We study the query version of constrained minimum link paths between two points inside a simple polygon with $n$ vertices such that there is at least one point on the path, visible from a query point. Initially, we solve this problem for two given points $s$, $t$ and a query point $q$. Then, the proposed solution is extended to a general case for three arbitrary query points $s$, $t$ and $q$. In the former, we propose an algorithm with $O(n)$ preprocessing time. Extending this approach for the latter case, we develop an algorithm with $O(n^3)$ preprocessing time. The link distance of a $q$-$visible$ path between $s$, $t$ as well as the path are provided in time $O(\log n)$ and $O(k+\log n)$, respectively, for the above two cases, where $k$ is the number of links.

翻译：我们研究一个简单多边形内两个点与一美元顶点之间的受限最低链接路径的查询版本,这样这条路径上至少有一个点,可以从一个查询点看出。最初,我们为两个给定点解决了这个问题,一个是美元,一个是美元,一个是美元,一个是美元,一个是美元。然后,建议的解决办法扩大到三个任意查询点的一般情况,一个是美元,一个是美元,一个是美元,另一个是美元。在前者,我们建议一种有O(n)美元预处理时间的算法。在后一种情况下,我们开发了一个有美元(n)3美元预处理时间的算法。在美元、美元和美元之间,一个是美元,一个是可见路径的连接距离,分别是美元,一个是美元,一个是美元,一个是美元,一个是美元,一个是美元,两个是美元(k)美元,是上述两个是链接的数量。