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Computational Geometry and Modeling

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G22.3033.007 Spring 2005

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Course Information

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

Lectures |
Wed 5:00-6:50, WWH 613 (Note room change! |

Office Hours |
Mon 3:00-4:00, and by appointment |

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

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Course Description

Computational Geometry has traditionally
emphasized combinatorial analysis and efficient
algorithmic techniques to solve a variety of
geometric problems. Most of these problems
are linear problems, involving points and piecewise
linear objects (e.g., polytopes).
In recent years, the push to extend such techniques
to nonlinear geometric problems such as curves and
surfaces have exposed many new issues:
non-robustness issues,
treatment of degeneracy,
computation of curves and surfaces,
algebraic computation,
numerical techniques.
All these occur in the fertile "**CAN**"
(the interface between **C**ombinatorial,
**A**lgebraic and **N**umerical computation).

Lecture Notes will be provided.
No previous background in Computational Geometry
or Algebraic Computation is assumed.
An advance course in algorithms is required.
Programming in C/C++ will be required.

Students naturally ask about the relation to a
similar course
I had given earlier. Although the motivation hasn't changed, the
present course will be more theoretical and algebraic.
About half of this course will focus on the theory of algebraic curves.

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Textbook and References

- Lecture Notes are partly taken from my manuscript with Kurt Mehlhorn,
Robust Geometric Computation
- The only textbook we require is
**H.Edelsbrunner**, *Geometry and Topology for Mesh Generation*,
Cambridge Press, 2001.

We will cover slightly over 1/2 of this book.

- Mathematical background for Curves comes from two books:
**R.J.Walker**, *Algebraic Curves*,
Springer-Verlag, Berlin-New York 1978.

**J.W.Bruce and P.J.Giblin**, *Curves and Singularities*,
Cambridge University Press (2nd Edition), 1992.

[Walker] treats the algebraic theory and [Bruce-Giblin]
treats the analytic (differential) aspects of curves.
We will cover about 1/2 of [Walker], and even less from [Bruce-Giblin].

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Course Work

Grade is based on 2 tests (20%+30%) and homework (50%).

Homework includes programming assignments.

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

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Some Useful Links