曲面立体共存モデラの位相数学モデルと「集合演算」(第2報) : 曲面に拡張された「集合演算」

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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.
公益社団法人精密工学会の論文
1992-07-05