空间贡献软件为创建笛卡儿层和Geohash 代码提供工具，并且为创建Lucene查询和过滤器对象提供工具。
The spatial contrib offers tools for creating Cartesian tiers and Geohash codes, as well as tools for creating Lucene query and filter objects.
分析和计算的空间问题，一般可采用两类坐标系：笛卡儿直角坐标系和极坐标系。
There are two kinds of coordinates, Cartesian coordinates and polar coordinates, with which spatial issues are analyzed and calculated.
但是，当我们从物理的角度审视这一问题时，就会发现可以把这个曲面嵌入一个三维空间中，粒子的运动可以在笛卡儿坐标下分解为三个互相正交的方向。
However, when examining the same problem in the physical point of view, the motion of the particle can also be described in the three-dimensional coordinates.
本文利用线性空间笛卡儿积的思想，给出了关于上述结论的简洁的、严密的逻辑证明。
Given a simple rigorous proof for the theorem by structuring Cartesian product of linear Spaces.
本文利用线性空间笛卡儿积的思想，给出了关于上述结论的简洁的、严密的逻辑证明。
Given a simple rigorous proof for the theorem by structuring Cartesian product of linear Spaces.
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