Geometric Modelling Using Non-Uniform Catmull-Clark Surfaces

多年来，在计算机中表示几何形状的事实上的标准方法一直是非均匀有理B样条（NURBS）。然而，NURBS有一些众所周知的局限性。其中之一是曲面相交问题：如果你相交两个NURBS曲面，结果不能完全表示为修剪的NURBS曲面，原因可以用代数几何证明。 本计画将探讨如何将NURBS曲面转换成不损失数据的非均匀Catmull-Clark曲面，以及如何将两个非均匀Catmull-Clark曲面的交线表示成单一的非均匀Catmull-Clark曲面。 NURBS的第二个问题是它们不能无缝地表示具有任意拓扑复杂性的形状。 这个项目将探讨如何将两个或多个NURBS曲面的并集表示为一个连续的NURBS曲面。

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.