Improved Conceptual Design Using Implicit Solid Modeling

这个项目的目标是创建一个强大的概念设计系统，在这个系统中，实体由一个单一的潜在函数来描述（而不是像传统的建模器那样由大量的面、体积元素或表面斑块来近似描述）。这种几何设计的表述，被称为隐式实体建模（ISM），提供了三个明显的优势：(1)一种直观的、易于学习的实体建模方法。(2)定义固体形状的所有基本数据都是用精确、合理的算法指定和操作的，这保证了所进行的几何性能评估试验的鲁棒性和可靠性。(3)点/实体分类（确定一个点是在给定实体的内部、表面还是外部），传统上用于实体建模的基本几何测试，简化为简单地评估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，建立了一个有效的基于精确计算的ISM概念设计系统，并用于探索如何利用ISM势函数提供的距离度量来开发改进的工程设计工具。使用计算机代数系统实现底层的精确计算，并使用包括包络理论和消去理论在内的代数几何技术创建扫描固体（对建模偏移曲面和路径规划至关重要）。一个polygonizer被整合到标准图形硬件上，提供快速可视化的能力，并提供合适的输出格式，这样ISM系统就可以作为传统实体建模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意义涉及传统工程设计领域的进步，如雕刻表面描述、最佳布局、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，扩大工程设计研究的范围。＊＊＊

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. ***