SIAM Journal on Scientific Computing, Volume 43, Issue 5, Page A3155-A3183, January 2021.
We present a novel particle management method using the characteristic mapping framework. In the context of explicit evolution of parametrized curves and surfaces, the surface distribution of marker points created from sampling the parametric space is controlled by the area element of the parametrization function. As the surface evolves, the area element becomes uneven and the sampling suboptimal. In this method we maintain the quality of the sampling by precomposition of the parametrization with a deformation map of the parametric space. This deformation is generated by the velocity field associated to the diffusion process on the space of probability distributions and induces a uniform redistribution of the marker points. We also exploit the semigroup property of the heat equation to generate a submap decomposition of the deformation map which provides an efficient way of maintaining evenly distributed marker points on curves and surfaces undergoing extensive deformations.

中文翻译：

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一种用于粒子管理的扩散驱动特征映射方法

SIAM 科学计算杂志，第 43 卷，第 5 期，第 A3155-A3183 页，2021 年 1 月。
我们提出了一种使用特征映射框架的新型粒子管理方法。在参数化曲线和曲面的显式演化的背景下，通过对参数化空间进行采样而创建的标记点的曲面分布由参数化函数的面积元素控制。随着表面的演变，区域元素变得不均匀并且采样不理想。在这种方法中，我们通过参数化与参数空间的变形图的预组合来保持采样的质量。这种变形是由与概率分布空间上的扩散过程相关的速度场产生的，并导致标记点的均匀重新分布。