Leírás
A Jordan curve $\gamma$ is a simple closed curve in the plane that divides the plane into two path-connected components, namely the \emph{interior} and \emph{exterior} of $\gamma$, denoted $\tilde\gamma$ and $\hat\gamma$ respectively. Given an arrangement $\Gamma$ of Jordan curves in the plane satisfying a specified property $\Pi$, a \emph{sweep curve} $\gamma\in\Gamma$ and a point $p\in\tilde\gamma$. \emph{Sweeping} is the process of continuous deformation of $\gamma$ to the point $p$ so that throughout the process the point $p$ lies in $\tilde\gamma$ and the arrangement satisfies the property $\Pi$. Sweeping is one of the most fundamental and powerful tools in computational and combinatorial geometry. Snoeyink and Hershberger in 1989 studied this topic for arrangements of curves satisfying "pairwise intersection" constraints. In this talk I will be reviewing this concept, along with two recent works on its generalizations.
This is based on joint works with Rahul Gangopadhyay, Rajiv Raman and Saurabh Ray.