Research in Solid Modeling: Boundary-to-CSG Conversion

实体建模作为一种工业上可行的技术的发展速度是由20世纪70年代S对实体进行布尔运算的理论和算法的发展所致，即将构造性(CSG)表示转换为边界表示(B-REP)。在夏皮罗和沃斯勒1989-91年的工作之前，从边界到CSG(称为BCSG)的逆转换的理论和算法在很大程度上是未知的。他们基于细胞的方法在数学上是可靠的，并已在实验中实施，但几个重要的实际问题仍然悬而未决。这项研究通过以下目标解决这些问题：(1)开发基于单元的BCSG转换的显著更好的算法；(2)开发BCSG的公开可用实现，最初用于自然二次曲面域，可用于一个或多个开放体系结构(即公共)B-REP建模系统；以及(3)理论和技术的发展，使用新的代数面片和构造壳表示，使BCSG转换为适应自由形式的固体。这项研究将使CSG重新成为工业上可行的固体表示，并将使完全对称的双重表示建模系统得以建立，该系统应该比今天的仅B-REP系统强大得多。

The development of solid modeling as an industrially viable technology was paced by the development, in the 1970's, of theory and algorithms for boolean operations on solids, i.e. for converting constructive (CSG) representations into boundary representations (B-reps). Theory and algorithms for the inverse conversion, from boundary to CSG (called BCSG), were largely unknown prior to the work of Shapiro and Vossler in 1989-91. Their cell-based methods are mathematically sound and have been implemented experimentally, but several important practical issues remain open. This research addresses those issues through the following goals: (1) development of significantly better algorithms for cell-based BCSG conversion; (2) development of a publicly available implementation of BCSG, initially for a domain of natural quadric surfaces, that is usable with one or more open architecture (i.e. public) B-rep modeling systems; and (3) development of theory and techniques, using new algebraic-patch and constructive-shell representations, to enable BCSG conversion to accommodate freeform solids. This research will re-establish CSG as an industrially viable representation for solids, and will enable fully symmetric dual- representation modeling systems to be built which should be considerably more powerful than today's B-rep-only systems.