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# 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