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Unbalanced Hermite Interpolation with Tschirnhausen Cubics

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Computational and Information Science (CIS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3314))

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Abstract

A method for constructing a cubic Pythagorean hodograph (PH) curve (called a Tschirnhausen cubic curve as well) satisfying unbalanced Hermite interpolation conditions is presented. The resultant curve interpolates two given end points, and has a given vector as the tangent vector at the starting point. The generation method is based on complex number calculation. Resultant curves are represented in a Bézier form. Our result shows that there are two Tschirnhausen cubic curves fulfilling the unbalanced Hermite interpolation conditions. An explicit formula for calculating the absolute rotation number is provided to select the better curve from the two Tschirnhausen cubic curves. Examples are given as well to illustrate the method proposed in this paper.

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Author information

Authors and Affiliations

  1. School of Software, Tsinghua University, Beijing, 100084, P. R. China

    Jun-Hai Yong & Hua Su

Authors
  1. Jun-Hai Yong
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  2. Hua Su
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Editor information

Editors and Affiliations

  1. School of Electronic Science and Technology, Anhui University, Hefei, Anhui, China

    Jun Zhang

  2. College of Science, Donghua University, 1882 Yan’an Xilu Road, 20051, Shanghai, China

    Ji-Huan He

  3. BASICS, Department of Computer Science and Engineering, Shanghai Jiao Tong University, 200030, Shanghai, China

    Yuxi Fu

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© 2004 Springer-Verlag Berlin Heidelberg

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Yong, JH., Su, H. (2004). Unbalanced Hermite Interpolation with Tschirnhausen Cubics. In: Zhang, J., He, JH., Fu, Y. (eds) Computational and Information Science. CIS 2004. Lecture Notes in Computer Science, vol 3314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30497-5_165

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  • DOI: https://doi.org/10.1007/978-3-540-30497-5_165

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24127-0

  • Online ISBN: 978-3-540-30497-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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