Technical section
Extended octtree representation of general solids with plane faces: Model structure and algorithms

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Abstract

The Octtree encoding is an alternative representation scheme for solid objects that allows very simple algorithms for Boolean set operations. Extended Octtrees, which contain three extra node types (Face, Edge and Vertex) in addition to the classical nodes, inherit this advantage while being much more compact and allowing the exact representation of polyhedral objects. In the first part of this paper, the initial Extended Octtree model is generalized in order to support general vertices with n faces. After this, specific algorithms for the Boolean operations and Octtree visualization are presented. In particular, the algorithm for Boolean set operations is simple and treats all particular cases; it is based on the direct computation of the result of the operation between terminal nodes in a set of simple situations, while more complex cases are treated by subdivision. Some examples are presented, and the performance of the implemented algorithm is discussed.

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