Subdivision-based Algorithms for Surface Modeling

基于细分的曲面建模算法

• 批准号: 9988528
• 负责人: Denis Zorin
• 金额: $ 27.96万
• 依托单位: New York 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: 2000-08-15 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9988528&HistoricalAwards=false
• 关键词: Subdivision; based; Algorithms; Surface; Modeling

Subdivision was initially conceived as an extension of splines to control meshes ofarbitrary topology. Subdivision algorithms, while being more flexible and general,retain a number of useful properties of splines. Most importantly, the surfaces generatedby these algorithms have a natural hierarchical structure and are computedusing simple local rules. This allows the design of efficient hierarchical, local, andadaptive algorithms for rendering, manipulation, collision detection and intersectionof such surfaces. Subdivision surfaces are rapidly gaining wide acceptance inthe industry. In recent years, substantial progress has been made in understandingthe properties of the subdivision surfaces, especially smoothness properties. However,subdivision still lacks the body of well understood and reliable algorithmsavailable for splines and a few practically important aspects of subdivision, suchas subdivision rules for boundaries and singular features, do not have a rigoroustheoretical foundation. Aside from smoothness, no other property of subdivisionsurfaces has been studied in detail. At the same time, some fundamental limitationsof the commonly used stationary subdivision schemes became apparent. For example,practical curvature-continuous subdivision surfaces necessarily have a "flat."spot near extraordinary vertices, and the surfaces acquire ripples near vertices ofhigh valence. The proposed research has three main objectives:Advance the theory of stationary subdivision to include all important practicalcases, and develop the theory necessary to understand fairness, meshquality, and approximation properties of subdivision.Develop robust algorithms for common geometric operations such as com-puttingcollisions and intersections of subdivision surfaces;Explore nonstationary subdivision schemes which retain locality, and identifyways to improve the quality of the resulting surfaces without sacrificingthe performance.The three components are unified by a common goal: the development of asurface representation supporting highly efficient, local, hierarchical and adaptivealgorithms for geometric modeling.

细分最初被认为是样条曲线的扩展，用于控制任意拓扑的网格。细分算法虽然更加灵活和通用，但保留了样条线的许多有用属性。最重要的是，这些算法生成的表面具有自然的层次结构，并使用简单的局部规则进行计算。这允许设计高效的分层、局部和自适应算法，用于渲染、操作、碰撞检测和此类表面的相交。细分曲面正在迅速获得业界的广泛接受。近年来，在理解细分曲面的特性，特别是平滑度特性方面取得了实质性进展。然而，细分仍然缺乏可用于样条的易于理解和可靠的算法，并且细分的一些实际重要方面，例如边界和奇异特征的细分规则，没有严格的理论基础。除了平滑度之外，没有详细研究细分曲面的其他属性。与此同时，常用的固定细分方案的一些基本局限性也变得明显。例如，实际的曲率连续细分曲面必然在异常顶点附近具有“平坦”点，并且曲面在高价顶点附近获得波纹。所提出的研究有三个主要目标：推进平稳细分理论以涵盖所有重要的实际案例，并发展理解细分的公平性、网格质量和近似性质所需的理论。开发用于计算细分曲面的碰撞和相交等常见几何操作的鲁棒算法；探索保留局部性的非平稳细分方案，并确定方法 在不牺牲性能的情况下提高生成表面的质量。这三个组件由一个共同目标统一起来：开发支持高效、局部、分层和自适应几何建模算法的表面表示。