Geometric Modelling Using Non-Uniform Catmull-Clark Surfaces

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For many years, the de-facto standard method for representing geometric shapes in a computer has been non-uniform rational B-splines (NURBS). However, NURBS have some well-known limitations. One of them is the surface intersection problem: if you intersect two NURBS surfaces, the result cannot be represented exactly as a trimmed NURBS surface for reasons that can be proven using algebraic geometry. This project will explore ways of converting NURBS surfaces into non-uniform Catmull-Clark surfaces (NURCC) without data-loss, and how to express the intersection of two NURCCs as a single NURCC. A second problem with NURBS is that they cannot seamlessly represent shapes with arbitrary topological complexity. This project will explore how to represent the union of two or more NURBS surfaces as a single continuous NURCC surface.