论文标题
四边形网格第三代：基于亚伯-Jacobi理论的优化奇异性配置
Quadrilateral Mesh Generation III: Optimizing Singularity Configuration Based on Abel-Jacobi Theory
论文作者
论文摘要
这项工作提出了一种严格且实用的算法，用于生成异晶四重差异差异，以产生四元网格的生成。这项工作基于代数曲线的亚伯 - 雅各比理论。算法管道可以总结如下：计算同源组；计算全体形态差异组；构建表面和雅各比品种的周期矩阵；为给定的除数计算Abel-Jacobi图；通过整数编程优化除数以满足亚伯 - 雅各布条件；通过RICCI流动在除数处使用圆锥形奇异性计算平坦的Riemannian度量；等距浸入分裂的表面上，并将规范性全态差异拉回表面，以获得Meromorormormormormormormormormormorthic Quartic差异；构建电动机图以生成所得的t栅。提出的方法是严格且实用的。 T-MESH结果可用于直接构建T-Spline。实验结果证明了所提出算法的效率和疗效。
This work proposes a rigorous and practical algorithm for generating meromorphic quartic differentials for the purpose of quad-mesh generation. The work is based on the Abel-Jacobi theory of algebraic curve. The algorithm pipeline can be summarized as follows: calculate the homology group; compute the holomorphic differential group; construct the period matrix of the surface and Jacobi variety; calculate the Abel-Jacobi map for a given divisor; optimize the divisor to satisfy the Abel-Jacobi condition by an integer programming; compute the flat Riemannian metric with cone singularities at the divisor by Ricci flow; isometric immerse the surface punctured at the divisor onto the complex plane and pull back the canonical holomorphic differential to the surface to obtain the meromorphic quartic differential; construct the motor-graph to generate the resulting T-Mesh. The proposed method is rigorous and practical. The T-mesh results can be applied for constructing T-Spline directly. The efficiency and efficacy of the proposed algorithm are demonstrated by experimental results.
