Topological Model and "Set-Operations" in a Surface- and -Solid Modeller. (2nd Report). "Set Operations" Extended to Surfaces.
鈴木 建彦, Shigeki Tanimoto · Journal of the Japan Society for Precision Engineering · 1992
This paper describes the concept, necessity, an algorithm and topological meaning of an extended set operation in a surface-and-solid model.In this model the operations not only between two solids, but also between a solid and a surface or between two surfaces are performed.One of the most important operations in the model is an extended set operation.But the set operation including a surface can not be expressed in the form of Boolean union, difference or intersection.Hence it should not be called a set operation in itself.It is named a divide-and-join operation.It is realized by using terminal circuits, which are the boundaries of 2-dimensional cell complex.Its algorithm associates well with the theory of topology.There are three topological conditions to ensure the divide-and-join operation : (1) dividability of the two shells by an intersectional curve which has no self-intersection, (2) keepability of cell properties for each face and edge, and (3) orientability on the common terminal circuits.