Quadrangulation through morse-parameterization hybridization
Quadrangulation through morse-parameterization hybridization
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DOI：
10.1145/3197517.3201354
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
Xianzhong Fang;H. Bao;Y. Tong;M. Desbrun;Jin Huang
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文献类型：
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作者：
Xianzhong Fang;H. Bao;Y. Tong;M. Desbrun;Jin Huang
我们介绍了一种方法，以将基于摩尔斯的方法的理论保证与参数化方法的实际优势结合在一起的任意三角态表面的四边形网格。我们首先通过eigensolver构造了几个高斯 - 纽顿迭代，一个周期性的四维矢量字段与输入网格上的用户提供的帧字段和/或一组功能对齐。然后，基于最佳周期矢量场的差异能量，沿着生成树沿跨越树贪婪地计算了一个现场对齐的参数化，从该树的大部分表面上可以有效提取四方元。然后对元素覆盖的几个区域进行了更新，并将周期矢量场的第一个组件用作摩尔斯函数来提取剩余的四边形。这种混合参数化和基于摩尔斯的四分之一的四键键方法不仅很快（贪婪地构建了参数化，并且仅需在少数未透明的贴片中添加摩尔斯的函数），而且可以保证提供具有功能与功能与特征的四分之一的网眼。非分级单元格在任意表面上与输入框架场密切匹配。我们表明，我们的方法比基于摩尔斯的技术要快得多，因为它不需要密集的输入网格，并且比具有复杂功能的模型上的基于参数化的技术要比基于参数化的技术更强大。
We introduce an approach to quadrilateral meshing of arbitrary triangulated surfaces that combines the theoretical guarantees of Morse-based approaches with the practical advantages of parameterization methods. We first construct, through an eigensolver followed by a few Gauss-Newton iterations, a periodic four-dimensional vector field that aligns with a user-provided frame field and/or a set of features over the input mesh. A field-aligned parameterization is then greedily computed along a spanning tree based on the Dirichlet energy of the optimal periodic vector field, from which quad elements are efficiently extracted over most of the surface. The few regions not yet covered by elements are then upsampled and the first component of the periodic vector field is used as a Morse function to extract the remaining quadrangles. This hybrid parameterization- and Morse-based quad meshing method is not only fast (the parameterization is greedily constructed, and the Morse function only needs to be upsampled in the few uncovered patches), but is guaranteed to provide a feature-aligned quad mesh with non-degenerate cells that closely matches the input frame field over an arbitrary surface. We show that our approach is much faster than Morse-based techniques since it does not require a densely tessellated input mesh, and is significantly more robust than parameterization-based techniques on models with complex features.