Paper Info
Title
Topologically guaranteed univariate solutions of underconstrained polynomial systems via no-loop and single-component tests
Abstract
We present an algorithm which robustly computes the intersection curve(s) of an under-constrained piecewise polynomial system consisting of n equations with n + 1 unknowns. The solution of such a system is typically a curve in Rn+1. This work extends the single solution test of [6] for a set of algebraic constraints from zero dimensional solutions to univariate solutions, in Rn+1. Our method exploits two tests: a no loop test (NLT) and a single component test (SCT) that together isolate and separate domains D where the solution curve consists of just one single component. For such domains, a numerical curve tracing is applied. If one of those tests fails, D is subdivided. Finally, the single components are merged together and, consequently, the topological configuration of the resulting curve is guaranteed. Several possible application of the solver, like 3D trisector curves or kinematic simulations in 3D are discussed.
Year
DOI
Venue
2010
10.1145/1839778.1839811
Computer-Aided Design
Keywords
DocType
Volume
Underconstrained polynomial systems,Trisector curves,Flecnodal curve,Univariate solution spaces,Kinematic synthesis,Surface–surface intersection
Conference
43
Issue
ISSN
Citations 
8
Computer-Aided Design
7
PageRank 
References 
Authors
0.48
12
3
Name
Order
Citations
PageRank
Michael Barton111112.52
Gershon Elber21924182.15
Iddo Hanniel319712.98