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# topology of surface

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### Transcript

• 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. Topology _the nurbs surface_Non Uniform Rational B-Splines
• 3. Topology _the nurbs surface
• 4. Topology _design
• 5. Topology _the nurbs surface_Continuity & Patches
• 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. Topology _the nurbs surface
• 8. Topology _the nurbs surface
• 9. Topology _the Moebius Strip
• 10. Topology _the Moebius Strip
• 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. Topology _the Klein Bottle
• 13. Topology
• 14. Topology _Thickening the Surface
• 15. Topology _Thickening the Surface
• 16. Topology _The Human Ear
• 17. Topology _The Human Ear
• 18. Topology _The Human Ear
• 19. The Dissected Body
• 20. Topology _from Surface to Flesh
• 21. Topology _Andreas Vesalius
• 22. Flesh
• 23. Flesh
• 24. Flesh
• 25. Flesh
• 26. Flesh
• 27. Flesh
• 28. Flesh
• 29. Flesh
• 30. Flesh
• 31. Flesh
• 32. Flesh
• 33. Flesh
• 34. Flesh