Algebraic Distance Field for Meshless Analysis of Free Form CAD Models

Abstract

In the class of problems containing embedded boundaries, the fields approximating behavior on the boundaries are often blended with approximations built on the underlying domain using weight functions. For example, analysis of objects in which bounding surfaces are embedded into regularly structured grids, or when the boundaries are moved by the governing physics as in crack propagation or solidification problems. The blending weight functions in the approximations are typically dependent on the distance from the bounding surface. For general domains, bounded by free form curves or surfaces, the distance fields have to be constructed numerically. This may require either a polytope approximation to the boundary and/or an iterative solution to determine the exact distance to the boundary. In this paper, we describe a purely algebraic, and computationally efficient, technique for constructing distance measures as level sets from Non-Uniform Rational B-Splines (NURBS) boundaries that retain the geometric exactness of the boundaries while eliminating the need for iterative distance calculation.