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Loop Subdivision Surface Based Progressive Interpolation

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Abstract

A new method for constructing interpolating Loop subdivision surfaces is presented. The new method is an extension of the progressive interpolation technique for B-splines. Given a triangular mesh M, the idea is to iteratively upgrade the vertices of M to generate a new control mesh \(\overline{M}\) such that limit surface of \(\overline{M}\) would interpolate M. It can be shown that the iterative process is convergent for Loop subdivision surfaces. Hence, the method is well-defined. The new method has the advantages of both a local method and a global method, i.e., it can handle meshes of any size and any topology while generating smooth interpolating subdivision surfaces that faithfully resemble the shape of the given meshes. The meshes considered here can be open or closed.

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Authors and Affiliations

  1. Department of Computer Science, University of Kentucky, Lexington, KY, 40506, U.S.A.

    Fu-Hua (Frank) Cheng, Feng-Tao Fan, Cong-Lin Huang & Jia-Xi Wang

  2. Department of Mathematics and Computer Science, Virginia State University, Petersburg, VA, 23806, U.S.A.

    Shu-Hua Lai

  3. School of Software, Tsinghua University, Beijing, 100084, China

    Jun-Hai Yong

Authors
  1. Fu-Hua (Frank) Cheng
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  2. Feng-Tao Fan
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  3. Shu-Hua Lai
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  4. Cong-Lin Huang
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  5. Jia-Xi Wang
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  6. Jun-Hai Yong
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Corresponding author

Correspondence to Fu-Hua (Frank) Cheng.

Additional information

Research work presented here is supported by NSF of USA under Grant No. DMI-0422126. The last author is supported by the National Natural Science Foundation of China under Grant Nos. 60625202, 60533070.

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Cheng, FH.(., Fan, FT., Lai, SH. et al. Loop Subdivision Surface Based Progressive Interpolation. J. Comput. Sci. Technol. 24, 39–46 (2009). https://doi.org/10.1007/s11390-009-9199-2

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  • DOI: https://doi.org/10.1007/s11390-009-9199-2

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