Globally Adaptive and Locally Regular Point Discretization of Implicit Surface Geometries
Point discretization of implicitly defined curved surfaces is required throughout computer-aided design, engineering analysis, and scientific computing. These applications often impose that surfaces are sampled with local regularity and global curvature adaptivity for unambiguous geometry representation. Finding a numerically well-conditioned point discretization, however, is not trivial, even for simple analytic surfaces. We present an algorithm for finding near-optimal surface point distributions governed by a prescribed resolution field on a curved surface. The algorithm works by approximately minimizing a global potential over local point-point interactions. We leverage a high-order meshfree level-set method to implicitly describe the surface and to perform all required projections without additional surface-attractive forces. To accelerate convergence, the algorithm dynamically fuses and inserts points where a local excess or lack is detected, for which it introduces an integral support measure. We test the proposed algorithm on a variety of shapes, ranging from parametric to non-parametric surfaces. We find point discretizations with different curvature adaptivity and low deviation from the prescribed target spacing. In all cases, the presented algorithm rapidly and robustly converges to the final number and distribution of surface points.