4.7 Article

Fields on Symmetric Surfaces

Journal

ACM TRANSACTIONS ON GRAPHICS
Volume 31, Issue 4, Pages -

Publisher

ASSOC COMPUTING MACHINERY
DOI: 10.1145/2185520.2185607

Keywords

symmetry; n-rosy field; quad mesh

Funding

  1. Direct For Computer & Info Scie & Enginr
  2. Div Of Information & Intelligent Systems [0905502] Funding Source: National Science Foundation
  3. Direct For Computer & Info Scie & Enginr
  4. Office of Advanced Cyberinfrastructure (OAC) [1047932] Funding Source: National Science Foundation

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Direction fields, line fields and cross fields are used in a variety of computer graphics applications ranging from non-photorealistic rendering to remeshing. In many cases, it is desirable that fields adhere to symmetry, which is predominant in natural as well as man-made shapes. We present an algorithm for designing smooth N-symmetry fields on surfaces respecting generalized symmetries of the shape, while maintaining alignment with local features. Our formulation for constructing symmetry fields is based on global symmetries, which are given as input to the algorithm, with no isometry assumptions. We explore in detail the properties of generalized symmetries (reflections in particular), and we also develop an algorithm for the robust computation of such symmetry maps, based on a small number of correspondences, for surfaces of genus zero.

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