Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
439704 | Computer-Aided Design | 2011 | 10 Pages |
We present an algorithm which robustly computes the intersection curve(s) of an underconstrained piecewise polynomial system consisting of nn equations with n+1n+1 unknowns. The solution of such a system is typically a curve in Rn+1Rn+1. This work extends the single solution test of Hanniel and Elber (2007) [6] for a set of algebraic constraints from zero-dimensional solutions to univariate solutions, in Rn+1Rn+1. Our method exploits two tests: a no-loop test (NLT) and a single-component test (SCT) that together isolate and separate domains DD 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, DD is subdivided. Finally, the single components are merged together and, consequently, the topological configuration of the resulting curve is guaranteed. Several possible applications of the solver, namely solving the surface–surface intersection problem, computing 3D trisector curves, flecnodal curves or kinematic simulations in 3D are also discussed.
► Computing the intersection curve(s) of an underconstrained piecewise polynomial system. ► A generalization of the single solution test for the n×(n+1)n×(n+1) systems. ► A no-loop test guarantees that the intersection curve has no loops. ► A single-component test ensures that the sought curve consists of just one component.