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Interpolating triangular meshes by Loop subdivision scheme

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Abstract

Using the limit point formula of the Loop subdivision scheme, we propose a very simple and efficient method for constructing interpolation surface of triangular meshes by Loop subdivision scheme. The excellent properties of the method are: (1) Locality: the perturbation of a given vertex only influences the surface shape near this vertex. (2) Efficiency: the locations of new points can be computed with explicit formulae. (3) Easiness in implementation: only the geometric rule of the first step should be modified. (4) Freedom: for each edge, there is one degree of freedom to adjust the shape of the interpolation surface. (5) Easiness in generalization: it is easy to generalize our method to other approximation subdivision schemes with explicit formulae to compute limit point.

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References

  1. Li G. Construction of subdivision schemes and fitting techniques based on subdivision surfaces (in Chinese). Report of post-doctoral, Hangzhou: Zhejiang University, 2003

    Google Scholar 

  2. Catmull E, Clark J. Recursively generated B-spline surface on arbitrary topological meshes. Comput Aid Des, 1978, 10:350–355

    Article  Google Scholar 

  3. Loop C. Smooth subdivision surfaces based on triangles. Master Thesis, Utah University, USA, 1987

    Google Scholar 

  4. Zorin D, Schröder P. Subdivision for modeling and animation. Course Notes of SIGGRAPH 2000. ACM SIGGRAPH, 2000

  5. Dyn N, Levin D, Gregory J A. A butterfly subdivision scheme for surface interpolatory with tension control. ACM Trans Graph, 1 1990, 9:160–169

    Article  MATH  Google Scholar 

  6. Zorin D, Schröder P, Sweldens W. Interpolating subdivision for meshes with arbitrary topology. Comput Graph, 1996, 30:189–192

    Google Scholar 

  7. Kobbelt L. Interpolatory subdivision on open quadrilateral nets with arbitrary topology. Comput Graph Forum, 1996, 15:409–420

    Article  Google Scholar 

  8. Hoppe H, DeRose T, Duchamp M, et al. Piecewise smooth surface reconstruction. Comput Graph, 1994, 28:295–302

    Google Scholar 

  9. Nasri A. Polyhedral subdivision methods for free-form surfaces. ACM Trans Graph, 1987, 6:29–73

    Article  MATH  Google Scholar 

  10. Brunet P. Including shape handles in recursive subdivision surfaces. Comput Aid Geometr Des, 1988, 5:41–50

    Article  MATH  MathSciNet  Google Scholar 

  11. Halstead M, Kass M, DeRose T. Efficient, fair interpolation using Catmull-Clark surface. Comput Graph, 1993, 27:35–44

    Google Scholar 

  12. Zheng J, Cai Y. Interpolation over arbitrary topology meshes using a two-phase subdivision scheme. IEEE Trans Visual Comput Graph, 2006, 12:301–310

    Article  Google Scholar 

  13. Warren J, Weimer H. Subdivision Methods for Geometric Design: A Constructive Approach. San Francisco: Morgan Kaufmann Publishers, 2002

    Google Scholar 

  14. Ma W, Ma X, Tso S K, et al. A direct approach for subdivision surface fitting from a dense triangle mesh. Comput Aid Des, 2004, 36:525–536

    Article  Google Scholar 

  15. Yang X. Surface interpolation of meshes by geometric subdivision. Comput Aid Des, 2005, 37:497–508

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Institute of Applied Mathematics and Engineering Computations, Hangzhou Dianzi University, Hangzhou, 310018, China

    ChongYang Deng

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    GuoZhao Wang

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  1. ChongYang Deng
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  2. GuoZhao Wang
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Correspondence to ChongYang Deng.

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Deng, C., Wang, G. Interpolating triangular meshes by Loop subdivision scheme. Sci. China Inf. Sci. 53, 1765–1773 (2010). https://doi.org/10.1007/s11432-010-4049-y

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  • DOI: https://doi.org/10.1007/s11432-010-4049-y

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