基于样条的平面图调和映射参数化
On the Spline-Based Parameterisation of Plane Graphs via Harmonic Maps
AI总结：
本文提出一种基于样条和调和映射的平面图参数化框架，支持局部材料参数设置，适用于等几何分析数值模拟及经典网格提取。
摘要：
本文提出了一种针对平面图的基于样条的参数化框架。平面图由形成闭环的曲线集合来表征，这些闭环围成了需要单独参数化的平面面。在此，我们重点关注在面间界面上保持一致的参数化。对每个面进行单独参数化允许施加局部不同的材料参数，这在弹性力学和热传递等工程领域有应用。对于各个面的参数化，我们采用了调和映射的概念。该平面图的基于样条的参数化适用于基于等几何分析的数值模拟，或可用于提取任意密度的经典网格。特定应用的特征可以在样条层面或网格提取步骤中融入几何的数学描述。
英文摘要：
This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby, we focus on parameterisations that are conforming across the interfaces between the faces. Parameterising each face individually allows for the imposition of locally differing material parameters which has applications in various engineering disciplines, such as elasticity and heat transfer. For the parameterisation of the individual faces, we employ the concept of harmonic maps. The plane graph's spline-based parameterisation is suitable for numerical simulation based on isogeometric analysis or can be utilised to extract arbitrarily dense classical meshes. Application-specific features can be built into the geometry's mathematical description either on the spline level or in the mesh extraction step.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
