Computing contours by successive solution of quintic polynomial equations

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Computing contours by successive solution of quintic polynomial equations

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 10 , Issue 4 (December 1984) table of contents

Pages: 463 - 472

Year of Publication: 1984

ISSN:0098-3500

Author

Albrecht Preusser

Konrad-Zuse-Zentrum fu¨r Informationstechnik Berlin

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 1, Downloads (12 Months): 38, Citation Count: 6

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references cited by index terms review

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	AKIMA, H. A method of bivariate interpolation and smooth surface fitting for values given at irregularly distributed points. OT Rep. 75-70, U.S. Government Printing Office, Washington D.C., Aug. 1975.
	2	Hiroshi Akima, A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points, ACM Transactions on Mathematical Software (TOMS), v.4 n.2, p.148-159, June 1978 [doi>10.1145/355780.355786]
	3	LAWSON, C.L. Software for C 1 surface interpolation. Mathemat=cal Software, Vol. 3, John R. Rice, EcL Academic Press, New York, 1977.
	4	MARLOW, S., AND POWELL, M.J.D. A Fortran subroutine for plotting the part of a conic that is reside a given triangle. Rep. R-8336, Atomic Energy Research Establishment, Harwell, England, 1976.
	5	POWELL, M.J.D. Piecewise quadratic surface fitting for contour plotting. Software for Numerical Mathematics, D.J. Evans, Ed. Academic Press, New York, 1974.
	6	PREUSSER, A. Bivariate Interpolation uber Dreieckselementen durch Polynome 5. Ordnung mit CrKontmuitat. Zeitschr {. Vermessungswesen 109, 6 (June 1984), 292-301.
	7	Albrecht Preusser, Algorithm 626 TRICP: a contour plot program triangular meshes, ACM Transactions on Mathematical Software (TOMS), v.10 n.4, p.473-475, Dec. 1984 [doi>10.1145/2701.2772]
	8	William V. Snyder, Algorithm 531: Contour Plotting [J6], ACM Transactions on Mathematical Software (TOMS), v.4 n.3, p.290-294, Sept. 1978 [doi>10.1145/355791.355800]
	9	ZIENKIEWlCZ, O.C. The Finite Element Method, 3rd ed. McGraw-Hill, New York, 1977.

CITED BY 6

	Albrecht Preusser, Efficient formulation of a bivariate nonic C2-hermite polynomial on triangles, ACM Transactions on Mathematical Software (TOMS), v.16 n.3, p.246-252, Sept. 1990
	Albrecht Preusser, Algorithm 684: C1- and C2-interplation on triangles with quintic and nonic bivariate polynomials, ACM Transactions on Mathematical Software (TOMS), v.16 n.3, p.253-257, Sept. 1990
	Albrecht Preusser, Algorithm 626 TRICP: a contour plot program triangular meshes, ACM Transactions on Mathematical Software (TOMS), v.10 n.4, p.473-475, Dec. 1984
	Robert R. Dickinson , Richard H. Bartels, The definition, editing, and contouring of surfaces for the analysis of field problems, ACM SIGCHI Bulletin, v.17 n.SI, p.109-114, May 1987
	Robert R. Dickinson , Richard H. Bartels , Allan H. Vermeulen, The Interactive Editing and Contouring of Empirical Fields, IEEE Computer Graphics and Applications, v.9 n.3, p.34-43, May 1989
	Chandan Singh , Jaswinder Singh, Accurate contour plotting using 6-node triangular elements in 2D, Finite Elements in Analysis and Design, v.45 n.2, p.81-93, January, 2009

INDEX TERMS

Classification:
G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS
G.1.1 Interpolation
Subjects: Spline and piecewise polynomial interpolation
G.1.5 Roots of Nonlinear Equations
Subjects: Polynomials, methods for

I. Computing Methodologies
I.3 COMPUTER GRAPHICS
I.3.5 Computational Geometry and Object Modeling
Subjects: Curve, surface, solid, and object representations

General Terms:
Algorithms, Design

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These two papers describe a method, and the corresponding FORTRAN program, for generating contours of a piecewise quintic function defined over a triangulated region. The algorithm uses Akima's method [1] to generate the surface from scattered d more...

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