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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/4805 |
| Date | 25 April 2007 |
| Creators | Ouchi, Koji |
| Contributors | Friesen, Donald, Keyser, John |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 838575 bytes, electronic, application/pdf, born digital |
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