Comparison of 3D Models (Jakob Schödl)

Abstract:

In this thesis, I explore different methods for the comparison of 3D models, with the aim of benchmarking the capabilities of Large Language Models (LLMs) in generating 3D shapes. OpenSCAD, a descriptive functional language for CAD models, was used as the representation of the compared and generated shapes.

I decided to implement three comparison approaches: Firstly, the comparison of a set of global features of the triangle mesh, such as its volume or bounding box ratios; secondly, a comparison based on the geometric intersection of both 3D models; and thirdly, an analysis of the topological structure using Multiresolutional Reeb Graphs (MRGs).

For evaluating the approaches, six types of perturbations were applied to numerous 3D shapes. The distance of the modified shapes to their unmodified version was used to characterise their reaction to different possible faults in LLM-generated 3D models, such as missing parts or invalid proportions.

Each of the methods capture different aspects of similarity. While the volumetric distance yields results that are easily predictable and explainable, the comparison of global features is the computationally most lightweight solution. Comparing MRGs correlates with the human perception of similarity the most, as the topological structure of an object is taken into account.

This work provides a foundation for benchmarking and fine-tuning any LLMs that are used for generating 3D models.

STARTING

David Fresacher