Geometric Modelling Using Non-Uniform Catmull-Clark Surfaces

使用非均匀 Catmull-Clark 曲面进行几何建模

• 批准号: 9912411
• 负责人: Thomas Sederberg
• 金额: $ 26.5万
• 依托单位: Brigham Young University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-05-15 至 2004-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9912411&HistoricalAwards=false
• 关键词: Geometric; Modelling; Using; Non; Uniform

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.

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-Splines(NURBS)。但是，NURBS有一些众所周知的限制。其中之一是曲面相交问题：如果两个NURBS曲面相交，由于可以使用代数几何证明的原因，结果无法精确表示为修剪的NURBS曲面。该项目将探索如何在不丢失数据的情况下将NURBS曲面转换为非均匀Catmull-Clark曲面(NURCC)，以及如何将两个NURCC的交集表示为一个NURCC。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。这个项目将探索如何将两个或多个NURBS曲面的并集表示为单个连续的NURCC曲面。