欧氏1-一组静态和移动点的中心
Euclidean 1-center of a set of static and mobile points
摘要：
在本文中，我们考虑的问题，计算的欧几里德1-中心函数的代数参数方程的$\mathbb{R}^d$，$d \geq 2$，$n$静态点和$m$具有由有理参数函数定义的运动点的系统。我们证明了相应的欧氏1-中心函数是分段可微函数，并导出了它的精确参数代数方程。在已知静止点的位置和运动点的有理参数方程的情况下，我们提出了一种计算欧氏1-中心函数参数方程的算法。
英文摘要：
In this paper, we consider the problem of computing the algebraic parametric equation of the Euclidean 1-center function in $\mathbb{R}^d$, $d \geq 2$, for a system of $n$ static points and $m$ mobile points having motion defined by rational parametric functions. We have shown that the corresponding Euclidean 1-center function is a piecewise differentiable function and have derived its exact parametric algebraic equation. If the positions of the static points and the rational parametric equations of the motion of the mobile points are given, we have proposed an algorithm that computes the parametric equation of the Euclidean 1-center function.
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。
