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• # Cell complex单元复形

### 概念

（1）Piecewise linear complex (PLC) 分段线性复合形

（2）Cell complex 单元复形 [1] （胞腔复形？ 元胞复形）

A separable space  that is a union of non-intersecting cells. Here, by a -dimensional cell one means a topological space that is homeomorphic to the interior of the unit cube of dimension . If for each -dimensional cell  of  one is given a continuous mapping  from the -dimensional cube  into  such that: 1) the restriction  of  to the interior  of  is one-to-one and the image  is the closure  in  of  (here  is a homeomorphism of  onto ); and 2) the set , where  is the boundary of , is contained in the union  of the cells  of , then  is called a cell complex; the union  is called the skeleton of dimension  of the cell complex . An example of a cell complex is a simplicial polyhedron.

A subset  of a cell complex  is called a subcomplex if it is a union of cells of  containing the closures of such cells. Thus, the -dimensional skeleton  of  is a subcomplex of . Any union and any intersection of subcomplexes of  are subcomplexes of .

Any topological space can be regarded as a cell complex — as the union of its points, which are cells of dimension 0. This example shows that the notion of a cell complex is too broad; therefore narrower classes of cell complexes are important in applications, for example the class of cellular decompositions or CW-complexes (cf. CW-complex).

https://www.encyclopediaofmath.org/index.php/Cell_complex

（3）Linear Cell Complex 线性单元复形 （参考

（4）2D Arrangements  [2]

给定一组平面曲线（planar curves）, arrangement是将平面分解subdivision of the plane为0维zero-dimensional, 一维（线）one-dimensional 二维（面）单元 two-dimensional cells, 称作节点vertices、边 edges和面元 faces

技巧：

生成一个Cell complex之后，用ArcGIS相交Intersect工具，利用范围裁剪。

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