SpaceMesh: A Continuous Representation for Learning Manifold Surface Meshes

TL;DR

SpaceMesh introduces a novel neural network-based method for directly generating complex, manifold polygonal meshes with guaranteed local structure, enabling diverse, high-quality mesh generation and advanced geometry processing.

Contribution

It proposes a continuous latent connectivity space at each mesh vertex, allowing direct, flexible, and topologically general mesh generation with guaranteed manifoldness.

Findings

Generates diverse, high-quality meshes from datasets

Ensures edge-manifoldness through cyclic neighbor relationships

Enables effective learning of geometry processing tasks like mesh repair

Abstract

Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup lacking local structure. This work presents a scheme to directly generate manifold, polygonal meshes of complex connectivity as the output of a neural network. Our key innovation is to define a continuous latent connectivity space at each mesh vertex, which implies the discrete mesh. In particular, our vertex embeddings generate cyclic neighbor relationships in a halfedge mesh representation, which gives a guarantee of edge-manifoldness and the ability to represent general polygonal meshes. This representation is well-suited to machine learning and stochastic optimization, without restriction on connectivity or topology. We first explore the basic properties of this representation, then use it to fit distributions of meshes from large datasets. The resulting models generate diverse meshes with tessellation structure learned from the dataset population, with concise details and high-quality mesh elements. In applications, this approach not only yields high-quality outputs from generative models, but also enables directly learning challenging geometry processing tasks such as mesh repair.