Loop detection in surface patch intersections
Computer Aided Geometric Design
Computer Aided Geometric Design
A bibliography on roots of polynomials
Journal of Computational and Applied Mathematics
A new approach to the surface intersection problem
Computer Aided Geometric Design
Tracing surface intersections with validated ODE system solver
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Solving nonlinear polynomial systems in the barycentric Bernstein basis
The Visual Computer: International Journal of Computer Graphics
Subdivision methods for solving polynomial equations
Journal of Symbolic Computation
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
Computer Aided Geometric Design
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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.