Trimming local and global self-intersections in offset curves/surfaces using distance maps

TLDR: A robust and efficient algorithm for trimming both local and global self-intersections in offset curves and surfaces is presented, based on the derivation of a rational distance map between the original curve or surface and its offset.

Abstract: A robust and efficient algorithm for trimming both local and global self-intersections in offset curves and surfaces is presented Our scheme is based on the derivation of a rational distance map between the original curve or surface and its offset By solving a bivariate polynomial equation for an offset curve or a system of three polynomial equations for an offset surface, all local and global self-intersection regions in offset curves or surfaces can be detected The zero-set of polynomial equation(s) corresponds to the self-intersection regions These regions are trimmed by projecting the zero-set into an appropriate parameter space The projection operation simplifies the analysis of the zero-set, which makes the proposed algorithm numerically stable and efficient Furthermore, in a post-processing step, a numerical marching method is employed, which provides a highly precise scheme for self-intersection elimination in both offset curves and surfaces The effectiveness of our approach is demonstrated using several experimental results