BOX-SKELETONS OF DISCRETE SOLIDS

The Medial Axis Transform (MAT) was defined by Plum in the 1960s as an alternate description of the shape of an object. Since then, its pote ntial applicability in a wide range of engineering domains has been ac knowledged. However, this potential has never quite been realized, exc ept recently in two dimensions. One reason is the difficulty in defini ng algorithms for finding the MAT, especially in three dimensions. Ano ther reason is the lack of incentive for modelling designs directly in MATs. Given this impasse, some lateral thinking appears to be in orde r. Perhaps the MAT per se is not the only skeleton which can be used. Are there other, more easily derived skeletons, which share those prop erties of the MAT which are of interest in engineering design? In this work, we identify a set of properties of the MAT which, we argue, are of primary interest. Briefly, these properties are dimensional reduct ion (in the sense of having no interior), homotopic equivalence, and i nvertibility. For the restricted class of discrete objects, we define an algorithm for identifying a point set, called a skeleton, which sha res these properties with the MAT. Furthermore, this skeleton is to th e box-norm (L(infinity) norm) what the MAT is to the Euclidean norm, a nd hence the deviation of this skeleton from the MAT is bounded. The a lgorithm will be developed for both 2D and 3D cases. Proofs of correct ness of the algorithm shall be indicated. The use of this skeleton in automated numerical analysis of injection moulded parts shall be demon strated on industrial-sized parts. The use of the 3D skeleton in aidin g automatic mesh generation for finite element analysis is also of int erest, and shall be discussed. Copyright (C) 1996 Elsevier Science Ltd