Geometric Modeling CSCE 645/VIZA 675

1. Geometric Modeling CSCE 645/VIZA 675 Dr. Scott Schaefer

2. Course Information • Instructor • Dr. Scott Schaefer • HRBB 527B • Office Hours: MW 10:15am – 11:15am (or by appointment) • Website: http://courses.cs.tamu.edu/schaefer/645_Fall2010

3. Geometric Modeling • Surface representations • Industrial design

4. Geometric Modeling • Surface representations • Industrial design • Movies and animation

5. Geometric Modeling • Surface representations • Industrial design • Movies and animation • Surface reconstruction/Visualization

6. Topics Covered • Polynomial curves and surfaces • Lagrange interpolation • Bezier/B-spline/Catmull-Rom curves • Tensor Product Surfaces • Triangular Patches • Coons/Gregory Patches • Differential Geometry • Subdivision curves and surfaces • Boundary representations • Surface Simplification • Solid Modeling • Free-Form Deformations • Barycentric Coordinates

7. What you’re expected to know • Programming Experience • Assignments in C/C++ • Simple Mathematics Graphics is mathematics made visible

8. How much math? • General geometry/linear algebra • Matrices • Multiplication, inversion, determinant, eigenvalues/vectors • Vectors • Dot product, cross product, linear independence • Proofs • Induction

9. Required Textbook

10. Grading • 50% Homework • 50% Class Project • No exams!

11. Class Project • Topic: your choice • Integrate with research • Originality • Reports • Proposal: 9/15 • Update #1: 10/13 • Update #2: 11/10 • Final report/presentation: 12/13

12. Class Project Grading • 10% Originality • 20% Reports (5% each) • 5% Final Oral Presentation • 65% Quality of Work http://courses.cs.tamu.edu/schaefer/645_Fall2010/assignments/project.html

13. Questions?

14. Vectors

15. Vectors

16. Vectors

17. Vectors

18. Vectors

19. Vectors

20. Vectors

21. Points

22. Points

23. Points

24. Points

25. Points • 1 p=p • 0 p=0 (vector) • c p=undefined where c 0,1 • p – q = v (vector)

26. Points

27. Points

28. Points

29. Points

30. Points

31. Points

32. Points

33. Points

34. Barycentric Coordinates

35. Barycentric Coordinates

36. Barycentric Coordinates

37. Barycentric Coordinates

38. Barycentric Coordinates

39. Barycentric Coordinates

40. Barycentric Coordinates

41. Convex Sets • If , then the form a convex combination

42. Convex Hulls • Smallest convex set containing all the

43. Convex Hulls • Smallest convex set containing all the

44. Convex Hulls • If pi and pj lie within the convex hull, then the line pipj is also contained within the convex hull

45. Convex Hulls • If pi and pj lie within the convex hull, then the line pipj is also contained within the convex hull

46. Convex Hulls • If pi and pj lie within the convex hull, then the line pipj is also contained within the convex hull

47. Convex Hulls • If pi and pj lie within the convex hull, then the line pipj is also contained within the convex hull

48. Convex Hulls • If pi and pj lie within the convex hull, then the line pipj is also contained within the convex hull

49. Convex Hulls • If pi and pj lie within the convex hull, then the line pipj is also contained within the convex hull

50. Convex Hulls • If pi and pj lie within the convex hull, then the line pipj is also contained within the convex hull