Minkowski sum computation of B-spline surfaces

Abstract

We propose a method for computing the Minkowski sum of two free-form surfaces, given in a tensor product B-spline representation in R3. The Minkowski sum (typically a three dimensional volume), is represented by its boundary surface(s), also referred to as the envelope. The envelope is obtained via an algebraic equation solving approach (in the parameter space of the input geometries), followed by mapping the parametric solution to Euclidean space and filtering of redundant solution patches. The suggested method is applicable to a fairly general class of input surfaces, allowing non-convex regions, boundary curves and C1 discontinuities, while providing a solution with topological guarantee. Test results are provided, demonstrating the suggested method using a triangular mesh approximation of the Minkowski sum envelope surface.