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Geometric Modeling of Smooth Surfaces using Triangular Patches

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Theory and Practice of Geometric Modeling

Abstract

Surfaces designed in a Computer graphics environment have many applications, including the design of cars, airplains, shipbodies and modeling robots. The generation of smooth surfaces from a set of three-dimensional data points is a key problem in the Geld of Computer Aided Geometric Design. An overview of fundamental triangular concepts is given and new results are presented.

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References

  • Barnhill (1974): Smooth interpolation over triangles in Barnhill-Riesenfeld (eds.): Computer Aided Geometric Design, Academic Press, New York, p. 45–70

    Google Scholar 

  • Barnhill (1983): Computer Aided Surface Representation and Design in Barnhill-Boehm (eds.): Surfaces in CAGD, North Holland, Amsterdam, p. 1–24

    Google Scholar 

  • Barnhill-Birkhoff-Gordon (1973): Smooth interpolation in triangles, J. Approx. Theory 8, p. 114–128

    Article  Google Scholar 

  • Barnhill-Gregory (1975a): Compatible smooth interpolation in triangles, J. Approx. Theory 15, p. 214–225

    Article  Google Scholar 

  • Barnhill-Gregory (1975b): Polynomial interpolation to boundary data on triangles, Math. Comp. 29, p. 726–735

    Article  MathSciNet  Google Scholar 

  • Farin (1979): Subsplines über Dreiecken, Diss. TU Braunschweig

    Google Scholar 

  • Gregory (1974): Smooth interpolation without constraints in Barnhill-Riesenfeld (eds.): Computer Aided Geometric Design, Academic Press, New York, p. 71–88

    Google Scholar 

  • Gregory (1978): A blending function interpolant for triangles in Handscomb (eds.): Multivariate Approximation, Academic Press, New York, p. 279–287

    Google Scholar 

  • Gregory (1983): C 1 rectangular and non rectangular surface patches in Barnhill-Boehm (eds.): Surfaces in CAGD, North Holland, Amsterdam, p. 25–33

    Google Scholar 

  • Gregory-Charrot (1980): A C 1-Triangular Interpolation Patch for Computer Aided Geometric Design, Computer Graphics and Image Processing 13. p. 80–87

    Article  Google Scholar 

  • Hagen (1985): Geometric Spline Curves, Computer Aided Geometric Design 2, p. 223–227

    Article  MathSciNet  MATH  Google Scholar 

  • Hagen (1986): Geometric Surface Patches without Twist Constaints, Computer Aided Geometric Design 3, p. 179–184

    Article  MathSciNet  MATH  Google Scholar 

  • Hagen-Pottmann (1988): Curvature Continuous Triangular Interpolants, to be published in the proceedings of the conference “Mathematical Methods in CAGD” Oslo 1988

    Google Scholar 

  • Nielson (1979): The side vertex method for interpolation in triangles, J. Approx. Theory 25, p. 318–336

    Article  MathSciNet  MATH  Google Scholar 

  • Nielson (1987): A transfinite, visually continuous, triangular interpolant in Farin (ed.): Geometric Modeling, Applications and New Trends SIAM, Philadelphia, p. 235–246

    Google Scholar 

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© 1989 Springer-Verlag Berlin Heidelberg

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Hagen, H. (1989). Geometric Modeling of Smooth Surfaces using Triangular Patches. In: Straßer, W., Seidel, HP. (eds) Theory and Practice of Geometric Modeling. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61542-9_4

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  • DOI: https://doi.org/10.1007/978-3-642-61542-9_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64866-3

  • Online ISBN: 978-3-642-61542-9

  • eBook Packages: Springer Book Archive

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