Boolean Operations of Simple Cellular Solid Models : Part 1,Development of a Three-Dimensional Modeling System

Abstract

Previously reported topology-based simple cellular solid models and their Boolean operations are theoretically defined. These solid models are defined by giving constraint conditions to cell complex chains having inner cells (mathematical models of objects on databases) in Euclidean space. Their Boolean operations are defined by threetuples of common subdivision operation, set operations, and cellular mapping, basic operations of cell complex chains. These solid models and their Boolean operations are applied to a three-dimensional modeler. In this modeler, Boolean operations of two solid models which have boundary elements (vertexes, deges and faces) in contact can be carried out. Deference between cellular decomposition models, boundary models and simple cellular models is discussed.