J. A. Brewer
Abstract
The method of parabolic blending for curve and surface interpolation originally conceived by A. W. Overhauser is applied to the interactive free-form design of three dimensional objects. A significant advantage of the algorithm is the user-oriented control of surface shape that is achieved because one interactively manipulates only coordinates on the design surface, as opposed to parametric slopes or design points.The algorithm is demonstrated using an interactive 3D design system that executes in a dual-minicomputer refresh graphics environment without special 3D hardware. The system provides high level data generation commands and direct visual interaction with structured 3D data using a multi-purpose 3D cursor and shaping tool. Objects composed of points, lines, curves and surfaces of different forms may be interactively created and manipulated.
- Coons, S. A. Surfaces for computer-aided design of space forms. Project MAC, M.I.T. (June 1967). Google Scholar
Digital Library
- Armit, A. P. Computer systems for interactive design of three-dimensional shapes. Ph.D. Thesis, University of Cambridge Computer Lab (November 1970).Google Scholar
- Bezier, P. E. Emploi des Machines a Commande Numerique, Masson et Cie, Paris, France (1970).Google Scholar
- Riesenfeld, R. F. Applications of B-spline approximation to geometric problems of computer-aided design. Ph.D. Thesis, Syracuse University (1972). Google ScholarDigital Library
- Clark, J. H. Designing surfaces in 3-D. CACM 19, 8 (August 1976), 454-460. Google ScholarDigital Library
- Overhauser, A. W. Analytic definition of curves and surfaces by parabolic blending. Scientific Research Staff Publication, Ford Motor Company (May 1968).Google Scholar
- Rogers, D. F. and Adams, J. A. Mathematical elements for computer graphics. McGraw-Hill, Inc. (1976), 133-138. Google ScholarDigital Library
- Brewer, J. A. and Anderson, D. C. Techniques for interactive three dimensional design. To be published in the proceedings of the ACM/SIGGRAPH Workshop on "User-Oriented Design of Interactive Graphics Systems". Pittsburqh, PA. (October 1976). Google ScholarDigital Library
- Brewer, J. A. Three Dimensional Design by Graphical Man-Computer Communication. Ph.D. Thesis, Purdue University (May, 1977). Google ScholarDigital Library
Index Terms
- Visual interaction with overhauser curves and surfaces
Recommendations
Visual interaction with overhauser curves and surfaces
SIGGRAPH '77: Proceedings of the 4th annual conference on Computer graphics and interactive techniquesThe method of parabolic blending for curve and surface interpolation originally conceived by A. W. Overhauser is applied to the interactive free-form design of three dimensional objects. A significant advantage of the algorithm is the user-oriented ...
Fast and local fairing of B-spline curves and surfaces
GMP'08: Proceedings of the 5th international conference on Advances in geometric modeling and processingThe paper proposes a fast fairing algorithm for curves and surfaces. It first defines a base algorithm for fairing curves, which is then extended to the surface case, where the isocurves of the surface are faired. The curve fairing process involves the ...
Technical section: Rational cubic spline interpolation with shape control
A rational cubic spline, with shape control parameters, has been discussed here with the view to its application in computer graphics. It incorporates both conic sections and parametric cubic curves as special cases. An efficient scheme is presented ...
Comments