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Geometric Modeling CSCE 645/VIZA 675

Geometric Modeling CSCE 645/VIZA 675. Dr. Scott Schaefer. Course Information. Instructor Dr. Scott Schaefer HRBB 527B Office Hours: MW 9:00am – 10:00am (or by appointment) Website: http://courses.cs.tamu.edu/schaefer/645_Spring2013. Geometric Modeling. Surface representations

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Geometric Modeling CSCE 645/VIZA 675

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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 9:00am – 10:00am (or by appointment) • Website: http://courses.cs.tamu.edu/schaefer/645_Spring2013

  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: 2/7 • Update #1: 3/7 • Update #2: 4/9 • Final report/presentation: 4/25

  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_Spring2013/assignments/project.html

  13. Honor Code • Your work is your own • You may discuss concepts with others • Do not look at other code. • You may use libraries not related to the main part of the assignment, but clear it with me first just to be safe.

  14. Questions?

  15. Vectors

  16. Vectors

  17. Vectors

  18. Vectors

  19. Vectors

  20. Vectors

  21. Vectors

  22. Points

  23. Points

  24. Points

  25. Points

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

  27. Points

  28. Points

  29. Points

  30. Points

  31. Points

  32. Points

  33. Points

  34. Points

  35. Barycentric Coordinates

  36. Barycentric Coordinates

  37. Barycentric Coordinates

  38. Barycentric Coordinates

  39. Barycentric Coordinates

  40. Barycentric Coordinates

  41. Barycentric Coordinates

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

  43. Convex Hulls • Smallest convex set containing all the

  44. Convex Hulls • Smallest convex set containing all the

  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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