General planar quadrilateral mesh design using conjugate direction field

  • Weiwei Xu
  • Jun Wang
  • Lifeng Zhu
  • Baining Guo
  • Falai Chen
  • Guoping Wang

SA '11 Proceedings of the 2011 SIGGRAPH Asia Conference |

Published by ACM

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We present a novel method to approximate a freeform shape with a planar quadrilateral (PQ) mesh for modeling architectural glass structures. Our method is based on the study of conjugate direction fields (CDF) which allow the presence of ±k/4(k ∈ Z) singularities. Starting with a triangle discretization of a freeform shape, we first compute an as smooth as possible conjugate direction field satisfying the user’s directional and angular constraints, then apply mixed-integer quadrangulation and planarization techniques to generate a PQ mesh which approximates the input shape faithfully. We demonstrate that our method is effective and robust on various 3D models.