Convex polyhedral meshing for robust solid modeling

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.

Automated summary

The study introduces a new technique for creating a mesh of convex polyhedra representing the interior volume of a triangulated input surface. This approach is highly tolerant to defects in the input and ensures that the input surface is accurately represented as the union of polygonal facets of the output volume mesh. By leveraging the concept of indirect geometric predicate, the algorithm provides a combination of robustness and speed that enables the practical implementation of robust yet flexible solid modeling systems. Extensive testing on the Thingi10k dataset has demonstrated that the method outperforms existing techniques in terms of robustness, precision, and performance.