Exact predicates, exact constructions and combinatorics for mesh CSG

TL;DR

This paper presents an exact mesh intersection algorithm that accurately computes boolean operations and CSG on polygon soups using specialized predicates, exact representations, and remeshing techniques, improving robustness and precision.

Contribution

It introduces a comprehensive, exact mesh intersection method with new geometric kernels and a robust approach to handle complex configurations in CSG and mesh repair.

Findings

The algorithm accurately computes mesh intersections and boolean operations.

It outperforms previous methods on standard datasets.

The proposed kernels effectively handle complex geometric configurations.

Abstract

This article introduces a general mesh intersection algorithm that exactly computes the so-called Weiler model (also called an arrangement) and that uses it to implement boolean operations with arbitrary multi-operand expressions, CSG (constructive solid geometry) and some mesh repair operations. From an input polygon soup, the algorithm first computes the co-refinement, with an exact representation of the intersection points. Then, the decomposition of 3D space into volumetric regions (Weiler model) is constructed, by sorting the facets around the non-manifold intersection edges (radial sort), using specialized exact predicates. Finally, based on the input boolean expression, the triangular facets that belong to the boundary of the result are classified. To implement all the involved predicates and constructions, two geometric kernels are proposed, tested and discussed (arithmetic expansions and multi-precision floating-point). As a guiding principle,the combinatorial information shared between each step is kept as simple as possible. It is made possible by treating all the particular cases in the kernel. In particular, triangles with intersections are remeshed using the (uniquely defined) Constrained Delaunay Triangulation, with symbolic perturbations to disambiguate configurations with co-cyclic points. It makes it easy to discard the duplicated triangles that appear when remeshing overlapping facets. The method is tested and compared with previous work, on the existing "thingi10K" dataset (to test co-refinement and mesh repair) and on a new "thingiCSG" dataset made publicly available (to test the full CSG pipeline) on a variety of interesting examples featuring different types of "pathologies"