Index of Slides

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  1. Representing Smooth Surfaces
  2. Overview
  3. Introduction: Motivation
  4. ``Representing'' ``Smooth'' ``Surfaces''?
  5. Explicit Surfaces
  6. Ruled Surfaces
  7. Mathematical Properties
  8. Implicit Surfaces
  9. Implicit Surfaces -- Advantages
  10. Implicit Surfaces -- Disadvantages
  11. Enumerating points on the Surface
  12. Conversion: Implicit ==> Polygonal Mesh
  13. Which 3-D cells?
  14. Convert the surface in cell into a polygon
  15. Adaptive Criteria
  16. Parametric Surfaces and Subdivision Surfaces
  17. Motivations
  18. Parametric Surface---Definition
  19. Parametric Surface---Advantages
  20. Plotting parametric surfaces
  21. Trimmed Parametric Surfaces
  22. Parametric Surfaces---Naive approach
  23. Splines Surfaces
  24. Example in 2-D: B-spline
  25. Example in 3-D
  26. Extraordinary Vertices---A complication
  27. Loss of Smoothness
  28. Subdivision Surfaces
  29. What function to repeat?
  30. Other desirable mathematical properties
  31. Midedge Subdivision Scheme
  32. Other Popular Subdivision Schemes
  33. Doo-Sabin subdivision
  34. Other Subdivision Schemes
  35. Geri's Game
  36. Constructive Solid Geometry
  37. Primitive Solids
  38. Example Image: Bowl with stars
  39. Advantages and Disadvantages
  40. Ray-tracing a CSG solid
  41. Collision Detection of two CSG solids
  42. Boundary Representation
  43. Boundary Representation
  44. Voxel-based representation
  45. The Task
  46. Naive method
  47. Better: Marching Cubes Algorithm
  48. Marching Cubes: Figures
  49. Skull
  50. Relationship to other class topics
  51. Relationship to other class topics
  52. Annotated Bibliography
  53. Any questions?