On the Complexity of the CSG Tree Extraction Problem

TL;DR

This paper examines the computational complexity involved in deriving Constructive Solid Geometry (CSG) trees from point-cloud data and primitive shapes, highlighting the challenges in the search space for this problem.

Contribution

It provides an analysis of the complexity of the CSG tree extraction problem, a topic not extensively explored before.

Findings

The search space for CSG tree extraction is highly complex.

Determining optimal CSG trees is computationally challenging.

The paper clarifies the theoretical difficulty of the problem.

Abstract

In this short note, we discuss the complexity of the search space for the problem of finding a CSG expression (or CSG tree) corresponding to an input point-cloud and a list of fitted solid primitives.