论文标题
一种动力学系统方法，用于沿刚体运动的多型匹配的形状匹配
A dynamical systems approach for the shape matching of polytopes along rigid-body motions
论文作者
论文摘要
我们提出了一种动态系统方法，用于沿刚体运动的多型集合中的几何匹配。每个多层可以用顶点和边缘或面孔来表征。对于几何匹配，我们提出了一个动力系统系统，用于质心的演化和多型的旋转，以匹配刚体运动下的顶点，该系统可以分解为翻译和旋转的组成。我们提出的动力系统作用于产品空间$（{\ Mathbb r}^d \ times so（d））^n $。质心的演变可以通过耦合的线性二阶动力学系统描述，具有扩散的线性耦合，而在$（d）^n $上，Lohe矩阵模型描述了顶点的旋转。特别是，与以前的作品相比，LOHE矩阵模型是从某些物理原理中得出的，在该作品中，LOHE矩阵模型被用作系统动力学。这是LOHE矩阵模型的早期作品之间的对比差异，该工程已被采用了矩阵的骨料建模。我们还提供了一个分析结果，从而为一致多型的集合提供了完整的形状匹配，并提供了几个数值示例，以视觉上说明分析结果。
We present a dynamical systems approach for geometric matchings in an ensemble of polytopes along rigid-body motions. Each polytope can be characterized by a vertex set and edge or faces determined by vertices, and polygons and simplexes correspond to a polytope. For a geometric matching, we propose a system of dynamical system for the evolution of centroids and rotations of polytopes to match the vertices under rigid-body motions which can be decomposed as a composition of translation and rotations. Our proposed dynamical system acts on the product space $({\mathbb R}^d \times SO(d))^N$. The evolution of centroids can be described by the coupled linear second-order dynamical system with diffusive linear couplings, whereas rotations for the matching of vertices are described by the Lohe matrix model on $SO(d)^N$. In particular, the Lohe matrix model has been derived from some set of physical principles compared to previous works in which the Lohe matrix model were employed as a system dynamics. This is a contrasted difference between earlier works on the Lohe matrix model which has been adopted a priori for an aggregate modeling of matrices. We also provide an analytical result leading to the complete shape matchings for an ensemble of congruent polytopes, and several numerical examples to illustrate analytical results visually.
