The area query, to find all elements contained in a specified area from a certain set of spatial objects, is a very important spatial query widely required in various fields. A number of approaches have been proposed to implement this query, the best known of which is to obtain a rough candidate set through spatial indexes and then refine the candidates through geometric validations to get the final result. When the shape of the query area is a rectangle, this method has very high efficiency. However, when the query area is irregular, the candidate set is usually much larger than the final result set, which means a lot of redundant detection needs to be done, thus the efficiency is greatly limited. In view of this issue, we propose a method of iteratively generating candidates based on Voronoi diagrams and apply it to area queries. The experimental results indicate that with our approach, the number of candidates in the process of area query is greatly reduced and the efficiency of the query is significantly improved.

中文翻译：

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基于 Voronoi 图的区域查询

区域查询是从一定的空间对象集合中找出包含在指定区域内的所有元素，是各个领域广泛需要的非常重要的空间查询。已经提出了多种方法来实现该查询，其中最著名的是通过空间索引获得粗略的候选集，然后通过几何验证细化候选以获得最终结果。当查询区域的形状为矩形时，该方法效率非常高。然而，当查询区域不规则时，候选集通常远大于最终结果集，这就意味着需要进行大量的冗余检测，从而大大限制了效率。针对这个问题，我们提出了一种基于 Voronoi 图迭代生成候选的方法，并将其应用于区域查询。