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Switching Function Based Representation — an Alternative to Quadtree Encoding for Manufacturing Systems

Authors
Journal
CIRP Annals - Manufacturing Technology
0007-8506
Publisher
Elsevier
Publication Date
Volume
34
Issue
1
Identifiers
DOI: 10.1016/s0007-8506(07)61748-x
Disciplines
  • Mathematics

Abstract

In many CAD/CAM applications associated with manufacturing processes it is necessary not only to perform many set (Boolean) operations, but also to geometrically compare two objects to each other and to analyze, from a functionality point of view, any differences between them. One particular example is NC part program verification whereby a part “machined” via simulation is compared against a desired part already stored in a computer data base. For such applications it is advantageous to use volumetric modelers and Spatial Ennumeration techniques, such as Octree Encoding. In this paper a new concept for geometric modeling data structure is proposed as an alternative to Octree encoding. This data structure is based upon object representation via switching functions in a Gray coded space and oriented towards fast performing of set operations. The memory requirements for both Quadtree and for 2-dimensional switching function are analyzed. Although Quadtree is superior for worst case analysis, it is not necessarily so for practical cases.

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