Convex polyhedral meshing for robust solid modeling

TL;DR

This paper presents a robust method for creating convex polyhedral meshes from complex, defect-laden surfaces, enabling reliable solid modeling operations with high efficiency and accuracy.

Contribution

The authors introduce a novel convex polyhedral meshing technique that tolerates input defects and guarantees exact surface representation, improving robustness and performance in solid modeling.

Findings

Successfully processed all Thingi10k models with high robustness.

Outperforms existing methods in precision and speed.

Enables reliable boolean and Minkowski sum operations on defective inputs.

Abstract

We introduce a new technique to create a mesh of convex polyhedra representing the interior volume of a triangulated input surface. Our approach is particularly tolerant to defects in the input, which is allowed to self-intersect, to be non-manifold, disconnected, and to contain surface holes and gaps. We guarantee that the input surface is exactly represented as the union of polygonal facets of the output volume mesh. Thanks to our algorithm, traditionally difficult solid modeling operations such as mesh booleans and Minkowski sums become surprisingly robust and easy to implement, even if the input has defects. Our technique leverages on the recent concept of indirect geometric predicate to provide an unprecedented combination of guaranteed robustness and speed, thus enabling the practical implementation of robust though flexible solid modeling systems. We have extensively tested our method on all the 10000 models of the Thingi10k dataset, and concluded that no existing method provides comparable robustness, precision and performances.