Abstract
Linguistic models of physical solids have been widely studied for use in the kernels of CAD/CAM systems. These models are useful because they guarantee topological correctness of computer representations of physical solids. This papers outlines a new model, based in the graph grammars, that manipulates the bounding manifolds of physical solids. Proof of topological validity of this linguistic representation scheme proceeds as follows. First, the start graph is shown to be representative of a solid, then productions in the two dimensional grammar are shown to be syntactically complete and closed in the solids. Thus one starts with a solid topology, and any application of a graph production results in a solid topology.
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References
A. Baer, C. Eastman, and M. Henrion. Geometric modeling: a survey. Computer-aided Design, 11:253–272, 1979.
I. Braid, R. Hillyard, and I. Stroud. Stepwise construction of polyhedra in geometric modeling. In K. Brodie, editor, Mathematical Methods in Computer Graphics and Design, Academic Press, 1980.
H. Chiyokura and F. Kimura. A method of representing the solid design process. IEEE Computer Graphics and Applications, 5(3):32–41, 1985.
P. Fitzhorn. The formal languages of solid representations. ACM Transactions on Graphics, 1987. (in review).
R. Gonzalez and M. Thomason. Syntactic Pattern Recognition. Addison-Wesley, Reading, PA, 1978.
L. Levy and K. Yueh. On labelled graph grammars. Computing, 20:109–125, 1978.
W. Lin and K. Fu. A syntactic approach to 3-D object representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6:351–364, 1984.
M. Mantyla. An inversion algorithm for geometric models. Computer Graphics, 16(3):51–60, 1982.
M. Mantyla. A note on the modeling space of Euler operators. Computer Vision, Graphics, and Image Processing, 26:45–60, 1984.
M. Mantyla and R. Sulonen. GWB: a solid modeler with Euler operators. IEEE Computer Graphics and Applications, 2:17–32, 1982.
U. Montanari. Separable graphs, planar graphs and web grammars. Information Control, 16:243–267, 1970.
M. Nagl. Formal languages of labelled graphs. Computing, 16:113–137, 1976.
M. Nagl. A tutorial and bibliographical survey on graph grammars. In H. Ehrig V. Claus and G Rozenberg, editors, Graph Grammars and their Applications to CS and Biology, Springer-Verlag, 1979.
A.A.G. Requicha. Representations of rigid solids: theory, methods and systems. ACM Computing Surveys, 12:437–464, 1980.
G. Stiny and L. March. Design machines. Environment and Planning, B, 8:245–255, 1981.
P. Wilson. Euler formulas and geometric modeling. IEEE Computer Graphics and Applications, 5:24–36, 1985.
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© 1987 Springer-Verlag Berlin Heidelberg
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Fitzhorn, P. (1987). A linguistic formalism for engineering solid modeling. In: Ehrig, H., Nagl, M., Rozenberg, G., Rosenfeld, A. (eds) Graph-Grammars and Their Application to Computer Science. Graph Grammars 1986. Lecture Notes in Computer Science, vol 291. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18771-5_54
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DOI: https://doi.org/10.1007/3-540-18771-5_54
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