论文标题
粒子管理的扩散驱动的特征映射方法
A diffusion-driven Characteristic Mapping method for particle management
论文作者
论文摘要
我们使用特征映射框架提出了一种新颖的粒子管理方法。在参数化曲线和表面的明确演变的背景下，由采样空间创建的标记点的表面分布由参数函数的面积元素控制。随着表面的发展，面积元素变得不平衡，采样次优。在这种方法中，我们通过使用参数空间的变形图预先组合参数化来维持采样的质量。该变形是由与概率分布空间相关的速度场产生的，并诱导标记点的均匀重新分布。我们还利用热方程的半群属性来生成变形图的子纸分解，该分解提供了一种有效的方法，可以在曲线和表面上保持均匀分布的标记点，并经历广泛的变形。
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 pre-composition 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.
