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In this paper, we consider the problem of computing the algebraic parametricequation of the Euclidean 1-center function in $\mathbb{R}^d$, $d \geq 2$, fora system of $n$ static points and $m$ mobile points having motion defined byrational parametric functions. We have shown that the corresponding Euclidean1-center function is a piecewise differentiable function and have derived itsexact parametric algebraic equation. If the positions of the static points andthe rational parametric equations of the motion of the mobile points are given,we have proposed an algorithm that computes the parametric equation of theEuclidean 1-center function.

Euclidean 1-center of a set of static and mobile points