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Geometric Modeling Course Overview (CSCE 645/VIZA 675) - Fall 2010

Join Dr. Scott Schaefer for an in-depth exploration of Geometric Modeling in CSCE 645/VIZA 675. This course covers essential topics such as polynomial curves and surfaces, surface representations, and differential geometry, focusing on applications in industrial design, movies, and animation. Students are expected to have programming experience in C/C++ and a foundational understanding of linear algebra. Assessment includes homework and a class project that promotes innovation and research integration. For more details on assignments and office hours, visit the course website.

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Geometric Modeling Course Overview (CSCE 645/VIZA 675) - Fall 2010

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  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

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