual File Edit Search Logo Help to kone a x iy in epeat n rt x fd y gen a sy end kone 55 10 0 4 36 d y 360 x 6 28 cos a k y 360 x 6 28 cos a Ba Gl dh 28 4 oslo i EX PropertyEditorPanel cam2J8ActionPerformed ts PropertyEditorPanel cam3BActionPerformed PropertyEditorPanel cam238ActionPerformed PropertyEditorPanel cam1BActionPerformed PropertyEditorPanel cam3BActionPerformed Educational Technology Lab National and Kapodistrian University of Athens http etl uoa gr Authors Kynigos Chr Moustaki Fot Psycharis Giorgos MaLT Manual 1 Introduction MaLT is a programmable constructionist environment that allows the creation exploration and dynamic manipulation of 3d geometrical objects It is designed integrate the symbolic notation in the form of Logo programs with the dynamic manipulation of 3d geometrical objects that are graphically represented a 3d Turtle Scene The geometrical objects visualised in the environment s Turtle Scene are either constructed by the user when running logo procedures and commands or inserted by the user after selecting them from a library that offers numerous ready made stereometric objects such as cylinders and cones Employing multiple linked representations MaLT allows any actions performed on one of its representations to generate immediate changes to another one or the rest of its representations provi
5. and the object inserting procedure begins Deselecting the icon the New Object procedure is aborted Insert Object It consummates the object insertion procedure After the object is inserted the insert Object procedure deactivates Delete Object It removes the selected object off the Scene A pop up window asks the user whether the wants to proceed or not Unfold Object It causes the generation of a 2d object that has the same Ee Z EDUCATIONAL TECHNOLOGY LAB ETL NKUA 4 MaLT Manual area as the selected object The button is active only if there is a selected object and if the selected object can be unfolded New Activity It deletes any ready made object in the Scene and begins a new activity for the user Save It saves the activity in an already existing file or a new file if the activity is not saved before Save as It saves the activity in a new file Camera button 1 Floor view The floor view camera is activated or deactivated Camera button 2 Side view The side view camera is activated or deactivated Camera button 3 Main view The main view camera is activated or deactivated Reset main view Resets camera 3 Light By clicking on this button a manipulable light source appears in the Scene Deselecting it the light source is removed 3 3 2 The Object Palette The Object Palette contains ready made objects which the user may insert in the Scene using the Insert Object button The
6. ands and procedures Follow the steps mentioned below to construct a dodecahedron Step 1 Define the Pentagon procedure to create a pentagon The dodecahedron will consist of 12 facets each of which will have the shape of a pentagon The following procedure describes the turtle moves to be performed so as to create a pentagon line 1 to pentagone a line 2 repeat 5 line 3 fd a rt 72 line 4 end line 5 pentagone 3 The pentagon will be constructed as the turtle will repeat 5 times line 2 the procedure fd a rt 72 The turtle will move forward maintaining its direction by a number of pixels that will be defined by the a variable As the pen is down the turtle will draw a line whose length will be a pixels After moving for a pixels the turtle will turn clockwise by 72 degrees As the fd a rt 72 repeats 5 times a pentagon whose sides is a pixels long will appear Try to run the procedure attributing an arithmetical value to the a variable e g 3 line 5 and observe the graphical result in the Turtle Scene d EDUCATIONAL TECHNOLOGY LAB ETL NKUA 12 MaLT Manual Figure 13 Running 5 times the fd a rt 72 procedure a 3 Step 2 Define the cup procedure to create six adjacent pentagons For the construction of the bottom half of the dodecahedron six pentagons will be needed The next procedure will help you create 6 adjacent pentagons forming a kind o
7. ation Tool and the Property Editor 3 1 The Turtle Scene 3 1 1 Description The Scene is a 3d grid like interface where 3d geometrical objects are graphically represented The 3d geometrical objects that appear in the Scene are either constructed by the user when running logo procedures or inserted by the user after selecting them from a library that offers numerous ready made stereometric objects such as cylinders spheres and cones The 3d turtle doesn t appear in the Scene by default The user must type and run at the Logo Editor at least one command that produces a graphical result in the Scene so as to make the turtle visible The trace the turtle leaves when moving inside the Scene a thin 3D cylindrical line is selectable Clicking on this trace causes the 1dVT tool to activate and appear on the right part of the interface right below the Logo area 3 1 2 Scene camera manipulation The user may look at her his constructions inside the Scene from different Sa Z EDUCATIONAL TECHNOLOGY LAB ETL NKUA 2 MaLT Manual viewpoints Three cameras are available The first one is placed on the top of the Scene and shows the Floor View of the 3d constructions inside the Scene The second one is placed on the one of the Scene s sides and shows the Side View of the 3d constructions inside the Scene The third one is the main camera of the Scene and is turned towards the negative direction of the Z axis as shown to the XYZ
8. d expand to include games hopefully playable by many on the web 4 2 In terms of deployment In the time of the project we used MaLT as one of the main pieces of software taught in two regular master s courses titled Methodology and Didactics of Mathematics and Didactics of Special Subjects with new Technologies respectively We also used MaLT in a large scale initiative of the Ministry of Education targeting 4000 mathematics teachers to receive a 96 hour course in using digital media in the teaching of mathematics We were part of a project within this initiative to train 100 mathematics teacher educators and carried out a 350 hour course to 20 of them and took part in the teaching of all the others MaLT featured as the 3d version of Turtleworlds an ETL designed widely available software We made MaLT available on the ETL website and advertised it as a resource in these courses Sa 2 EDUCATIONAL TECHNOLOGY LAB ETL NKUA 17
9. ding meaningful feedback to its users 2 Last evolutions of the DDA The MaLT environment is now using jMonkey a java based game engine that renders complex 3d scenes significantly fast which results in boosting substantially the Turtle Scene s performance Therefore any object manipulations in the Turtle Scene direct or indirect now provoke the environment s immediate graphical response in speeds comparable to other 2d dynamic geometry tools A second change made was the inclusion of a set of ready made stereometric objects and a special GUI to dynamically manipulate important features and measure areas volumes segments and locations A third change was the development of a GUI to make the environment more useable and a final change was the inclusion of dynamic controllers for camera movement The elements modified since the last deliverable and the elements introduced in the new MaLT are presented below in detail 3 Description of the final form of the DDA The new MaLT environment consists of two main areas the left and the right one The left area the larger one constitutes the environment s Turtle Scene where user constructed or ready made 3d figures are graphically visualized The component that appears on the right area however is of the user s choice By clicking on the corresponding tab on the top of the right area the user may select between two different components to display the Logo Editor including the Vari
10. e Turtle Scene Notice that the sixth pentagon the one on the base of the figure is not logo constructed but Shaped by the other five ones T EDUCATIONAL TECHNOLOGY LAB ETL NKUA a MaLT Manual 3D MODELER MATHS Logo Editor Property Editor to pentagone ta repeat 5 fd a rt 72 end pentagone 3 to cup ta arccos 0 5 sin 72 pentagone 3 lr 2 arccos 0 5 sin 72 fdi a rt 72 end cuplis i to dodecahedron a theta rt theta cup ia rt 18 up 2 arecos 0 5 sin 72 1t 18 fdl a 4 i I B aata mam il E a M i asl Oia ESR BUA A A Aner Lroreremryeversruy at ML 11e 1da037d9 PENTAGONE ML 11e 1da037d9 java 33 at ML11e1da037d9 init ML 11e 1da037d9 java 134 at gr talent machinelab logoruntime MLApp 4 run MLApp java 197 at gr talent machinelab logoruntime MLApp run MLApp java 149 at threeImpact base ThreeImpactPanel start Native Method at gr talent machinelab MLEditor MachineLab3D 3 run MachineLab3D java 9 1 Figure 15 Running the cup procedure a 3 Step 3 Define the dodecahedron procedure to create the figure For the construction of the dodecahedron you will need two cup procedures The first one will create bottom half of the dodecahedron and the second one the upper half The upper half will be a reversed cup line 14 to dodecahedron a theta line 15 rt theta line 16 cup a line
11. e variable to be represented the colour of the selected axis turns to green Logo Property Editor File Edit Search Logo Help to rect a b ic yap Su repeat fd ra rtlic fd b rt led c end The variable A will be represented in the X axis recti 3 50 p 3 1 0 0 1 A 72 B 2 0 10 0 1 Metapinn B The variable B will be represented in the Y axis Metaph C c 0 e j io Figure 6 Defining which variable will be represented in which 2dVT axis Step 5 Drag the mouse on the pad and define a relationship between the variables The mouse can be freely dragged on the 2dVT s pad leaving a trace behind Each position on the pad corresponds to a specific value for each of the selected variables By dragging the mouse on the 2dVT a functional relationship between the two variables is defined The changes in the mouse s position cause changes to the 1dVT sliders values as well as to the figure in the Scene according to this functional relationship The resulting line on the 2dVT pad corresponds to the graph of this functional relationship File Edit View 0S sell Figure 7 Creating the y x functional relationship between the two variables te EDUCATIONAL TECHNOLOGY LAB ETL NKUA 8 MaLT Manual 3 4 3 Working with the Vector Variation Tool VVT Just l
12. edure of at least three variables and is activated when clicking on the icon next to the 1dVT A pop up menu appears so as for the user to select which variable will to correlate to r and 98 r stands for length 8 for the angle between the vector s projection on the xz plane and the z axis and for the angle between the vector and the xz plane The three variables values can be manipulated by dragging and rotating vectors in the VVT window that appears 3D MODELER MATHS Logo Editor Property Editor File Edit Search Logo Help to parallelogramB a b ic repeat 2 fd a rt c fdizb rt 180 c end to slide a b c id up 90 Lr d repeat 2 parallelogramB a b c Lr 90 end slide 3 60 90 NDU AAN mm iMX Figure 2 The Turtle Scene and Logo Editor in the final version of MaLT 3 3 The Property Editor Just like the Logo tab the Property Editor tab is situated on the right part of the new MaLT interface It is designed to provide the user a library of ready made objects which she he may insert in the Scene and manipulate them by editing its properties It consists of the Toolbar the Palette and the main area of the Property Editor 3 3 1 The Toolbar In order to insert and manipulate ready made objects the user has at his disposal several features in the form of icons at the Editor s Toolbar These are New Object Clicking on the New Object icon the Object Palette opens up
13. es Define your object s Name Colour Transparency Position X Y Z Radius and Height Step 4 Insert your object in the Turtle Scene Press the Insert Object icon on the Toolbar so as to make the cone appear in the Turtle Scene After inserting the object the MaLT environment calculates the object s All Area Side Area and Volume and provides their values on the Editor s corresponding fields Step 5 Manipulate your object The little white spheres that appear on your object are its handles By clicking and dragging a handle you may modify your object s dimensions These changes become visible not only graphically in the Scene but also on the Editor s fields as the Radius and Height values also change TO move your object in the XY plane click at any point on its surface and drag it towards the direction you wish to move it By using both the left and the right mouse button you may also drag your object along the Z axis When clicking at any point of the Scene the object is deselected its handles disappear and its surface appearance turns from grid like to solid like To select it again just click on it Es 2 EDUCATIONAL TECHNOLOGY LAB ETL NKUA 10 MaLT Manual Logo Editor Property Editor BEOXBD BAAD OOE e Pallete Edit the values to change the cone s ae i properties Heght Side Ar Click on the handles HIY AN _ Pisco and drag them to Rie change its dimensions Figure 10 A c
14. f cup The dihedral angle between two adjacent pentagons for the formation of a dodecahedron equals to 2 arccos 0 5 sin 72 line 6 to cup a line 7 repeat 5 line 8 rr 2 arccos 0 5 sin 72 line 9 pentagone a line 10 Ir 2 arccos 0 5 sin 72 line 11 fd a rt 72 line 12 end line 13 cup 3 The bottom part of the dodecahedron will be constructed as the turtle will repeat 5 times line 7 the procedure line 8 rr 2 arccos 0 5 sin 72 line 9 pentagone a line 10 Ir 2 arccos 0 5 sin 72 line 11 fd a rt 72 2 EDUCATIONAL TECHNOLOGY LAB ETL NKUA 13 MaLT Manual Initially the turtle will rotate to the right by 2 arccos 0 5 sin 72 degrees i e the degrees of the dodecahedron s dihedral angle line 8 The pentagon procedure will be executed and the first pentagon will appear It s side length will be defined by the a variable line 9 The turtle will then return to the position it held before the execution of the pentagon procedure The turtle will rotate to the left by 2 arccos 0 5 sin 72 degrees i e the degrees of the dodecahedron s dihedral angle line 10 It will then move forward by a number of pixels that will be defined by the a variable and turn clockwise by 72 degrees Figure 14 Running lines 8 11 Try to run the procedure attributing an arithmetical value to the a variable e g 3 line 8 and observe the graphical result in th
15. g the 1d Variation Tool The 1dVT doesn t appear in the MaLT s interface by default In order to make it visible and work with it follow the steps mentioned below Step 1 Type at the Logo Editor a procedure of at least one variable to rect a b c repeat 2 fd a rt c fd b rt 180 c end Step 2 Run the procedure using an arithmetical value for each variable Type the procedure s name and inside the parentheses type the arithmetic values for each variable rect 20 30 40 Press F6 to run the command A rectangle corresponding to these specific values appears in the Turtle Scene Es 2 EDUCATIONAL TECHNOLOGY LAB ETL NKUA 6 MaLT Manual Step 3 Click on the turtle s trace When clicking on the turtle s trace the 1dVT appears on the Logo Tab just below the Logo Editor Logo Editor Property Editor File Edit Search Logo Help cy Wee bee repeat 2 fd rai rtii c fdi b ct 180 c end to rect The Logo procedure rect 20 30 40 4 I Parameters of procedure RECT Variable j Value The procedure s three variables Change the variation s step Drag the pointers to change the variables original values Change the range of the variation Figure 5 The 1d Variation Tool 1dVT The 1dVT consists of three sliders each of which corresponds to one of the rect procedure s variables Dragging one of the sliders causes t
16. he figure in the Scene to change as the values of the variable change consequently and the logo procedure is executed again and again using each time a new arithmetic value for the variable To clear the Turtle Scene press F5 3 4 2 Working with the 2d Variation Tool Just like the 1dVT the 2dVT doesn t appear in the MaLT s interface by default In order to make it visible and work with it follow the steps mentioned below Step 1 Type at the Logo Editor a procedure of at least two variables to rect a b c up 90 repeat 2 fd a rt c fd b rt 180 c end Step 2 Run the procedure using an arithmetical value for each variable rect 7 3 55 Press F6 to run the command A rectangle corresponding to these specific values appears in the Turtle Scene Step 3 Click on the turtle s trace When clicking on the turtle s trace the 1dVT appears on the Logo Tab just below the Logo Editor while the 2dVT appears in a separate window However the 2dVT is not yet activated Ee Z EDUCATIONAL TECHNOLOGY LAB ETL NKUA 7 MaLT Manual Step 4 Select which variable will be represented in which axis The 2dVT is activated through the 1dVT Right beside each variable s name in the 1dVT there is an icon displaying a red orthogonal bi axial system Choose the vertical or the horizontal axis on the icon so as to define in which of the 2dVT s axis the selected variable will be represented When clicking on the axis you wish th
17. ike the 1dVT and the 2dVT the VVT doesn t appear in the MaLT s interface by default In order to make it visible and work with it follow the steps mentioned below Step 1 Type at the Logo Editor a procedure of at least three variables and run the procedure Click on the turtle s trace in the 3d Scene to rect a b c up 90 repeat 2 fd a rt c fd b rt 180 c end rect 7 3 55 Step 2 Select which variable will represent r 0 and The VVT is activated when clicking on one of the icons displaying a polar coordinate system on the 1dVT slider The pop up menu that appears will help you define whether the selected variable will represent in the polar coordinate system the r the length the 8 the angle between the vector s projection on the xy plane and the x axis or the the angle between the vector and the xy plane coordinate Step 3 Manipulating the r 0 and values The VVT consists of two vector like representations the constituent projections and a resultant vector representation Using the first vector like representation you may dynamically manipulate the vector s length and rotate it to control the value of angle 8 while using the second one you may manipulate the vector s length and rotate it to control the value of angle The changes performed on the two vector like representations are reflected on the resultant vector representation which is not available for direct manipulations The po
18. kinds of objects the user may insert are Logo Editor Property Editor Spheres HG AO O Cylinders Ne E Cones The Toolbar Pyramids Orthogons Canonical Prismatics Canonical Polygons P The Palette s available types Lines of objects Canonical Prismatic j Planes Canonical Polygon Line Segments es Fiane Circles Figure 3 The Toolbar and the Object Palette 3 3 3 Property Editor The Property Editor is activated each time the user selects a ready made object from the 3d Scene The type of the selected object appears in the Palette while the Property Editor s fields just below the Object Palette become available to the user so as to modify the attributed values Changing a value in one of the Property Editor s fields produces an immediate visual result to the object inserted in the Scene The Property Editor is also activated each time the user begins an object inserting procedure by clicking on the New Object button Since the properties to be defined in the Property Editor are not the same for all the available types of ready made objects the user has to choose first from the Palette the kind of object she he wishes to insert The default values for the selected type appear on the Editor The user may modify these values so as to define the kind of properties her his object wishes to hold Although for each type different properties appear on the Property Editor yet there is a
19. lar and the Cartesian values are represented graphically by the vectors their selves and their projections and numerically in the text boxes just below the vectors Any manipulations performed to the vector presentations are visualised in the Turtle Scene as the figure constructed changes dynamically Parameters of procedure RECT i p A 10 0 1 gt Metafimn C B 2 0 B 10 0 1 4 Click on the variable s polar coordinate icon Choose whether A will be represented by r 8 org Metaph B i Metai C aa erd Ea 2 EDUCATIONAL TECHNOLOGY LAB ETL NKUA 9 MaLT Manual EJ Vector Variation Tool The text boxes show the r 8 x yand z values Drag and rotate the vectors to change the r 8 and coordinates Figure 9 The Vector Variation Tool VVT 3 4 4 Inserting and manipulating ready made stereometric objects To insert ready made objects in the Turtle Scene click on the Property Editor tab and follow the steps mentioned below Step 1 Activate the Editor Click on the New Object icon on the Editor s Toolbar to initialise the inserting procedure Step 2 Select the type of object to insert Choose from the Palette s pop up menu the type of object you wish to insert in the Turtle Scene Notice that the properties on the area below the Palette change according to the type of object you choose Choose for example a cone Step 3 Define your object s properti
20. one inserted in the Turtle Scene The Property Editor s objects can also be inserted through the Logo Editor using logo commands specialised for each type of object 3 4 5 Manipulating the camera viewpoints In the new MaLT environment the user has at his disposal three cameras Each one offers a different viewpoint of the ready made and logo constructed geometrical objects in the environment s Turtle Scene The selection of the viewpoint from which you may observe your constructions is performed through the Property s Editor Toolbar Dax Deag Figure 11 The third camera is currently activated in the Property Editor s Toolbar Property Editor Click on 1 2 or 3 to select the viewpoint Camera 1 is placed on the top of the Scene and shows the Floor View of the constructions inside the Scene Camera 2 is placed on the one of the Scene s sides and shows the Side View of the constructions inside the Scene Camera 3 is the main camera of the Scene and is turned towards the negative direction of the Z axis It is the only camera whose position the user may change using logo commands or combinations of keyboard buttons te EDUCATIONAL TECHNOLOGY LAB ETL NKUA 11 MaLT Manual Figure 12 The Camera 1 Camera 2 and Camera 3 viewpoint 3 4 6 Creating logo constructed 3d stereometric objects In the MaLT environment the user may also construct complex stereometric objects using simple logo comm
21. representation below It is the only camera whose position the user may change using logo commands or combinations of keyboard buttons Y o Shift W the camera zooms in o Shift S the camera zooms out o Shift A the camera moves left on a circumference of a sphere X o Shift D the camera moves right on a circumference of a sphere o Shift Q the camera moves up on a 7 circumference of a sphere o Shift E the camera moves down on a Figure 1 The semantics of circumference of a sphere the XYZ coordination o Shift X resets camera to its initial position system 3 2 The Logo Editor and Variation Tools 3 2 1 The Logo Editor The Logo Editor opens up when clicking on the Logo tab situated on the right area of the MaLT environment It consists of two interfaces a Program Editor where the user may type commands define new procedures and execute them and a Parser where the user may view the output of his actions on the Editor By running logo procedures and logo commands in the Logo Editor the user may construct 3d figures in the Turtle Scene create and manipulate 3d stereometric objects e g cylinders spheres and cones and control the camera so as to change the selected viewpoint A logo command is executed when placing the cursor at the command s line and pressing the keyboard s Insert button while when pressing the F6 button the whole procedure is executed regardless of the line the cursor is placed 3 2 2 Variation Tool
22. s The MaLT Variation Tools provide users the opportunity to dynamically manipulate the values of an executed Logo procedure s variables In the final version of MaLT it consists of the Uni dimensional Variation Tool 1dVT the Two dimensional Variation Tool and the Vector Variation Tool The Uni dimensional Variation Tool 1dVT The 1dVT appears just below the Logo Editor only after the user defines a Logo procedure runs it attributing specific values to each of its variables and clicks on the trace the turtle has left behind when constructing the graphical outcome of the procedure in the 3d Scene It consists of number line like sliders each of which corresponds to one of the variables used in the Logo procedure The Two dimensional Variation Tool 2dVT The 2dVT allows the co variation of two of the Logo procedure s variables and is activated when selecting those two variables from a window that appears right next to the Sa Z EDUCATIONAL TECHNOLOGY LAB ETL NKUA 3 MaLT Manual 1dVT The user decides which variable will correspond to which axis the X or the Y on the 2dVT s orthogonal pad and drags the mouse on the pad s interface to co vary of the two variables values The Vector Variation Tool VVT The VVT allows the co variation of three variables by using two 2d representations of a vector defined by these variables according to an r 8 polar semantic in the 3d space The VVT requires a Logo proc
23. set of standard properties that appear for all the types of objects These are Sa Z EDUCATIONAL TECHNOLOGY LAB ETL NKUA 5 MaLT Manual Name Each object in the 3d Scene has a unique name by which it is addressed when running logo procedures Colour A palette of colours from which the user may select the one for her his object appears Transparency The value of the object s transparency appears The given values should be between 0 and 255 The Toolbar q Logo Editor Property Editor BORSA SHAD OOPEC F rate The Palette Transparency Position X 0 000 Y 0 000 z 0 000 The object s properties to be aila al Radius 1 1 000 Radius 2 1 000 5 000 37 699 31 416 15 708 Figure 4 The Turtle Scene and the Property Editor tab in the new MaLtT Other kinds of properties that may appear according to the type of the object inserted in the Turtle Scene are the Radius Height Sides Length Width Length of diagonal Centre Point and Position X Y Z Apart from the Property fields whose values are defined by the user there is also a set of fields whose values are calculated automatically by the environment when the object is inserted in the Turtle Scene These also vary according to the object s type The most common of them are the All Area Side Area and Volume 3 4 Using the MaLT Environment s features 3 4 1 Usin
Download Pdf Manuals
Related Search