Fast, Exact, Linear Booleans

Abstract

We present a new system for robustly performing Boolean operations on linear, 3D polyhedra. Our system is exact, meaning that all internal numeric predicates are exactly decided in the sense of exact geometric computation. Our BSP-tree based system is 16-28× faster at performing iterative computations than CGAL's Nef Polyhedra based system, the current best practice in robust Boolean operations, while being only twice as slow as the non-robust modeler Maya. Meanwhile, we achieve a much smaller substrate of geometric subroutines than previous work, comprised of only 4 predicates, a convex polygon constructor, and a convex polygon splitting routine. The use of a BSP-tree based Boolean algorithm atop this substrate allows us to explicitly handle all geometric degeneracies without treating a large number of cases.

Research and application of Boolean operation for triangular mesh model of underground space engineering—Boolean operation for triangular mesh model

“…However, this method is memory occupied. Reference is designed for sculpting, which is used for BSP. However, most of the systems are likely to use B‐reps, not BSP trees.…”

BSP-fields: An exact representation of polygonal objects by differentiable scalar fields based on binary space partitioning

“…This can be avoided by switching to pure predicate evaluation based on initial plane equations as discussed in [34] [2]. This is another area of our future research.…”

Toward Better Surface Tracking for Fluid Simulation

“…8 However, geometrically exact continuous collision detection (that is, detecting whether moving geometry comes into contact) had been less studied. Work had been done on producing robust, but not exact, collision tests, 3 but these robust tests almost always rely on setting a userdefined safety parameter to account for numerical error in the geometric computations.…”