  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.
