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 Manifolds
To measure distances and angles on manifolds, the manifold must be
Riemannian. A Riemannian manifold is a differentiable manifold in
which each tangent space is equipped with an inner product 〈⋅,⋅〉
in a manner which varies smoothly from point to point. Given two
tangent vectors u and v, the inner product 〈u,v〉 gives a real
number. The dot (or scalar) product is a typical example of an inner
product. This allows one to define various notions such as length,
angles, areas (or volumes), curvature, gradients of functions and
divergence 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 be
embedded within 3-Dimensional space. The surface has some
very interesting properties, such as being one-sided, like the
Moebius strip; being closed, yet having no "inside" like a torus
or a sphere; and resulting in two Moebius strips if properly cut
in 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