Ph.D Thesis

Ph.D StudentPoranne Roi
SubjectTopics in Shape Optimization and Exploration
DepartmentDepartment of Computer Science
Supervisor PROF. Chaim Craig Gotsman
Full Thesis textFull thesis text - English Version


Shapes are the primary objects of research in the field of geometry processing. Shape optimization is the task of improving a defined set of features of a shape, while adhering to some rules. Shape explorations concerns with finding variations to a shape or deforming it, using a user friendly interface.

In the first part of this work, we discuss two classical problems in geometry processing. The first problem is surface reconstruction from point clouds, where a surface is fit to a set of points, sampled from a real world object. We provide a generalization of the well-known Radial Basis Function approach and show that it outperforms other surface reconstruction algorithms. The second problem is 2D shape deformation, where we derive a new type of barycentric coordinates that have higher order interpolation abilities.

The second part of this work is more oriented toward the field known as architectural geometry. We discuss Polyhedral Meshes (PMs), i.e. meshes with planar faces, which are commonly used in of PMs, but nonetheless general enough to handle many types of constraints, which can be solved in interactive times. In addition, we analyze the manifold of PMs, and show that it can be decomposed into a set of maximal linear subspaces. Based on this decomposition, we deliver new tools for exploring the manifold, that are more powerful than the state-of-the-art.