Methods for Constructing Surfaces on Surfaces
Part of the Computer Graphics — Systems and Applications book series (COMPUTER GRAPH.)
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.
KeywordsTangent Plane Geodesic Distance Geometric Design Scattered Data Triangular Grid
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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- 1.Barnhill, R.E. (1977), Representation and approxiamtion of surfaces, in Mathematical Software III, J. R. Rice, ed., Academic Press, New York, 69–120.Google Scholar
- 4.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.Google Scholar
- 5.Barnhill, R.E. and Ou, H.S. (1990), Surfaces defined on surfaces, Computer Aided Geometric Design 7.Google Scholar
- 6.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.ssGoogle Scholar
- 7.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.Google Scholar
- 9.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.Google Scholar
- 10.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.Google Scholar
- 14.Herron, G.J. (1979), Triangular and Multisided Patch Schemes, Ph.D. Thesis, Mathematics Department, University of Utah, Salt Lake City.Google Scholar
- 18.Pottmann, H. and Eck, M. (1990), Modified multiquadric methods for scattered data interpolation over a sphere, Computer Aided Geometric Design 7.Google Scholar
- 19.Ramaraj, R. (1986), Interpolation and display of scattered data over a sphere, Masters Thesis, Computer Science Department, Arizona State University, Tempe.Google Scholar
- 20.Renka, R.J. (1984), Interpolation of data on the surface of a sphere, ACM Trans. Math. Software, 417–436.Google Scholar
- 21.Sederberg, T.W. and Parry, S.R. (1986), Free-form Deformation of Solid Geometric Models, SIGGRAPH ’86 Conference Proceedings, 151–160.Google Scholar
- 22.Shepard, D. (1968), A two-dimensional interpolation function for irregularly-spaced data, Proceedings of the 1968 ACM National Conference, 517–524.Google Scholar
© Springer-Verlag Berlin Heidelberg 1991