Computational p-Willmore Flow with Conformal Penalty
Computational p-Willmore Flow with Conformal Penalty
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DOI：
10.1145/3369387
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发表时间：
2019-07
期刊：
影响因子：
--
通讯作者：
A. Gruber;E. Aulisa
中科院分区：
文献类型：
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作者：
A. Gruber;E. Aulisa
Mondino [2011] 的工作中引入的无符号 p-Willmore 泛函概括了重要的几何泛函，用于测量浸没表面的面积和 Willmore 能量。目前，Dziuk [2008] 工作中的技术适用于将该函数的第一个变体计算为弱形式方程组，随后用于开发 R3 中闭合曲面的 p-Willmore 流模型。该模型适用于表面积和封闭体积的约束，并且显示出单调降低 p-Willmore 能量。此外，还制定了基于惩罚的正则化程序，以防止沿流的人为网格退化；受到 Kamberov 等人的工作中导出的共形条件的启发。 [1996]，该过程鼓励在封闭和定向表面浸没过程中保持角度。接下来，讨论了两个过程的有限元离散化，给出了运行流程的算法，并介绍了网格编辑的应用。
The unsigned p-Willmore functional introduced in the work of Mondino [2011] generalizes important geometric functionals, which measure the area and Willmore energy of immersed surfaces. Presently, techniques from the work of Dziuk [2008] are adapted to compute the first variation of this functional as a weak-form system of equations, which are subsequently used to develop a model for the p-Willmore flow of closed surfaces in R3. This model is amenable to constraints on surface area and enclosed volume and is shown to decrease the p-Willmore energy monotonically. In addition, a penalty-based regularization procedure is formulated to prevent artificial mesh degeneration along the flow; inspired by a conformality condition derived in the work of Kamberov et al. [1996], this procedure encourages angle-preservation in a closed and oriented surface immersion as it evolves. Following this, a finite-element discretization of both procedures is discussed, an algorithm for running the flow is given, and an application to mesh editing is presented.