Fast Exact Booleans for Iterated CSG using Octree-Embedded BSPs

TL;DR

This paper introduces octree-embedded BSPs, a robust and efficient volumetric data structure for iterated CSG operations, achieving high performance through optimized algorithms and acceleration structures.

Contribution

The paper presents a novel octree-embedded BSP data structure with robust plane-based geometry and optimized algorithms for fast iterated CSG operations.

Findings

Performs up to 2.5 million mesh-plane cuts per second

Creates 40-50 million BSP nodes for CSG

Demonstrates efficiency in sweep volumes and milling simulation

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.