Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Solid Modeling: A Historical Summary and Contemporary Assessment
IEEE Computer Graphics and Applications
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It is shown that planar, bounded regions determined by a general class of closed curves, comprised of n edges, k of which are not straight, may be represented by a binary tree with n + 2k leaves, each of which is a halfspace. At most, n+k distinct halfspaces are required. Each straight edge determines one planar halfspace and each nonstraight edge determines two halfspaces. By a suitable subdivision of the nonstraight edges, the results may be applied to almost any closed curve, but, in this case, there is not a simple, a priori upper bound on the number of leaves in the tree. These representations may be used to obtain extrusions, solids of revolution and other solid entities.