论文标题
基于施加的奇异性配置的可集成跨场生成 - 2D歧管情况 -
Integrable cross-field generation based on imposed singularity configuration -- the 2D manifold case --
论文作者
论文摘要
这项工作为基于用户施加的奇异性配置在2D歧管上生成可集成的跨场的数学基础。在本文中，我们要么使用自然出现的奇异性，例如，通过解决非线性问题或用作输入用户定义的奇异性模式，可能具有高价奇异性，通常不会出现在跨场计算中。这种奇异性集在Abel-Jacobi的有效奇异性配置条件下的约束。本文的主要贡献是开发公式，该公式允许通过仅分辨出两个线性PDE的分辨率从给定的一组奇点计算可集成的各向同性2D跨场。为了解决可能的次优奇点分布的问题，我们还介绍了基于用户施加的奇异性模式生成可集成的各向异性2D跨场的数学设置。开发的配方同时支持各向同性和各向异性块结构的四方网格生成。 关键字：可集成的2D跨场，有效的奇异性配置，Quad布局，Quad Meshing
This work presents the mathematical foundations for the generation of integrable cross-field on 2D manifolds based on user-imposed singularity configuration. In this paper, we either use singularities that appear naturally, e.g., by solving a non-linear problem, or use as an input user-defined singularity pattern, possibly with high valence singularities that typically do not appear in cross-field computations. This singularity set is under the constraint of Abel-Jacobi's conditions for valid singularity configurations. The main contribution of the paper is the development of a formulation that allows computing an integrable isotropic 2D cross-field from a given set of singularities through the resolution of only two linear PDEs. To address the issue of possible suboptimal singularities' distribution, we also present the mathematical setting for the generation of an integrable anisotropic 2D cross-field based on a user-imposed singularity pattern. The developed formulations support both an isotropic and an anisotropic block-structured quad mesh generation. Keywords: integrable 2D cross-field, valid singularity configuration, quad layout, quad meshing
