topology of surface

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topology of surface

  1. 1. Pratt Institute _School of Architecture _Sensation Tectonics Arch 522C.09/.10: _Introduction to 3D Modeling and Visualization_Instructor: _Robert Brackett _Robert.Brackett3@gmail.com_Instruction: _Tuesdays , 6:00 – 9:00_Credits: _03_Classification: _Elective
  2. 2. Topology _the nurbs surface_Non Uniform Rational B-Splines
  3. 3. Topology _the nurbs surface
  4. 4. Topology _design
  5. 5. Topology _the nurbs surface_Continuity & Patches
  6. 6. Topology _the nurbs surface_Manifolds_Riemannian ManifoldsTo measure distances and angles on manifolds, the manifold must beRiemannian. A Riemannian manifold is a differentiable manifold inwhich each tangent space is equipped with an inner product 〈⋅,⋅〉in a manner which varies smoothly from point to point. Given twotangent vectors u and v, the inner product 〈u,v〉 gives a realnumber. The dot (or scalar) product is a typical example of an innerproduct. This allows one to define various notions such as length,angles, areas (or volumes), curvature, gradients of functions anddivergence of vector fields.
  7. 7. Topology _the nurbs surface
  8. 8. Topology _the nurbs surface
  9. 9. Topology _the Moebius Strip
  10. 10. Topology _the Moebius Strip
  11. 11. Topology _the Klein Bottle_ A Klein Bottle is a 4-Dimensional topography that cannot beembedded within 3-Dimensional space. The surface has somevery interesting properties, such as being one-sided, like theMoebius strip; being closed, yet having no "inside" like a torusor a sphere; and resulting in two Moebius strips if properly cutin two.
  12. 12. Topology _the Klein Bottle
  13. 13. Topology
  14. 14. Topology _Thickening the Surface
  15. 15. Topology _Thickening the Surface
  16. 16. Topology _The Human Ear
  17. 17. Topology _The Human Ear
  18. 18. Topology _The Human Ear
  19. 19. The Dissected Body
  20. 20. Topology _from Surface to Flesh
  21. 21. Topology _Andreas Vesalius
  22. 22. Flesh
  23. 23. Flesh
  24. 24. Flesh
  25. 25. Flesh
  26. 26. Flesh
  27. 27. Flesh
  28. 28. Flesh
  29. 29. Flesh
  30. 30. Flesh
  31. 31. Flesh
  32. 32. Flesh
  33. 33. Flesh
  34. 34. Flesh

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