Adaptive Geometry Compression Based on 4-Point Interpolatory Subdivision Schemes

  • Hui Zhang
  • Jun-Hai Yong
  • Jean-Claude Paul
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4153)


We propose an adaptive geometry compression method based on 4-point interpolatory subdivision schemes. It can work on digital curves of arbitrary dimensions. With the geometry compression method, a digital curve is adaptively compressed into several segments with different compression levels. Each segment is a 4-point subdivision curve with a subdivision step. In the meantime, we provide high-speed 4-point interpolatory subdivision curve generation methods for efficiently decompressing the compressed data. In the decompression methods, we consider both the open curve case and the closed curve case. For an arbitrary positive integer k, formulae of the number of the resultant control points of an open or closed 4-point subdivision curve after k subdivision steps are provided. The time complexity of the new approaches are O(n), where n is the number of the points in the given digital curve. Examples are provided as well to illustrate the efficiency of the proposed approaches.


geometry compression subdivision scheme 4-point subdivision interpolatory subdivision high-speed curve generation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hui Zhang
    • 1
  • Jun-Hai Yong
    • 1
  • Jean-Claude Paul
    • 1
    • 2
  1. 1.School of SoftwareTsinghua UniversityBeijingP.R. China
  2. 2.CNRSFrance

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