Rectangles are used to approximate objects, or sets of objects, in a plethora of applications, systems and index structures. Many tasks, such as nearest neighbor search and similarity ranking, require to decide if objects in one rectangle A may, must, or must not be closer to objects in a second rectangle B, than objects in a third rectangle R. To decide this relation of "Spatial Domination" it can be shown that using minimum and maximum distances it is often impossible to detect spatial domination. This spatial gem provides a necessary and sufficient decision criterion for spatial domination that can be computed efficiently even in higher dimensional space. In addition, this spatial gem provides an example, pseudocode and an implementation in Python.

中文翻译：

---

多维矩形的完全且充分的空间支配

矩形用于在大量应用程序、系统和索引结构中近似对象或对象集。许多任务，例如最近邻搜索和相似性排序，需要确定一个矩形 A 中的对象是否可以、必须或不得与第二个矩形 B 中的对象比第三个矩形 R 中的对象更接近。关于“空间支配”，可以证明使用最小和最大距离通常不可能检测到空间支配。这种空间宝石为空间支配提供了必要且充分的决策标准，即使在更高维度的空间中也可以高效计算。此外，这个空间宝石提供了一个示例、伪代码和 Python 实现。