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Construction of a hybrid sweep-CSG modeler—The sweep-CSG representation

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Abstract

Applying sweep operations on 2-D closed contours is a well known method for modelling 3-D solid objects. This paper deals with the implementation of a solid modeler with sweep as the basic representational scheme. In the modeler, a solid is defined by sweeping a planar polygon along a linear or curved trajectory. A sculptured solid may also be defined by using a beta-spline curve for the sweep polygon and a cubic B-spline curve for the sweep trajectory. By incorporating Boolean operations, a hybrid sweep-CSG solid modeler is implemented. The current implementation allows translational, rotational, and twisted sweep operations on a planar polygon composited of lines and arcs. In addition, a solid primitive can also be created by sweeping a planar closed beta-spline curve along a cubic B-spline curve.

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References

  1. Miyamoto, E.; Binford, T.O. (1975) Display generated by a generalized cone representation, Proceedings of the Conference on Computer Graphics, Pattern Recognition, & Data Structure, May, 385–387.

    Google Scholar 

  2. Agin, G.J.; Binford, T.O. (1976) Computer description of curved objects, IEEE Transactions on Computers, Vol, C-25, No. 4, April, 439–449.

    Google Scholar 

  3. Brooks, R.A. (1981) Symbolic reasoning among 3-D models and 2-D images, Artificial Intelligence Vol. 17, 285–348.

    Google Scholar 

  4. Klok, F. (1986) Two moving coordinate frame for sweeping along a 3-D trajectory, Computer Aided Geometric Design Vol 3, 217–229.

    Google Scholar 

  5. Shani, U.; Ballard, D.H. (1984) Splines as embeddings for generalized cylinders, Computer Vision, Graphics, and Image Processing 27, 127–156.

    Google Scholar 

  6. Coquillart, S. (1987) A control-point-based sweeping technique, IEEE Computer Graphics & Applications, Nov, 36–45.

    Google Scholar 

  7. Shiroma, Y.; Okino N.; Kakazu, Y. (1982) Research on 3-D geometric modeling by sweep primitives, Proceedings, CAD-82, 671–685.

  8. Woodwark, J.R.; Wallis, A.F. (1982) Graphical input to a Boolean solid modeller, Proceedings, CAD-82, 681–688.

  9. Vossler, Donald L. (1985) Sweep-to-CSG conversion using pattern recognition techniques, IEEE Computer Graphics & Applications, Aug. 61–68.

    Google Scholar 

  10. Rossignac, J.R. (1985) Blending and offsetting solid models, Ph.D.Dissertation, Department of Electrical Engineering, University of Rochester, July.

  11. Evan, R.C.; Koppelman, G.; Rajan, V.T. (1987) Shaping geometric objects by cumulative translational sweeps. IBM Journal of Research and Development Vol. 31, No. 3, May, 343–360.

    Google Scholar 

  12. Boyse, J.W. (1979) Interference detection among solids and surfaces, Communications of the ACM, Jan, Vol. 22, No. 1, pp. 3–9.

    Google Scholar 

  13. Sungurtekin, U.; Voelcker, H.B. (1986) Graphical simulation and automatic verification of NC machining programs, Proc. of IEEE Int. Conf. on Robotics and Automation, New York, 156–165.

  14. Wang, W.P.; Wang, K.K. (1986) Geometric modelling for swept volume of moving solids. IEEE Computer Graphics and Application, Oct, 8–17.

    Google Scholar 

  15. Hui, K.C. (1990) Solid modelling and its application in mould design—a sweep primitive approach, Ph.D. Dissertation, University of Hong Kong.

  16. Requicha, A.A.G. (1980) Representation for rigid solids: theory, methods and systems, ACM Computer Survey, Vol. 12, No. 4, 437–464.

    Google Scholar 

  17. Baer, A.; Eastman, C.; Henrion, M. (1979) Geometric modelling: a survey, Computer Aided Design, Vol. 11, No. 5, 253–272.

    Google Scholar 

  18. Roth, S.D. (1982) Ray casting for modeling solids, Computer Graphics & Image Processing, Vol. 18, No. 2, Feb 109–144.

    Google Scholar 

  19. Lee, Y.T.; Requicha, A.A.G. (1982) Algorithms for computing the volume and other integral properties of solids: I. known methods and open issues, Communications of ACM, Vol 25, No. 9, Sept. 635–642.

    Google Scholar 

  20. Lee, Y.T.; Requicha, A.A.G. (1982) Algorithms for computing the volume and other integral properties of solids: II. a family of algorithms based on representation conversion and cellular approximation, Communications of ACM, Vol 25, No. 9, Sept, pp. 642–650.

    Google Scholar 

  21. Hunt, W.A.; Volecker H.B. (1982) An exploratory study of automatic verification of program for numerically controlled machine tools, Technical Memo, No. 34, University of Rochester, Production Automation Project.

  22. Requicha, A.A.G. (1984) Boolean operations in solid modelling: boundary evaluation and merging algorithms, Technical Memo. No. 26, Production Automation Project, University of Rochester.

  23. Wilson, P.R. (1985) Euler formulas and geometric modelling, IEEE Computer Graphics and Applications, Vol. 5, No. 8, August, 24–36.

    Google Scholar 

  24. Faux, I.D.; Pratt, M.J. (1979) Computational Geometry for Design and Manufacture, New York: John Wiley and Sons

    Google Scholar 

  25. Tilove, R.B. (1980) Set membership classification: a unified approach to geometric intersection problems, IEEE Trans. on Computers, Vol. C-29, No. 10, Oct, 874–883.

    Google Scholar 

  26. Tiller, W. (1983) Rational B-spline for curve and surface representation, IEEE Computer Graphics & Applications, Sept, 61–69.

    Google Scholar 

  27. Piegl, L.; Tiller W. (1987) Curve and surface constructions using rational B-spline, Computer Aided Design, Vol. 19, Nov, 485–498.

    Google Scholar 

  28. Barsky, B.A.; DeRose, T.D. (1985) The beta2-spline: a special case of the beta-spline curve and surface representation. IEEE Computer Graphics & Application, Sept. 46–58.

    Google Scholar 

  29. Barsky, B.A. (1981) The beta-spline: a local representation based on shape parameters and fundamental geometric measure, Ph.D. Dissertation, University of Utah, Salt Lake City, Dec.

    Google Scholar 

  30. Barsky, B.A. (1983) Local control of bias and tension in beta-splines, ACM Transactions on Graphics, Vol. 2, No. 2, April, 109–134.

    Google Scholar 

  31. Ronald, N.G. (1986) Urn models and beta-splines, IEEE Computer Graphics & Applications, Feb. 57–64.

    Google Scholar 

  32. Goodman, T.N.T.; Unsworth, K. (1986) Manipulating shape and producing geometric continuity in β-spline curves, IEEE Computer Graphics & Applications, Feb. pp. 50–56.

    Google Scholar 

  33. Riesenfeld, R.F. (1973) Applications of B-spline approximation to geometric problems of computer-aided design, Ph.D. Dissertation, Syracuse University, May.

  34. Tan, S.T.; Yuen, M.M.F.; Hui, K.C. (1987) Modelling solids with sweep primitives, Computers in Mechanical Engineering, Vol. 6, No. 2, Sept, 60–73.

    Google Scholar 

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Hui, K.C., Tan, S.T. Construction of a hybrid sweep-CSG modeler—The sweep-CSG representation. Engineering with Computers 8, 101–119 (1992). https://doi.org/10.1007/BF01200106

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