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On Normals and Control Nets

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Mathematics of Surfaces XI

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3604))

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Abstract

This paper characterizes when the normals of a spline curve or spline surface lie in the more easily computed cone of the normals of the segments of the spline control net.

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References

  1. Boehm, W.: An affine representation of de Casteljau’s and de Boor’s rational algorithms. Computer Aided Geometric Design 10, 175–180 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  2. Floater, M.: Derivatives of rational Bézier curves. Computer Aided Geometric Design 9, 161–174 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  3. Floater, M.: Evaluation and properties of the derivative of a NURBS curve. In: Lyche, T., Schumaker, L. (eds.) Mathematical Methods in CAGD, Boston, Academic Press, pp. 261–274. Academic Press, London (1992)

    Google Scholar 

  4. Dyn, N.: Subdivision schemes in CAGD. In: Light, W. (ed.) Advances in Numerical Analysis. Volume II Wavelets, Subdivision Algorithms, and Radial Basis Functions, pp. 37–104. Oxford Science Publications, Wavelets (1992)

    Google Scholar 

  5. de Boor, C., Höllig, K., Riemenschneider, S.: Box splines. Springer, New York (1993)

    MATH  Google Scholar 

  6. Boehm, W.: Generating the Bézier points of triangular splines. In: Barnhill, R., Boehm, W. (eds.) Surfaces in Computer Aided Geometric Design, pp. 77–91. North-Holland Publishing Company, Amsterdam (1983)

    Google Scholar 

  7. Peters, J., Shiue, L.: Combining 4- and 3-direction subdivision. ACM Transactions on Graphics 23, 980–1003 (2004)

    Article  Google Scholar 

  8. Loop, C.T.: Smooth subdivision surfaces based on triangles. Master’s thesis, Department of Mathematics, University of Utah (1987)

    Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Ginkel, I., Peters, J., Umlauf, G. (2005). On Normals and Control Nets. In: Martin, R., Bez, H., Sabin, M. (eds) Mathematics of Surfaces XI. Lecture Notes in Computer Science, vol 3604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537908_14

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  • DOI: https://doi.org/10.1007/11537908_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28225-9

  • Online ISBN: 978-3-540-31835-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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