Learning Constrained Shape Spaces for Mesh Design

Abstract

Designing free-form structures in architecture is a difficult process, as constraints required for different building scenarios can be complex and typically require many design iterations involving multiple parties. Generating constrained three dimensional meshes through the use of neural networks provides an opportunity to simplify this process. In this paper we looked at generating constrained meshes using an autoencoder framework. Previous work had addressed methods for constraining free form quad meshes numerically, and more structured objects through the use of generative neural networks but generating free form constrained meshes has not been achieved thus far. In this work we present an autoencoder framework for generating quad meshes with constraints that fix vertices to specified points or planes. Results of mesh generation are limited to moderate, however emergent in our methodology is an additional contribution of creating an integration network that performs integrations converting quad meshes from edge length and dihedral angle representation to vertex coordinates. The performance of the integration network provides a number of benefits over numerical optimisation methods of integration, and also allows for smooth interpolation between meshes based on edge lengths and dihedral angles.