General planar quadrilateral mesh design using conjugate direction field

Yang Liu, 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.