Improved Conceptual Design Using Implicit Solid Modeling

使用隐式实体建模改进概念设计

• 批准号: 9312932
• 负责人: Duane Storti
• 金额: $ 25.57万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-09-15 至 1997-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9312932&HistoricalAwards=false
• 关键词: Improved; Conceptual; Design; Using; Implicit

9312932 Storti The goal of this project is to create a robust conceptual design system in which solids are described by a single potential function (rather than approximated by a multitude of faces, volume elements, or surface patches as in conventional modelers). This formulation of geometric design, called implicit solid modeling (ISM), offers three distinct advantages: (1) A straightforward approach to solid modeling which is intuitive and easy to learn. (2) All of the basic data which defines the shape of a solid is specified and manipulated using exact, rational arithmetic which guarantees that geometric property evaluation tests performed are robust and reliable. (3) Point/solid classification (determining whether a point lies inside, on the surface of, or outside a given solid), the fundamental geometric test traditionally used in solid modeling, reduces to simply evaluating the potential function and comparing its value to a specified threshold level. Moverover, evaluation of the potential function inherently provides (at no additional computational cost) a measure of the distance from the given point to the surface of the solid, which is exactly the information needed for intelligent engineering design. During the course of this research, an effective ISM conceptual design system based on exact computation is created and used to explore ways in which the distance measure provided by the ISM potential function can be used to develop improved engineering design tools. The underlying exact computations are achieved using a computer algebra system, and swept solids (essential for modeling offset surfaces and path planning) are created using tech niques from algebraic geometry including envelope theory and elimination theory. A polygonizer is incorporated to provide capability for rapid visualization on standard graphics hardware and availability of a suitable output format so that the ISM system can serve as a conceptual preprocessor for conventional solid modeling systems and rapid prototyping systems based on stereolithography. While the primary implications of this research involve advances in traditional areas of engineering design such as sculptured surface description, optimal layout, packaging, and motion planning, an additional goal of this project involves broadening the scope of engineering design research through enhanced interaction with investigators in the fields of computer algebra and algebraic geometry. ***

9312932 Storti本项目的目标是创建一个健壮的概念设计系统，其中实体由单个势函数描述(而不是像传统建模工具中那样由多个面、体积元素或曲面面片近似)。这种被称为隐式实体造型(ISM)的几何设计公式具有三个明显的优点：(1)直观、易学的实体造型方法。(2)所有定义实体形状的基本数据都是使用精确、有理的算法指定和处理的，这保证了所进行的几何性质评估测试是稳健和可靠的。(3)点/实体分类(确定一个点是位于给定实体的内部、表面还是外部)，这是传统上用于实体建模的基本几何测试，简化为简单地计算势函数并将其值与指定的阈值水平进行比较。此外，势函数的评估本质上提供了从给定点到固体表面的距离的测量(不需要额外的计算成本)，这正是智能工程设计所需的信息。在本研究过程中，我们建立了一个有效的基于精确计算的ISM概念设计系统，并将其用于探索如何利用ISM势函数提供的距离度量来开发改进的工程设计工具。基本的精确计算是使用计算机代数系统实现的，扫掠实体(对建立等距曲面和路径规划是必不可少的)是使用包括包络理论和消元理论在内的代数几何中的技术来创建的。结合了多边形化器以提供在标准图形硬件上的快速可视化的能力和适当的输出格式的可用性，使得ISM系统可以用作传统实体造型系统和基于立体光刻的快速原型系统的概念预处理器。虽然这项研究的主要影响涉及到传统工程设计领域的进步，如雕塑表面描述、最优布局、包装和运动规划，但该项目的另一个目标是通过加强与计算机代数和代数几何领域的研究人员的互动来扩大工程设计研究的范围。***