Algorithms for Data-Driven Geometric Stylization & Acceleration

Abstract

In this thesis, we investigate computer algorithms for creating stylized 3D digital content and numerical tools for processing high-resolution geometric data.

This thesis first addresses the problem of geometric stylization. Existing 3D content creation tools lack support for creating stylized 3D assets. They often require years of professional training and are tedious for creating complex geometries. One goal of this thesis is to address such a difficulty by presenting a novel suite of easy-to-use stylization algorithms. This involves a differentiable rendering technique to generalize image filters to filter 3D objects and a machine learning approach to renovate classic modeling operations. In addition, we address the problem by proposing an optimization framework for stylizing 3D shapes. We demonstrate how these new modeling tools can lower the difficulties of stylizing 3D geometric objects.

The second part of the thesis focuses on scalability. Most geometric algorithms suffer from expensive computation costs when scaling up to high-resolution meshes. The computation bottleneck of these algorithms often lies in fundamental numerical operations, such as solving systems of linear equations. In this thesis, we present two directions to overcome such challenges. We first show that it is possible to coarsen a geometry and enjoy the efficiency of working on coarsened representation without sacrificing the quality of solutions. This is achieved by simplifying a mesh while preserving its spectral properties, such as eigenvalues and eigenvectors of a differential operator. Instead of coarsening the domain, we also present a scalable geometric multigrid solver for curved surfaces. We show that this can serve as a drop-in replacement of existing linear solvers to accelerate several geometric applications, such as shape deformation and physics simulation.

The resulting algorithms in this thesis can be used to develop data-driven 3D stylization tools for inexperienced users and for scaling up existing geometry processing pipelines.