The Community for Technology Leaders
RSS Icon
Issue No.11 - November (1987 vol.7)
pp: 8-16
Zoltan Cendes , Carnegie Mellon University
Steven Wong , Carnegie Mellon University
New formulas for generating smooth surfaces over arbitrarily spaced data points are developed. The formulas are based on quadratic polynomials for the construction of derivative continuous surfaces rather than on the cubic polynomials generally used. The technique is based on a subdivision procedure, dividing each triangle in a triangulation of the data points into six subtriangles and fitting a quadratic Bezier surface patch over each subtriangle. THe formulas require only function and first derivative values at the data points and are easily evaluated in terms of the Bezier coefficients. Since two-dimensional quadratic polynomials contain only six terms, while 10 terms are required to evaluate a cubic, the new procedure significantly improves the efficiency of algorithms for drawing surfaces in computer-aided geometric design.
Zoltan Cendes, Steven Wong, "C1 Quadratic Interpolation over Arbitrary Point Sets", IEEE Computer Graphics and Applications, vol.7, no. 11, pp. 8-16, November 1987, doi:10.1109/MCG.1987.277064
1. S.A.Coons, MIT Project MAC-TR-41 , MIT 1967
2. P.Bezier, Numerical Control, Mathematics and Applications , Wiley 1972
3. G.Farin, Subsplines uber Dreiecken 1979
4. R.E.Barnhill, R.E.Barnhill, and W.Boehm, Surfaces in CAGD , 1983pp. 1-23
5. G.Farin, R.E.Barnhill, and W.Boehm, Surfaces in CAGD , 1983pp. 43-63
6. M.Powell and M.Sabin, "Piecewise Quadratic Approximation on Triangles," ACM Trans. Math. Softwarepp. 316-325 Dec. 1977
7. R.Sibson and G.Thomson, "A Seamed Quadratic Element for Contouring," The Computer Journalpp. 378-382 Nov. 1981
8. T.W.Sederberg and D.C.Anderson, "Steiner Surface Patches," CG&App. 23-36 May 1985
9. W.Boehm, G.Farin, and J.Kahmann, "A Survey of Curve and Surface Methods in CAGD," Computer Aided Geometric Design Vol. 1, No. 1, pp. 1-60 1984
10. E.A.Maxwell, General Homogeneous Coordinates , Cambridge Univ. Press 1960
11. G.Farin, "Designing C 1 Surfaces Consisting of Triangular Cubic Patches," Computer-Aided Designpp. 253-256 Sept. 1982
12. S.Marlow and M.J.D.Powell, "A Fortran Subroutine for Plotting the Part of a Conic That is Inside a Given Triangle," , Atomic Energy Research Establishment 1976
19 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool