“A unified approach to geometric modelling” by Forrest

  • ©A. Robin Forrest




    A unified approach to geometric modelling



    Whereas, historically, much of the effort on computer-aided geometric design has concentrated on the problems of representing so-called sculptured surfaces, there has recently been much interest in systems which can handle typical mechanical components by a volume modelling approach. The paper is concerned with the possibility of combining the two approaches and discusses the issues raised. A solution in terms of applying smoothing operators to a geometric coarse structure is proposed, with the added benefits of detecting and successfully handling anomalous regions in surfaces and leading to potential benefits in the analysis of geometric properties.


    1. Barnhill, R.E. & Riesenfeld, R.F. (Eds.) Computer Aided Geometric Design. Academic Press, New York, 1974.
    2. Baumgart, B.G. Geometric modelling for computer vision. AIM-249, STAN-CS-74-463, Stanford University, October 1974.
    3. Bézier, P.E. Mathematical and practical possibilities of UNISURF. In (1) above.
    4. Braid, I.C. The synthesis of solids bounded by many faces. Comm. ACM 18, 4 (Apr. 1975), 209-216.
    5. Braid, I.C. Six systems for shape design and representation – a review. Cambridge University CAD Group, CAD Group Doc. 87, May 1975.
    6. Braid, I.C. A new shape design system. Cambridge University CAD Group, CAD Group Doc. 89, March 1976.
    7. Braid, I.C. On storing and changing shape information. These proceedings.
    8. Catmull, E. & Clark, J. Recursively generated B-spline surfaces on arbitrary topologicical meshes. To appear.
    9. Chaikin, G.M. An algorithm for high-speed curve generation. Computer Graphics and Image Processing 3 (1974), 346-349.
    10. Coons, S.A. Surfaces for computer-aided design of space forms. Project MAC TR-41, M.I.T., June 1967.
    11. Doo, D. A method of smoothing highly irregular polyhedrons. Interactive Techniques in Computer Aided Design Conference, Bologna, Spetember 1978.
    12. Doo, D. Ph.D. dissertation, Brunel University, to appear.
    13. Forrest, A.R. Curves and surfaces for computer-aided design. Ph.D. dissertation, Cambridge University, July 1968.
    14. Forrest, A.R. Coons surfaces and multivariable functional interpolation. Cambridge University CAD Group, CAD Group Doc., Dec. 1971.
    15. Forrest, A.R. The definition of surfaces. Ingenieurs de 1’Automobile 44, l0 (Oct. 1971) 521-527.
    16. Forrest, A.R. On Coons and other methods for the representation of curved surfaces. Computer Graphics and Image Processing 1, (1972)
    17. Forrest, A.R. Computational geometry – achievements and problems. In (1) above.
    18. Forrest, A.R. Notes on Chaikin’s algorithm. University of East Anglia Computational Geometry Project CGP 74/1, (Dec. 1974).
    19. Forrest, A.R. Multivariate approximation problems in computational geometry. In Multivariate Approximation, D.C. Handscomb (Ed.), Academic Press, London, 1978.
    20. Loeb, A.L. Space Structures. Addison-Wesley, Reading, Mass. 1976.
    21. Riesenfeld, R.F. Applications of B-spline approximation to geometric problems of computer-aided design. Ph.D. dissertation, Syracuse University, 1973.
    22. Riesenfeld, R.P. On Chaikin’s algorithm. Computer Graphics and Image Processing 4, (1975), 304-310.
    23. Sabin, M.A. Numerical Master Geometry. British Aircraft Corporation, Weybridge (BAC) VTO/MS/146, (Aug. 1968).
    24. Sabin, M.A. Parametric surface equations for non-rectangular regions. BAC VTO/MS/147, (Oct. 1968).
    25. Sabin, M.A. Trinomial basis functions for interpolation in triangular regions (Bézier triangles). BAC VTO/MS/188, (July 1971).
    26. Sabin, M.A. B-spline interpolation over regular triangular lattices. BAC VTO/MS/195, (Oct. 1972).
    27. Sabin, M.A. A triangular element giving slope continuity over all boundaries using piecewise cubic interior. BAC VTO/MS/198, (July 1973).
    28. Sabin, M.A. Two slope-continuous triangular elements constructed from low order polynomial pieces. BAC VTO/MS/199, (July 1973).
    29. Sabin, M.A. A Bézier-like surface definition controlled by points joined in an arbitrary network. Kongsberg U.K. Ltd., (Sept. 1976).
    30. Sabin, M.A. The use of piecewise forms for the numerical representation of shape. Ph.D. dissertation, Computer and Automation Institute, Hungarian Academy of Sciences, 1977.
    31. Sabin, M.A. Various private communications, 1976-1978.
    32. Shamos, M.I. Computational geometry. Ph.D. dissertation, Yale University, (May 1978).
    33. Sutherland, I.E., Sproull, R.F. & Schumaker, R.A. A characterization of ten hidden-surface algorithms. ACM Computing Surveys 6, 1 (1974) 1-56.
    34. Weiler, K. & Atherton, P. Hidden surface removal using polygon area sorting. ACM SIGGRAPH Computer Graphics 11, 2 (Summer 1977).

ACM Digital Library Publication:

Overview Page: