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Composite Methods for Generating Surfaces

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Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 49))

Abstract

A central theme concerning interpolating sets and precision classes of linear transformations is developed. The ideas are illustrated with two sequences of topical examples:

  1. (a)

    Smooth surface construction on scattered data and

  2. (b)

    The numerical implementation of blending on rectangular grids. Special attention is drawn to composite methods involving pairs of projectors which do not commute.

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References

  1. R.E. Barnhill. Representation and approximation of surfaces. Mathematical Software III, Academic Press, 1977, pp. 69–120.

    Google Scholar 

  2. R.E. Barnhill and J.A. Gregory. Polynomial interpolation to boundary data on triangles. Math. Comp. 29 (1975), pp. 726–735.

    Article  MATH  MathSciNet  Google Scholar 

  3. J.C. Cavendish, W.J. Gordon, and C.A. Hall. Ritz-Galerkin approximation in blending function spaces, Numer. Math. 26 (1976), pp. 155–178.

    Article  MATH  MathSciNet  Google Scholar 

  4. W.J. Gordon. Distributive lattices and the approximation of multivariate functions. Approximations with Special Emphasis on Spline Functions, Academic Press, 1969, pp. 223–277.

    Google Scholar 

  5. W.J. Gordon and C.A. Hall. Transfinite element methods: Blending function interpolation over arbitrary curved element domains, Numer. Math. 21 (1973), pp. 109–129.

    Article  MATH  MathSciNet  Google Scholar 

  6. W.J. Gordon and J.A. Wixom. Pseudo-harmonic interpolation on convex domains, SIAM J. Numer. Anal. 11 (1974), pp. 909–933.

    Article  MATH  MathSciNet  Google Scholar 

  7. P.J. Green and R. Sibson. Computing Dirichlet tesselations in the plane, Computer J., 21 (1978), pp. 168–173.

    Article  MATH  Google Scholar 

  8. P. Lancaster and K. Salkauskas. A Survey of Curve and Surface Fitting. Published by the authors, Calgary, 1977.

    Google Scholar 

  9. C.L. Lawson. Software for Cl surface interpolation. Mathematical Software III, Academic Press, 1977, pp. 69–120.

    Google Scholar 

  10. M.J.D. Powell. Numerical Methods for fitting functions of two variables, The State of the Art in Numerical Analysis, ed. D. Jacobs, Academic Press, 1977, pp. 563–604.

    Google Scholar 

  11. D. Rhynsburger. Analytic delineation of Thiessen polygons, Geograph. Anal. 5 (1973), pp. 133–144.

    Google Scholar 

  12. S. Ritchie, Surface Representation by Finite Elements. M.Sc. Thesis, Dept. of Math, and Stat., Univ. of Calgary, 1978.

    Google Scholar 

  13. L.L. Schumaker. Fitting surfaces to scattered data. Approximation Theory II, Academic Press, 1976, pp. 203–268.

    Google Scholar 

  14. D.S. Watkins and P. Lancaster. Some families of finite elements, J. Inst. Math. Applies. 19 (1977), pp. 385–397.

    Article  MATH  MathSciNet  Google Scholar 

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© 1979 Springer Science+Business Media Dordrecht

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Lancaster, P. (1979). Composite Methods for Generating Surfaces. In: Sahney, B.N. (eds) Polynomial and Spline Approximation. NATO Advanced Study Institutes Series, vol 49. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9443-0_6

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  • DOI: https://doi.org/10.1007/978-94-009-9443-0_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-9445-4

  • Online ISBN: 978-94-009-9443-0

  • eBook Packages: Springer Book Archive

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