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Trimming Bézier Surfaces on Bézier Surfaces Via Blossoming

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Book cover Advances in Geometric Modeling and Processing (GMP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4975))

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Abstract

The problem of trimming Bézier surfaces on Bézier surfaces contains many cases, such as the subdivision, conversion and conjoining. Different methods have been given for some special cases. In this paper, by means of blossoming and parameter transformation, a united approach is given for this problem. The approach can be extended to trim Bézier patches on any polynomial or rational surfaces naturally.

This work is supported by NSFC under Grant 10571145.

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References

  1. Brueckner, I.: Construction of Bézier points of quadrilaterals from those of triangles. Computer-Aided Design 12, 21–24 (1980)

    Article  Google Scholar 

  2. DeRose, T.D., Goldman, R.N., Hagen, H., Mann, S.: Functional composition algorithms via blossoming. ACM Transactions on Graphics 12, 113–135 (1993)

    Article  MATH  Google Scholar 

  3. Farin, G.: Curves and Surfaces in Computer Aided Geometric Design, 3rd edn. Academic Press, San Diego (1993)

    Google Scholar 

  4. Feng, J.Q., Peng, Q.S.: Functional compositions via shifting operators for Bézier patches and their applications. Journa of Software 10, 1316–1321 (1999)

    Google Scholar 

  5. Goldman, R.N.: Subdivision algorithms for Bézier triangles. Computer-Aided Design 15, 159–166 (1983)

    Article  Google Scholar 

  6. Goldman, R.N., Filip, D.: Conversion from Bézier rectangles to Bézier triangles. Computer-Aided Design 19, 25–27 (1987)

    Article  MATH  Google Scholar 

  7. Goldman, R.N.: Pyramid Algorithms: A dynamic Programming Approach to Curves and Surfaces for Geometric Modeling. Morgan Kaufmann, San Francisco (2002)

    Google Scholar 

  8. Goldman, R.N.: Polar forms in geometric modeling and algebraic geometry. In: Contemporary mathematics:Topics on algebraic geometry and geometric modeling, vol. 334, pp. 3–24. AMS (2003)

    Google Scholar 

  9. Hu, S.M.: Conversion between two classes of Bézier surfaces and geometric continuity jointing. Applied Mathematics: A Journal of Chinese Universities 8, 290–299 (1993)

    MATH  Google Scholar 

  10. Hu, S.M.: Conversion of a triangular Bézier patch into three rectangular Bézier patches. Computer Aided Geometric Design 13, 219–226 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  11. Hu, S.M., Wang, G.Z., Jin, T.G.: Generalized subdivision of Bézier surfaces. Graphical Models and Image Processing 58, 218–222 (1996)

    Article  Google Scholar 

  12. Hu, S.M.: Conversion between triangular and rectangular Bézier patches. Computer Aided Geometric Design 18, 667–671 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  13. Lasser, D.: Tensor product Bézier surfaces on triangle Bézier surfaces. Computer Aided Geometric Design 19, 625–643 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Lasser, D.: Triangular subpatches of rectangular Bézier surfaces, Computers and Mathematics with Applications (2007), doi:10.1016/j.camwa.2007.04.049

    Google Scholar 

  15. Ramshaw, L.: Blossoms are polar forms. Systems Research Center Reports 34, Palo Alto, Califorinia (1989)

    Google Scholar 

  16. Ramshaw, L.: Blossoming: A connect-the-dots approach to splines. Systems Research Center Reports 19, Palo Alto, Califorinia (1987)

    Google Scholar 

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Falai Chen Bert Jüttler

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© 2008 Springer-Verlag Berlin Heidelberg

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Yang, LQ., Zeng, XM. (2008). Trimming Bézier Surfaces on Bézier Surfaces Via Blossoming. In: Chen, F., Jüttler, B. (eds) Advances in Geometric Modeling and Processing. GMP 2008. Lecture Notes in Computer Science, vol 4975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79246-8_50

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  • DOI: https://doi.org/10.1007/978-3-540-79246-8_50

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79245-1

  • Online ISBN: 978-3-540-79246-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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