| Abstract | Current geometric and solid modeling systems use semi-algebraic sets
for defining the boundaries of solid objects, curves and surfaces, geometric constraints with mating relationship in a mechanical assembly, physical contacts between objects, collision detection. It turns out that performing many of the geometric operations on the solid boundaries or interacting with geometric constraints is reduced to finding common solutions of the polynomial equations. Current algorithms in the literature based on symbolic, numeric and geometric methods suffer from robustness, accuracy or efficiency problems or are limited to a class of problems only.
In this paper we present algorithms based on multipolynomial resultants and matrix computations for solving polynomial systems. These algorithms are based on the linear algebra formulation of resultants of equations and in many cases there is an elegant relationship between the matrix structures and the geometric formulation. The resulting algorithm and highlight the performance of the algorithms on different examples. |
