Geometric constraint solver using multivariate rational spline functions

Abstract

We present a new approach to building a solver for a set of geometric constraints represented by multivariate rational functions. The constraints are formulated using inequalities as well as equalities. When the solution set has dimension larger than zero, we approximate it by fitting a hypersurface to discrete solution points. We also consider a variety of constraint solving problems common in geometric modeling. These include computing ray-traps, bisectors, sweep envelopes, and regions accessible during 5-axis machining.