# Point containment algorithms for constructive solid geometry with unbounded primitives

arXiv: https://arxiv.org/abs/2406.13030 · HTML: https://mlsanity.com/paper/2406.13030/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2024.

## Built on by (most cited first, 1 of 1)

- [GeoCAD: Local Geometry-Controllable CAD Generation with Large Language Models](https://mlsanity.com/paper/2506.10337/) (2025)

## Abstract (arXiv)

We present several algorithms for evaluating point containment in constructive solid geometry (CSG) trees with unbounded primitives. Three algorithms are presented based on postfix, prefix, and infix notations of the CSG binary expression tree. We show that prefix and infix notations enable short-circuiting logic, which reduces the number of primitives that must be checked during point containment. To evaluate the performance of the algorithms, each algorithm was implemented in the OpenMC Monte Carlo particle transport code, which relies on CSG to represent solid bodies through which subatomic particles travel. Two sets of tests were carried out. First, the execution time to generate a high-resolution rasterized image of a 2D slice of a detailed CSG model of the ITER tokamak was measured. Use of both prefix and infix notations offered significant speedup over the postfix notation that has traditionally been used in particle transport codes, with infix resulting in a 6× reduction in execution time relative to postfix. We then measured the execution time of neutron transport simulations of the same ITER model using each of the algorithms. The results and performance improvements reveal the same trends as for the rasterization test, with a 4.59× overall speedup using the infix notation relative to the original postfix notation in OpenMC.