ABSTRACT
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. Google ScholarDigital Library
- 2.Baumgart, B.G. Geometric modelling for computer vision. AIM-249, STAN-CS-74-463, Stanford University, October 1974.Google Scholar
- 3.Bézier, P.E. Mathematical and practical possibilities of UNISURF. In (1) above.Google Scholar
- 4.Braid, I.C. The synthesis of solids bounded by many faces. Comm. ACM 18, 4 (Apr. 1975), 209-216. Google ScholarDigital Library
- 5.Braid, I.C. Six systems for shape design and representation - a review. Cambridge University CAD Group, CAD Group Doc. 87, May 1975.Google Scholar
- 6.Braid, I.C. A new shape design system. Cambridge University CAD Group, CAD Group Doc. 89, March 1976.Google Scholar
- 7.Braid, I.C. On storing and changing shape information. These proceedings. Google ScholarDigital Library
- 8.Catmull, E. & Clark, J. Recursively generated B-spline surfaces on arbitrary topologicical meshes. To appear.Google Scholar
- 9.Chaikin, G.M. An algorithm for high-speed curve generation. Computer Graphics and Image Processing 3 (1974), 346-349.Google ScholarCross Ref
- 10.Coons, S.A. Surfaces for computer-aided design of space forms. Project MAC TR-41, M.I.T., June 1967. Google ScholarDigital Library
- 11.Doo, D. A method of smoothing highly irregular polyhedrons. Interactive Techniques in Computer Aided Design Conference, Bologna, Spetember 1978.Google Scholar
- 12.Doo, D. Ph.D. dissertation, Brunel University, to appear.Google Scholar
- 13.Forrest, A.R. Curves and surfaces for computer-aided design. Ph.D. dissertation, Cambridge University, July 1968.Google Scholar
- 14.Forrest, A.R. Coons surfaces and multivariable functional interpolation. Cambridge University CAD Group, CAD Group Doc., Dec. 1971.Google Scholar
- 15.Forrest, A.R. The definition of surfaces. Ingenieurs de 1'Automobile 44, l0 (Oct. 1971) 521-527.Google Scholar
- 16.Forrest, A.R. On Coons and other methods for the representation of curved surfaces. Computer Graphics and Image Processing 1, (1972)Google Scholar
- 17.Forrest, A.R. Computational geometry - achievements and problems. In (1) above.Google Scholar
- 18.Forrest, A.R. Notes on Chaikin's algorithm. University of East Anglia Computational Geometry Project CGP 74/1, (Dec. 1974).Google Scholar
- 19.Forrest, A.R. Multivariate approximation problems in computational geometry. In Multivariate Approximation, D.C. Handscomb (Ed.), Academic Press, London, 1978.Google Scholar
- 20.Loeb, A.L. Space Structures. Addison-Wesley, Reading, Mass. 1976.Google Scholar
- 21.Riesenfeld, R.F. Applications of B-spline approximation to geometric problems of computer-aided design. Ph.D. dissertation, Syracuse University, 1973. Google ScholarDigital Library
- 22.Riesenfeld, R.P. On Chaikin's algorithm. Computer Graphics and Image Processing 4, (1975), 304-310.Google ScholarCross Ref
- 23.Sabin, M.A. Numerical Master Geometry. British Aircraft Corporation, Weybridge (BAC) VTO/MS/146, (Aug. 1968).Google Scholar
- 24.Sabin, M.A. Parametric surface equations for non-rectangular regions. BAC VTO/MS/147, (Oct. 1968).Google Scholar
- 25.Sabin, M.A. Trinomial basis functions for interpolation in triangular regions (Bézier triangles). BAC VTO/MS/188, (July 1971).Google Scholar
- 26.Sabin, M.A. B-spline interpolation over regular triangular lattices. BAC VTO/MS/195, (Oct. 1972).Google Scholar
- 27.Sabin, M.A. A triangular element giving slope continuity over all boundaries using piecewise cubic interior. BAC VTO/MS/198, (July 1973).Google Scholar
- 28.Sabin, M.A. Two slope-continuous triangular elements constructed from low order polynomial pieces. BAC VTO/MS/199, (July 1973).Google Scholar
- 29.Sabin, M.A. A Bézier-like surface definition controlled by points joined in an arbitrary network. Kongsberg U.K. Ltd., (Sept. 1976).Google Scholar
- 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.Google Scholar
- 31.Sabin, M.A. Various private communications, 1976-1978.Google Scholar
- 32.Shamos, M.I. Computational geometry. Ph.D. dissertation, Yale University, (May 1978). Google ScholarDigital Library
- 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. Google ScholarDigital Library
- 34.Weiler, K. & Atherton, P. Hidden surface removal using polygon area sorting. ACM SIGGRAPH Computer Graphics 11, 2 (Summer 1977). Google ScholarDigital Library
Index Terms
- A unified approach to geometric modelling
Recommendations
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 ...
An application of color graphics to the display of surface curvature
In developing a mathematical representation for a surface, designers currently must use line drawing graphics to examine the curvature of a line in a plane, a two-dimensional analysis. By combining a result from differential geometry with the use of ...
An application of color graphics to the display of surface curvature
SIGGRAPH '81: Proceedings of the 8th annual conference on Computer graphics and interactive techniquesIn developing a mathematical representation for a surface, designers currently must use line drawing graphics to examine the curvature of a line in a plane, a two-dimensional analysis. By combining a result from differential geometry with the use of ...
Comments