单连通和非单连通的概念，研究哪些环路能界定曲面，可以用来对空间内部物体的形状进行分类。

This concept of being simply connected or not, and studying which loops bound surfaces or not can be used to classify shapes of things inside space.

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转身数的总和必须是零，这是为了避免陷入某些环路，比如大写字母 G 形状的环路（在纸上试着走一下这个形状，就会明白我的意思）。

The requirement that your turns sum to zero is necessary to keep you from getting caught in certain loops, such as one shaped like a capital G (try it out on paper to see what I mean).

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本文提出了一种把像素模拟与环路积分算法相结合，计算复杂形状面目标有效毁伤面积的新方法。

To calculate valid damage area of irregular targets, this paper creates a new method combine pixel simulation with circuit integral algorithm.

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