Abstract
Two powerful methods are shown for the construction of complex solid shapes with free-form surfaces: local modification operations for constructing rough shapes and their smoothing, and complete set operations among curved objects. For actually realizing these methods, it is necessary to develop a basic theory for treating problems which cannot be solved thoroughly by the conventional theories, such as smooth connection of surface patches under various restrictive conditions, and generation of irregular (nonrectangular) surface patches. Some theoretical results are described which are based on the control point approach of Bezier and which are useful for these problems. The two methods are integrated into our comprehensive solid modeling package GEOMAP-III which is soon to be operational and which will serve as a basis for sophisticated shape design and integrated CAD/CAM systems.
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References
P. E. Bézier, Numerical Control—Mathematics and Applications, John Wiley and Sons, London, England, 1972.
R. E. Barnhill and W. Böhm, eds., Surfaces in Computer Aided Geometric Design, North-Holland Publishing Company, Amsterdam, Netherlands, 1983.
R. E. Barnhill and R. F. Riesenfeld, eds., Computer Aided Geometric Design, Academic Press, New York, New York, 1974.
I. C. Braid, R. C. Hillyard, and I. A. Stroud, “Stepwise Construction of Polyhedra in Geometric Modeling,” Mathematical Methods in Computer Graphics and Design, Academic Press, London, England, 1980, pp. 123–141.
E. Catmull and J. Clark, “Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes,” Computer Aided Design, Vol. 10, No. 6, November 1978, pp. 350–355.
H. Chiyokura and F. Kimura, “Design of Solids with Free-Form Surfaces,” ACM Computer Graphics, Vol. 17, No. 3 (SIGGRAPH ’83 Conference Proceedings, Detroit, Michigan, July 25–29, 1983 ) pp. 289–298.
D. Doo, “Subdivision Algorithm for Smoothing Down Irregular Shaped Polyhedrons,” IEEE Proceedings of the International Conference on Interactive Techniques in Computer Aided Design, Bologna, Italy, September 21–23, 1978, pp. 157–165.
I. D. Faux and M. J. Pratt, Computational Geometry for Design and Manufacture, Ellis Horwood Limited, London, England, 1979.
A. R. Forrest, “A Unified Approach to Geometric Modeling,” ACM Computer Graphics, Vol. 12, No. 3 (SIGGRAPH ’78 Conference Proceedings, Atlanta, Georgia, August 23–25, 1978 ) pp. 264–269.
R. N. Goldman, “Quadrics of Revolution,” IEEE Computer Graphics and Applications, Vol. 3, No. 2, March/April 1983, pp. 68–76.
M. Higashi, I. Kohzen, and J. Nagasaka, “An Interactive CAD System for Construction of Shapes with High-Quality Surfaces,” Proceedings of CAPE ’83, Amsterdam, Netherlands, April 25–28, 1983, pp. 371–389.
M. Hosaka and F. Kimura, “An Interactive Geometrical Design System with Handwriting Input,” Proceedings of the 1977 IFIP Congress, Toronto, Canada, August 1977, pp. 167–172.
M. Hosaka and F. Kimura, “Synthesis Methods of Curves and Surfaces in Interactive CAD,” IEEE Proceedings of the International Conference on Interactive Techniques in Computer Aided Design, Bologna, Italy, September 21–23, 1978, pp. 151–156.
M. Hosaka and F. Kimura, “A Theory and Methods for Three Dimensional Free-Form Shape Construction,” Journal of Information Processing, Vol. 3, No. 3, Information Processing Society of Japan, 1980, pp. 140–151.
M. Hosaka and F. Kimura, “Interactive Input Methods for Free-Form Shape Design,” Man-Machine Communication in CAD/CAM, North-Holland Publishing Company, Amsterdam, Netherlands, 1981, pp. 103–118.
M. Hosaka and F. Kimura, “Methods of Surface Synthesis in GEOMAP-III,” Proceedings of MICAD ’82, Paris, France, 1982, p. 268–280.
M. Hosaka, F. Kimura and N. Kakishita, “A Unified Method for Processing Polyhedra,” Proceedings of the 1974 IFIP Congress, Stockholm, Sweden, August 1974, pp. 768–772.
IEEE Special Issue on Solid Modeling, IEEE Computer Graphics and Applications, Vol. 2, No. 2, March 1982.
S. Kawabe, F. Kimura, and T. Sata, “Generation of NC Commands for Sculptured Surface Machining for 3-Coordinate Measuring Data,” Annals of the CIRP, Vol. 29, No. 1, 1980, pp. 369–372.
S. Kawabe, F. Kimura, and T. Sata, “Automatic Generation of NC Commands for a 3-Coordinate Measuring Machine,” Proceedings of ICPE, Tokyo, Japan, 1980, pp. 941–946.
S. Kawabe, S. Shimura, M. Miyashita, F. Kimura, and T. Sata, “Programming for Machining Based on Workpiece Models in Computers,” Annals of the CIRP, Vol. 32, No. 1, 1983, pp. 351–355.
F. Kimura, Y. Yamaguchi, Y. Sasaki, K. Kido, and M. Hosaka, “Construction and Uses of an Engineering Data Base in Design and Manufacturing Environments,” File Structures and Data Bases for CAD, North-Holland Publishing Company, Amsterdam, Netherlands, 1982, pp. 95–116.
F. Kimura, T. Sata, and M. Hosaka, “Integration of Design and Manufacturing Activities based on Object Modeling,” Advances in CAD/CAM (PROLAMAT ’82), North-Holland Publishing Company, Amsterdam, Netherlands, 1983, pp. 375–385.
F. Kimura, S. Kawabe, T. Sata, and M. Hosaka, “A Study on Product Modeling for Integration of CAD/CAM,” Integration of CADI CAM, North-Holland Publishing Company, Amsterdam, Netherlands, 1983, pp. 227–251.
M. Mäntylä and R. Sulonen, “GWB: A Solid Modeler with Euler Operators,” IEEE Computer Graphics and Applications, Vol. 2, No. 7, September 1982, pp. 17–31.
R. F. Riesenfeld, “Application of B-Spline Approximations to Geometric Problems of Computer Aided Design,” Ph.D. Dissertation, Syracuse University, Syracuse, New York, May 1973.
R. F. Sarraga, “Algebraic Methods for Intersection of Quadric Surfaces in GMSolid,” Computer Vision, Graphics, and Image Processing, Vol. 22, No. 2, May 1983, pp. 222–238.
T. Sata, F. Kimura, and A. Amano, “Robot Simulation System as a Task Programming Tool,” Proceedings of lSIR, Tokyo, Japan, 1981, pp. 595–602.
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© 1984 Plenum Press, New York
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Kimura, F. (1984). Design Methods of Free-Form Surfaces and their Integration into the Solid Modeling Package GEOMAP-III. In: Pickett, M.S., Boyse, J.W. (eds) Solid Modeling by Computers. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2811-7_10
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DOI: https://doi.org/10.1007/978-1-4613-2811-7_10
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