A Survey of Methods for Converting Unstructured Data to CSG Models

TL;DR

This survey analyzes methods for recovering editable Constructive Solid Geometry (CSG) representations from unstructured 3D data, including point clouds and meshes, and juxtaposes them with alternative editable formats. It covers CAD-style conversions (polyhedron/B-rep to CSG) and extraction pipelines that proceed from primitive fitting to CSG generation, using strategies from program synthesis, evolutionary computation, and deep learning, with attention to higher-level representations such as sketches and procedural programs. It discusses the combinatorial complexity of CSG forms, introduces various expression families (DNF, UE, DTE, MTE, GE), and reviews optimization strategies aimed at reducing size and improving editability. The paper highlights practical progress, datasets, and multiple lines of future work toward more expressive, editable, and reusable solid representations, balancing fidelity with tractability and user control.

Abstract

The goal of this document is to survey existing methods for recovering CSG representations from unstructured data such as 3D point-clouds or polygon meshes. We review and discuss related topics such as the segmentation and fitting of the input data. We cover techniques from solid modeling and CAD for polyhedron to CSG and B-rep to CSG conversion. We look at approaches coming from program synthesis, evolutionary techniques (such as genetic programming or genetic algorithm), and deep learning methods. Finally, we conclude with a discussion of techniques for the generation of computer programs representing solids (not just CSG models) and higher-level representations (such as, for example, the ones based on sketch and extrusion or feature based operations).

Figures (16)

• Figure 1: Left: 3D point-cloud corresponding to a table. Middle: A CSG model for the table. Right: An edited version of the model, where the width, depth and height of the table-top were modified.
• Figure 2: Examples of inputs and data types.
• Figure 3: Illustration of natural and separating halfspaces. Left: A 2D solid. Middle: The natural halfspaces are shown in dashed lines (blue color). Right: The separating halfspaces are shown in dotted lines (red color).
• Figure 4: Illustration of fundamental products. Given the sets $A$ and $B$, the fundamental products are: $A \cap B$, $\overline{A} \cap B$, $A \cap \overline{B}$ and $\overline{A} \cap \overline{B}$.
• Figure 5: Typical pipeline for extracting a CSG expression from an input 3D point-cloud.