Fast Exact Booleans for Iterated CSG using Octree-Embedded BSPs (English)

Abstract We present octree-embedded BSPs, a volumetric mesh data structure suited for performing a sequence of Boolean operations (iterated CSG) efficiently. At its core, our data structure leverages a plane-based geometry representation and integer arithmetics to guarantee unconditionally robust operations. These typically present considerable performance challenges which we overcome by using custom-tailored fixed-precision operations and an efficient algorithm for cutting a convex mesh against a plane. Consequently, BSP Booleans and mesh extraction are formulated in terms of mesh cutting. The octree is used as a global acceleration structure to keep modifications local and bound the BSP complexity. With our optimizations, we can perform up to 2.5 million mesh-plane cuts per second on a single core, which creates roughly 40-50 million output BSP nodes for CSG. We demonstrate our system in two iterated CSG settings: sweep volumes and a milling simulation.

Highlights • Scalable high-performance CSG via octree-embedded BSPs. • Cutting-based BSP Booleans for iterated CSG. • Robust and efficient BSP to mesh conversion using in-place mesh cutting. • Fast and exact plane-based geometry representation via fixed-width integer arithmetic.