Exact polynomial system solving for robust geometric computation /
| Main Author: | |
|---|---|
| Other Authors: | , |
| Format: | Thesis eBook |
| Language: | English |
| Published: |
[College Station, Tex.] :
[Texas A&M University],
[2007]
|
| Subjects: | |
| Online Access: | Link to OAK Trust copy |
| Abstract: | I describe an exact method for computing roots of a system of multivariate polynomials with rational coefficients, called the rational univariate reduction. This method enables performance of exact algebraic computation of coordinates of the roots of polynomials. In computational geometry, curves, surfaces and points are described as polynomials and their intersections. Thus, exact computation of the roots of polynomials allows the development and implementation of robust geometric algorithms. I describe applications in robust geometric modeling. In particular, I show a new method, called numerical perturbation scheme, that can be used successfully to detect and handle degenerate configurations appearing in boundary evaluation problems. I develop a derandomized version of the algorithm for computing the rational univariate reduction for a square system of multivariate polynomials and a new algorithm for a non-square system. I show how to perform exact computation over algebraic points obtained by the rational univariate reduction. I give a formal description of numerical perturbation scheme and its implementation. |
|---|---|
| Item Description: | "Major Subject: Computer Science" Title from author supplied metadata (automated record created on Apr. 27, 2007.) Vita. Abstract. Electronic resource. |
| Format: | Mode of access: World Wide Web. System requirements: World Wide Web access and Adobe Acrobat Reader. |
| Bibliography: | Includes bibliographical references. |