Metric-Driven RoSy Fields Design and Remeshing

Yu-Kun Lai Tsinghua University Miao Jin University of Louisiana Xuexiang Xie Nanyang Technological University Ying He Nanyang Technological University Jonathan Palacios Nanyang Oregon State University Eugene Zhang Oregon State University Shi-Min Hu Tsinghua University Xianfeng David Gu Stony Brook University

Geometric Modeling and Processing mathscidoc:1608.16047

IEEE Transactions on Visualization and Computer Graphics, 16, (1), 95-108, 2010.1
This work introduces a rigorous and practical approach for automatic N-RoSy field design on arbitrary surfaces with user defined field topologies. The user has full control of the number, positions and indices of the singularities, the turning numbers of the loops, and is able to edit the field interactively. We formulate N-RoSy field construction as designing a Riemannian metric, such that the holonomy along any loop is compatible with the local symmetry of N-RoSy fields. We prove the compatibility condition using discrete parallel transport. The complexity of N-RoSy field design is caused by curvatures. In our work, we propose to simplify the Riemannian metric to make it flat almost everywhere. This approach greatly simplifies the process and improves the flexibility, such that, it can design N-RoSy fields with single singularity, and mixed-RoSy fields. To demonstrate the effectiveness of our approach, we apply our design system to pen-and-ink sketching and geometry remeshing.
RoSy Fields, Riemannian metric, geometry remeshing
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@inproceedings{yu-kun2010metric-driven,
  title={Metric-Driven RoSy Fields Design and Remeshing},
  author={Yu-Kun Lai, Miao Jin, Xuexiang Xie, Ying He, Jonathan Palacios, Eugene Zhang, Shi-Min Hu, and Xianfeng David Gu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160821110421987420358},
  booktitle={IEEE Transactions on Visualization and Computer Graphics},
  volume={16},
  number={1},
  pages={95-108},
  year={2010},
}
Yu-Kun Lai, Miao Jin, Xuexiang Xie, Ying He, Jonathan Palacios, Eugene Zhang, Shi-Min Hu, and Xianfeng David Gu. Metric-Driven RoSy Fields Design and Remeshing. 2010. Vol. 16. In IEEE Transactions on Visualization and Computer Graphics. pp.95-108. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160821110421987420358.
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