Research in Solid Modeling: Boundary-to-CSG Conversion

在20世纪70年代，实体建模作为一种工业上可行的技术的发展是由实体上布尔运算的理论和算法的发展所推动的，即将构造（CSG）表示转换为边界表示（B-reps）。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合理的，并且已经在实验中实现了，但几个重要的实际问题仍未解决。本研究通过以下目标来解决这些问题：(1)开发明显更好的基于细胞的BCSG转换算法；(2)开发公开可用的BCSG实现，最初用于自然二次曲面领域，可用于一个或多个开放架构（即公共）B-rep建模系统；(3)理论和技术的发展，使用新的代数补丁和构造壳表示，使BCSG转换适应自由形状固体。这项研究将重新建立CSG作为工业上可行的实体表示，并将使完全对称的双表示建模系统得以建立，这应该比今天的b -表示系统更强大。

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.