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Professor Chee Yap | Room: WWH 416, Tel: 998-3115, email: yap "at" cs.nyu.edu |

Lectures | Tue 5:00-6:50, WWH 813 |

Office Hours | Mon 4:00-5:00, and by appointment |

NYU Bboard | Class discussions, email lists, announcements, grades, etc.
Use your NYU NetID to login, then click our class link |

Invariably, the first step is to compute a combinatorial approximation of S from the given metric/local information. This combinatorial approximation is called a mesh (or complex). This is the meshing problem. Meshing is a critical step -- as the interface between continuous and discrete computation. The computation involves some combination of numerical and algebraic techniques. A big question is how to guarantee that this step is correct in the presense of numerical errors. (Most published algorithms have no guarantees.) The computational methods depend on the representation of the object. E.g., we would need very different algorithms if the surface S in the previous example were represented by Bezier patches.

The next step is to compute the desired topological property of S from an appropriate mesh representation. The mathematical and computational tools such as homology, Morse theory and subdivision schemes will be developed.

- We will cover two chapters from a forthcoming book
*Effective Computational Geometry for Curves and Surfaces*(Eds., J.-D.Boissonnat and M.Teillaud):*Computational Topology: An Introduction,*G.Rote and G.Vegter.*Meshing of Surfaces,*J.-D.Boissonnat, D.Cohen-Steiner, B.Mourrain, G.Rote, G.Vegter. - Book References:
*Geometry and Topology for Mesh Generation*, H.Edelsbrunner. Cambridge Press, 2001.*Topology for Computing*, A.Zomorodian. Cambridge University Press, 2005.*Subdivision Methods for Geometric Design*, J.Warren and H.Weimer. Morgan Kaufmann Pub., 2002. - The material on numerical-algebraic computation
will be taken:
*Robust Geometric Computation*, K.Mehlhorn, C.Yap. - Current Research Papers.

Grade is based on Homework (30%), 2 Tests (30%), Project (40%).

Homework includes programming assignments.

Programming will be in C/C++ and includes the use of the Core Library.

- Feel free to suggest links.
- Archive of Electronic Geometry Models: explore under models.
- C.T.J.Dodson's Course on Elementary Curves and Surfaces