Three-dimensional halfspace constructive solid geometry tree construction from implicit boundary representations

Abstract This paper presents a new method to compute constructive solid geometry (CSG) tree representations of an object whose faces consist of planar and non-planar surfaces. The algorithm described accepts as input a valid boundary representation of an object consisting of piecewise implicit surfaces, and computes a halfspace CSG representation of the object. A class of objects that are describable by the surfaces bounding them are valid input for the algorithm of this work, although methods currently exist to compute the additional information necessary to process non-describable quadric objects as well. This work builds on and complements the other work in this area, in which dominating halfspaces are used to simplify the b-rep to CSG conversion process. We include factored faces to enable the factorization of dominating halfspaces throughout the algorithm. Thus, an efficient disjoint decomposition of the solid is obtained as a matter of course in the algorithm, so that CSG minimization is generally not necessary. This work is motivated by reverse engineering of mechanical parts, in which a model of a part is recovered from information obtained by some sort of sensing technique (e.g. CAT scanning, laser range finding). The recovery of a valid CSG-tree description of an object from a boundary representation of it can provide useful information to an engineer in the area of reverse engineering and in other areas related to solid modeling as well. The CSG tree also provides a relatively neutral representation that can enhance form feature recognition and translation.

[1]  K. Tang,et al.  Algorithmic aspects of alternating sum of volumes. Part 2: Nonconvergence and its remedy , 1991, Comput. Aided Des..

[2]  Aristides A. G. Requicha,et al.  Solid modeling and beyond , 1992, IEEE Computer Graphics and Applications.

[3]  K. Tang,et al.  Algorithmic aspects of alternating sum of volumes. Part 1: Data structure and difference operation , 1991, Comput. Aided Des..

[4]  V. Shapiro,et al.  Efficient CSG Representations of Two-Dimensional Solids , 1991 .

[5]  David C. Gossard,et al.  Recognizing shape features in solid models , 1990, IEEE Computer Graphics and Applications.

[6]  I. Faux,et al.  Computational Geometry for Design and Manufacture , 1979 .

[7]  Thomas C. Bartee,et al.  Modern Applied Algebra , 1999 .

[8]  Tom Lyche,et al.  Mathematical methods in computer aided geometric design , 1989 .

[9]  Aristides A. G. Requicha,et al.  Integration of feature based design and feature recognition , 1995, Comput. Aided Des..

[10]  Donald L. Vossler.  Sweep-to-CSG Conversion Using Pattern Recognition Techniques , 1985, IEEE Computer Graphics and Applications.

[11]  D. M. Y. Sommerville.  Analytical geometry of three dimensions , 1934 .

[12]  D. P. Peterson.  Boundary to constructive solid geometry mappings: a focus on 2D issues , 1986 .

[13]  Vadim Shapiro,et al.  Separation for boundary to CSG conversion , 1993, TOGS.

[14]  Wei-Chung Lin,et al.  CSG-based object recognition using range images , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.

[15]  Vadim Shapiro,et al.  Construction and optimization of CSG representations , 1991, Comput. Aided Des..

[16]  Donald S. Fussell,et al.  Three-dimensional binary space partitioning tree and constructive solid geometry tree construction from algebraic boundary representations , 1999 .