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Triangulations in CAGD
January/February 1993 (vol. 13 no. 1)
pp. 47-52

Triangulations, which play an important role in approximation theory, finite-element methods, numerical analysis, and computer-aided geometric design (CAGD), are defined. Triangulations in the plane, in space, and on the surface of a sphere are discussed. The storing and construction of triangulations are also discussed.

1. L.L. Schumaker, "Triangulation Methods," inTopics in Multivariate Approximation, C.K. Chui, L.L. Schumaker, and F. Utreras, eds., Academic Press, New York, 1987, pp. 219-232.
2. F. P. Preparata and M. I. Shamos,Computational Geometry, an Introduction. New York: Springer-Verlag, 1985.
3. J.T. Oden and J. N. Reddy,An Introduction to the Mathematical Theory of Finite Elements, Wiley, New York, 1976.
4. J. F. Thompson, Z. U. A. Warsi, and C. W. Mastin,Numerical Grid Generation: Foundations and Applications. New York: Elsevier, 1985.
5. G. Farin,Curves and Surfaces for Computer Aided Geometric Design, Academic Press, Boston, 1988.
6. H. Hagen and H. Pottmann, "Curvature Continuous Triangular Interpolants," inMathematical Methods in Computer Aided Geometric Design, T. Lyche and L. Schumaker, eds., Academic Press, New York, 1989, pp. 373-384.
7. E. Quak and L.L. Schumaker, "Least Squares Fitting by Linear Splines on Data-Dependent Triangulations," inCurves and Surfaces, P.J. Laurent, A. LeMehaute, and L.L. Schumaker, eds., Academic Press, New York, 1991, pp. 387-390.
8. B. Hamann, "Modeling Contours of Trivariate Data,"Mathematical Modeling and Numerical Analysis, Vol. 26, 1992, pp. 51-75.
9. N. Dyn, D. Levin, and J.A. Gregory, "A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control,"ACM Trans. Graphics, Vol. 9, 1990, pp. 160-169.
10. L.L. Schumaker, "Reconstruction of 3D Objects from Cross Sections," inComputation of Curves and Surfaces, W. Dahmen, M. Gasca, and C. Micchelli, eds., Kluwer, Dordrecht, 1990, pp. 275-309.
11. G.M. Nielson and R. Ramaraj, "Interpolation over a Sphere Based upon a Minimum Norm Network,"CAGD, Vol. 4, No. 1-2, July 1987, pp. 41-57.
12. B. Joe, "Construction of Three-Dimensional Delaunay Triangulations Using Local Transformations,"CAGD, Vol. 8, No. 2, May 1991, pp. 123-142.

Larry L. Schumaker, "Triangulations in CAGD," IEEE Computer Graphics and Applications, vol. 13, no. 1, pp. 47-52, Jan.-Feb. 1993, doi:10.1109/38.180117
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