Slit Map: Conformal Parameterization for Multiply Connected Surfaces

  • Xiaotian Yin
  • Junfei Dai
  • Shing-Tung Yau
  • Xianfeng Gu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4975)


Surface parameterization is a fundamental tool in geometric modeling and processing. Different to most existing methods, this work introduces a linear method, called slit map, to conformally parameterize multiply connected disk-like surfaces with canonical domains, namely circular slit domain (annulus with concentric circular slits) or parallel slit domain (rectangle with parallel slits) equivalently. The construction is based on holomorphic one-forms, which is intrinsic, automatic and efficient. Slit map owns many merits over existing methods. The regularity of the image boundaries simplifies many geometric process, such as surface matching and etc; the full utilization of the parallel slit texture domain improves the packing efficiency for texture mapping; the positions of the slits are completely determined by the surface geometry and can be treated as the finger prints for surface classification. In the paper, both the underlying theory and the algorithm pipeline are explained. Preliminary experimental results are shown for several application purposes.


conformal parameterization slit map holomorphic one-form canonical parameter domain 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Xiaotian Yin
    • 1
  • Junfei Dai
    • 2
  • Shing-Tung Yau
    • 3
  • Xianfeng Gu
    • 1
  1. 1.Center for Visual ComputingState University of New York at Stony Brook 
  2. 2.Center of Mathematics ScienceZhejiang University 
  3. 3.Mathematics DepartmentHarvard University 

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