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Higher-Order Level-Set Method and Its Application in Biomolecular Surfaces Construction

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Abstract

We present a general framework for a higher-order spline level-set (HLS) method and apply this to biomolecule surfaces construction. Starting from a first order energy functional, we obtain a general level set formulation of geometric partial differential equation, and provide an efficient approach to solving this partial differential equation using a C 2 spline basis. We also present a fast cubic spline interpolation algorithm based on convolution and the Z-transform, which exploits the local relationship of interpolatory cubic spline coefficients with respect to given function data values. One example of our HLS method is demonstrated, which is the construction of biomolecule surfaces (an implicit solvation interface) with their individual atomic coordinates and solvated radii as prerequisites.

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Authors and Affiliations

  1. CVC, Department of Computer Science, Institute for Computational Engineering and Sciences University of Texas at Austin, Austin, TX, 78712, U.S.A.

    Chandrajit L. Bajaj

  2. LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences Chinese Academy of Sciences, Beijing, 100190, China

    Guo-Liang Xu & Qin Zhang

  3. School of Sciences, Beijing Information Science and Technology University, Beijing, 100192, China

    Qin Zhang

Authors
  1. Chandrajit L. Bajaj
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  2. Guo-Liang Xu
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  3. Qin Zhang
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Corresponding author

Correspondence to Chandrajit L. Bajaj.

Additional information

Bajaj is supported in part by NSF of USA under Grant No. CNS-0540033 and NIH under Grant Nos. P20-RR020647, R01-EB00487, R01-GM074258, R01-GM07308. Xu and Zhang are supported by the National Natural Science Foundation of China under Grant No. 60773165 and the National Basic Research 973 Program of China under Grant No. 2004CB318000. Zhang is also supported by Beijing Educational Committee Foundation under Grant No. KM200811232009.

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Bajaj, C.L., Xu, GL. & Zhang, Q. Higher-Order Level-Set Method and Its Application in Biomolecular Surfaces Construction. J. Comput. Sci. Technol. 23, 1026–1036 (2008). https://doi.org/10.1007/s11390-008-9184-1

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  • DOI: https://doi.org/10.1007/s11390-008-9184-1

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