1. Visualizing Geometric Shapes
Kelly Testa
Advisors: Chris Fernandes & Davide Cervone

2. Presentation Agenda Project Characteristics Current Progress
Background
Project Characteristics
Current Progress
Future Work

3. Original Program Uses
Classroom demos
Help with homework

4. Original Program
Geomview - tool that displays mathematical objects

5. Original Program
StageTools – modules that create and manipulate geometric objects

6. Problems with Original Program
To use the program
1. Load Linux environment
2. Setup Geomview
3. Load StageTools

7. Goals of a New Program More accessible to students and professors
Same capabilities as the original
Flexible enough for unknown features

8. Representing Geometric
Objects

9. Representing Geometric
Objects
Data
- points
- connections

10. Display Format
DomainCreators
Grid
Stripes
Patches

11. Display Format Ranges [-1, 1, 2] [3, 5, 2]
Points { (-1, 3), (-1, 4), (-1, 5), (0, 3), (0, 4), (0, 5), (1, 3), (1, 4), (1, 5) } -1 1 4 5 3

12. Display Format GridCreator {[0, 1], [1, 2], [3, 4],
[4, 5], [6, 7], [7, 8],
[0, 3], [3, 6], [1, 4],
[4, 7], [2, 5], [5, 8]} 5 5 8 8 2 2 4 4 1 7 7 1 3 6 3 6
PatchCreator
{ [0, 3, 4, 1],
[3, 6, 7, 4],
[1, 4, 5, 2],
[4, 7, 8, 5] }

13. Mapping Sets MapSetToSet class Curve: f: R  R3 f(t) = (t, t2, t3)
Surface: f: R2  R3
f(u,v) = (u, v, u*v)

14. Mapping Sets Example: f(u,v) = (u, v, u*v)
2-D point set (u,v)  3-D point set (x,y,z)
{ (-1, -1), (-1, 0), (-1, 1)}
 { (-1, -1, 1), (-1, 0, 0), (-1, 1, -1) }

15. Data Flow
User Input
Grid
Creator
Data
f(u,v)=(u,v,u*v)
Data
Viewer

16. Linked Geometric
Objects

17. My Images

18. Future Work Parser for Function String
GUI for creating the geometric object
Interfaces to change parameters
Graphical Display

19. Questions?