Student-Oriented Software for Application of Geometry in 3D Modeling

1. MASSEE 2003, Borovetz, Bulgaria Student-Oriented Softwarefor Application of Geometryin 3D Modeling Pavel Boytchev, Elica Team, Bulgariapavel@elica.net

2. Student-Oriented Software... • About Elica • Basic 3D objects and transformations • Turtle graphics and 3D • Challenges • Examples About Elica

3. About Elica Elica features • based on Elica Logo • tiny core but highly flexible • 3D in real time • it's free Some numbers • 300 registered users, 3000 downloads worldwide,30000 Elica home page views • Won the Logo Cartoon Contest at Eurologo 2003 3D objects

4. Basic 3D Objects Cube Sphere Cylinder Cone 3D transformations

5. Basic 3D Transformations • Transformations • Translation • Scaling • Rotation • Parameters • vector “center” for position • vector “radius” for size • vector “focus” for orientation • scalar “spin” for spinning Advantages

6. Advantages & Disadvantages • Advantages • Geometrical description of objects • Consistency of definitions • Absolute positioning and orientation • Easy to construct and animate fixed-joint objects • Disadvantages • Moderate problems with positions • Serious problems with orientations • Hard to construct flexible-joint objects • Not appropriate for young students Example

7. Example Pawn’s structure - 2 spheres - 2 hemispheres - 1 cone Turtle graphics

8. Turtle Graphics Traditional turtle triangular shape 2D drawings Space turtle 3D shape 3D drawings Merging techniques

9. Turtle Graphics and 3D Space turtle 1 vector for position 3 vectors for orientation Flexible body local transformation matrix at every joint Is it possible to mergeboth techniques? skeleton flesh 3D charactercreated andanimated in real time Object cloning

10. Object Cloning • Turtle vectors build a transformation matrix • Matrix applied to any simple or compound object • Turtle controls position and orientation Houses cloned by a 3D spherical turtle 3D characters

11. 3D Characters • At each joint the turtle • clones its coordinate system • defines attached fixed-joint objects • Cloned systems generate • local transformation matrices • Transformation matrices • control position and orientation of attached fixed-joint objects • they are automatically multiplied to generate overall transformation A man and a robot Advantages

12. Advantages & Disadvantages • Advantages • Flexible-joint objects • Easy to construct and animate complex models • It’s fun and can be used with 5-8 graders • Disadvantages • Needs up-to-date hardware • It's hard to use in local schools • However • 3D graphics course with local math school • Classes arranged in Game Clubs !!! Challenges

13. Challenges • Elica on the internet • Steps towards using Elica in classrooms • Focus on educational models Examples

14. Examples • “Chess Games” .......................... • “Urbanizing Turtle Land”......... • “Androids” ................................ The end

15. The End