Geometric Approaches for 3-Dimensional Shape Approximation

Abstract

Having 3D simulation models which represent the visual geometry and contact dynamics of arbitrary objects is important for achieving robust planning and control for robotic manipulation tasks and sim2real transfer. Currently, the most common solution for obtaining such models is generating them by hand. However, this process is not generalizable or scalable. Neural Radiance Fields (NeRFs) are able to generate photorealistic 3D renderings of arbitrary objects based only on a few RGB images. 3D meshes that are extracted from NeRFs are often complex and hard to use in simulation. In this thesis we propose geometric approaches based on convex optimization for simplifying such meshes into unions of primitive shapes so that they are faster and more accurate to simulate.