While structural width parameters (of the input) belong to the standard toolbox of graph algorithms, it is not the usual case in computational geometry. As a case study we propose a natural extension of the structural graph parameter of clique-width to geometric point configurations represented by their order type. We study basic properties of this clique-width notion, and show that it is aligned with the general concept of clique-width of relational structures by Blumensath and Courcelle (2006). We also relate the new notion to monadic second-order logic of point configurations. As an application, we provide several linear FPT time algorithms for geometric point problems which are NP-hard in general, in the special case that the input point set is of bounded clique-width and the clique-width expression is also given.

虽然（输入的）结构宽度参数属于图算法的标准工具箱，但它不是计算几何中的常见情况。作为一个案例研究，我们建议将集团宽度的结构图参数自然扩展到由其订单类型表示的几何点配置. 我们研究了这个集团宽度概念的基本属性，并表明它与 Blumensath 和 Courcelle (2006) 的关系结构的集团宽度的一般概念一致。我们还将新概念与点配置的一元二阶逻辑相关联。作为一个应用，我们为几何点问题提供了几种线性 FPT 时间算法，这些问题通常是 NP 难的，在输入点集是有界团宽的特殊情况下，还给出了团宽表达式。