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Non-uniform subdivision surfaces

非均匀细分曲面

基本信息

批准号：
EP/E025889/1
负责人：
Neil Dodgson
金额：
$ 45.44万
依托单位：
University of Cambridge
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2007
资助国家：
英国
起止时间：
2007 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FE025889%2F1
关键词：
Non uniform subdivision surfaces

项目摘要

The current standard representation for free-form surfaces, as used in aerospace, shipbuilding, automotive design and increasingly in consumer items, is the non-uniform rational B-spline (NURBS), which specifies a shape in terms of a regular grid of control points. A newer representation, subdivision surfaces, promises to provide significant advantages: in particular, they do not insist on total regularity of grid, thus allowing a shape to be defined more naturally by grids which locally follow the features of the shape. A simple example is the bottom of the windscreen pillar of a car, where the flow of the shape down the pillar needs to be blended with the fore-and-aft flow of the shape of the side of the car. A NURBS-based modelling system requires that the geometry be specified as a set of separate NURBS pieces. These must be laboriously joined together to ensure appropriate mathematical properties (e.g. continuity of curvature) across the joins and such properties can, in general, only be achieved approximately. A subdivision-based system, by contrast, handles such situations as part of the basic mechanism. The problem that prevents their wide use in the computer-aided design industry is that they are not a true superset of NURBS, being based on uniform grid theory. We intend to address the generalisation of subdivision to the non-uniform case, thus opening the way for the acceptance of this generalisation as the next standard. There are three strands to the proposed research: (a) extending subdivision to the non-uniform, rational case, which will make subdivision a true superset of NURBS for low orders (in particular the widely used cubics) for closed surfaces and the interiors of open surfaces; (b) extending subdivision to handle edge conditions at the edges of mesh pieces in analagous ways to NURBS so that open surfaces can be handled in their entiriety; (c) extending subdivision to handle the higher orders which are used in some computer-aided design systems, in particular to quintics.

自由曲面的当前标准表示形式（用于航空航天、造船、汽车设计以及越来越多的消费品）是非均匀有理 B 样条 (NURBS)，它根据控制点的规则网格指定形状。一种较新的表示形式，即细分曲面，有望提供显着的优势：特别是，它们不坚持网格的完全规则性，从而允许通过局部遵循形状特征的网格更自然地定义形状。一个简单的例子是汽车挡风玻璃支柱的底部，沿着支柱的形状流动需要与汽车侧面形状的前后流动混合。基于 NURBS 的建模系统要求将几何体指定为一组单独的 NURBS 片段。这些必须费力地连接在一起，以确保连接处具有适当的数学属性（例如曲率连续性），而这些属性通常只能近似实现。相比之下，基于细分的系统将这种情况作为基本机制的一部分来处理。阻碍它们在计算机辅助设计行业广泛使用的问题是它们不是基于均匀网格理论的 NURBS 的真正超集。我们打算解决非均匀情况下细分的泛化问题，从而为接受这种泛化作为下一个标准开辟道路。拟议的研究分为三个部分：（a）将细分扩展到非均匀、理性的情况，这将使细分成为闭合曲面和开放曲面内部的低阶（特别是广泛使用的立方体）的 NURBS 的真正超集； (b) 以与 NURBS 类似的方式扩展细分以处理网格块边缘的边缘条件，以便可以完整地处理开放曲面； (c) 扩展细分以处理一些计算机辅助设计系统中使用的高阶，特别是五次方程。