Computational Geometry and Modeling

G22.3033.007 Spring 2005

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Course Information

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 Combinatorial, Algebraic and Numerical 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.

Textbook and References

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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