SBIR Phase I: An Efficient Data Structure for R-Set Solids

*9661483黄这个小型企业创新研究第一阶段项目将为r集实体开发一种高效的数据结构，然后作为核心开发紧凑、可嵌入的3D几何引擎，用于2D到3D遗留工程数据转换、特征解释、几何推理、基于模拟的设计和医疗系统建模等应用。本文的研究将为非流形实体的表示提供科学和工程基础。它还将为需要嵌入式非流形实体模型表示、操作和推理的应用程序提供急需的工具包。传统的流形边界表示法不能表示非流形实体，非流形实体是由两个流形实体之间的正则化并集或差分运算自然产生的。在基本实体造型操作下，流形实体不闭合；r集实体是闭合的。最近关于r-集合实体的充分拓扑信息要求的研究为r-集合边界表示提供了具体的设计要求。组合分析的进步提供了基于设计要求系统地识别有效数据结构的技术。工业和学术研究中的许多CAD/CAE/CAM和医学成像3-D应用需要紧凑、可嵌入的3-D非流形几何引擎，而当前的商业实体建模系统并不是为此而设计的。这项研究的最终产品瞄准了这个市场。***

*** 9661483 Hwang This Small Business Innovation Research Phase I project will develop an efficient data structure for r-set solids that can then serve as the core to develop a compact, embeddable 3D geometric engine for applications such as 2D to 3D legacy engineering data conversion, feature interpretation, geometric reasoning, simulation based design, and medical systems modeling. This research will contribute to the science and engineering base in the representation of non-manifold solids. It will also provide a much needed toolkit for applications requiring embedded non-manifold solid model representation, manipulation, and reasoning. Traditional manifold boundary representations cannot represent non-manifold solids which result naturally from some regularized union or difference operations between two manifold solids. Manifold solids are not closed under fundamental solid modeling operations; r-set solids are. Recent research in sufficient topological information requirements for r-set solids provide concrete design requirements for r-set boundary representations. Advances in combinatorial analysis provide techniques to systematically identify an efficient data structure based on the design requirements. Many CAD/CAE/CAM and Medical Imaging 3-D applications in industry and academic research need a compact, embeddable 3-D non-manifold geometry engine that current commercial solid modeling systems are not designed for. The final product of this research targets that market. ***