Zoomorphic Design, Interchangeable Components, and Approximate Dissections: Three New Computational Tools for Open-Ended Geometric Desig

This thesis introduces three new computational tools that employ geometric methods to solve open-ended design problems, an emerging trend in Computer Graphics modeling research.;First, we present a computational tool for the design of zoomorphic objects---man-made objects that possess the form or appearance of an animal. Given a man-made shape with desirable functional qualities and an organic shape with desirable animalistic qualities, our tool geometrically merges the two shapes, incorporating the salient features of the organic shape while preserving the functionality of the man-made shape.;Second, inspired by mix-and-match toys such as Mr. Potato Head, we introduce a computational tool for designing interchangeable components that can form different objects with a coherent appearance. Our tool works by deforming and partitioning a set of initially incompatible input models. A key challenge is the novel geometric problem of minimally deforming the models and partitioning them such that the resulting components connect smoothly.;Third, we present a computational tool for creating geometric dissections, a set of pieces that can be re-arranged to form two distinct shapes. Previous techniques for creating dissections are limited to forming very simple or geometrically ideal shapes, whereas ours supports complex naturalistic shapes.;We experiment with and evaluate the above three tools in a variety of applications.