Abstract
Given data defined on a (domain) surface, we construct an interpolant, which is a “surface defined on a surface.” we provide four different solutions to this multidimensional problem.
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References
Barnhill, R.E. (1977), Representation and approxiamtion of surfaces, in Mathematical Software III, J. R. Rice, ed., Academic Press, New York, 69–120.
Barnhill, R.E. (1985), Surfaces in computer aided geometric design: A survey with new results, Computer Aided Geometric Design 2, 1–17.
Barnhill, RE, Birkhoff, G.B and Gordon, W.J. (1973), Smooth Interpolation in triangles, J. Approx. Theory 8, 114–128.
Barnhill, R.E., Makatura, G. T. and Stead, S. E. (1987), A new look at higher dimensional surfaces through computer graphics, in G.E. Farin, ed., ‘Geometric Modeling’, SIAM, Philadelphia, 123–129.
Barnhill, R.E. and Ou, H.S. (1990), Surfaces defined on surfaces, Computer Aided Geometric Design 7.
Barnhill, R.E., Piper, B.R. and Rescorla, K.L. (1987), Interpolation to arbitrary data on a surface, in G.E. Farin, ed., ‘Geometric Modeling’, SIAM, Philadelphia, 281–289.ss
Barnhill, R.E., Piper, B.R. and Stead, S. E. (1985), Surface representation for the graphical display of structured data, Computer Aided Geometric Design, 2 (1985), 185–187. A later form appears in The Visual Computer, 1 (1985), 108–111.
Barr, A.H. (1984), Global and local deformations of solid primitives, Computer Graphics 18, no. 3, 21–30.
Foley, T.A. (1989), Interpolation to scattered data on a spherical domain, in M. Cox and J. Mason, ed., ‘Algorithms for Approximation II’, Chapman and Hall, London.
Foley, T.A., Lane, D.A., Nielson, G.M., Franke, R. and Hagen H. (1990), Interpolation of scattered data on closed surfaces, Computer Aided Geometric Design 7.
Foley, T.A., Lane, D.A., Nielson, G.M. and Ramaraj, R. (1990), Visualizing functions over a sphere, I. E.E.E. Comp. Graphics and Applic. 10, no. 1, 32–40.
Hardy, R. L. (1971) Multiquadratic equations of topography and other irregular surfaces, J. Geophys. Res., 76, 1905–1915.
Hardy, R. L. and Goepfert, W.M. (1975), Least squares prediction of gravity anomalies, geoidal undulations, and deflections of the vertical with multiquadric harmonic functions, Geophys. Research Letters 2, 423–426.
Herron, G.J. (1979), Triangular and Multisided Patch Schemes, Ph.D. Thesis, Mathematics Department, University of Utah, Salt Lake City.
Lawson, C.L. (1984), C 1 Surface interpolation for scattered data on a sphere, Rocky Mountain J. Math. 14, 177–202.
Nielson, G.M. (1979), The side-vertex method for interpolation in triangles, Jour. Approx. Theory 25, 318–336.
Nielson, G.M. and Ramaraj, R. (1987), Interpolation over a sphere based upon a minimum norm network, Computer Aided Geometric Design 4, 41–57.
Pottmann, H. and Eck, M. (1990), Modified multiquadric methods for scattered data interpolation over a sphere, Computer Aided Geometric Design 7.
Ramaraj, R. (1986), Interpolation and display of scattered data over a sphere, Masters Thesis, Computer Science Department, Arizona State University, Tempe.
Renka, R.J. (1984), Interpolation of data on the surface of a sphere, ACM Trans. Math. Software, 417–436.
Sederberg, T.W. and Parry, S.R. (1986), Free-form Deformation of Solid Geometric Models, SIGGRAPH ’86 Conference Proceedings, 151–160.
Shepard, D. (1968), A two-dimensional interpolation function for irregularly-spaced data, Proceedings of the 1968 ACM National Conference, 517–524.
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© 1991 Springer-Verlag Berlin Heidelberg
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Barnhill, R.E., Foley, T.A. (1991). Methods for Constructing Surfaces on Surfaces. In: Hagen, H., Roller, D. (eds) Geometric Modeling. Computer Graphics — Systems and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76404-2_1
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DOI: https://doi.org/10.1007/978-3-642-76404-2_1
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