[从头学数学] 第273节 [计算几何] 多边形求交集

剧情提要：
阿伟看到了一本比较有趣的书，是关于《计算几何》的，2008年由北清派出版。很好奇
它里面讲了些什么，就来看看啦。


正剧开始：
星历2016年09月23日 11:58:19, 银河系厄尔斯星球中华帝国江南行省。

[工程师阿伟]正在和[机器小伟]一起研究[计算几何]]。

两个多边形求交集，比如下图：

最初很容易想到通过顶点在另一个多边形里的位置来判断。

<span style="font-size:18px;">#class Polygon():    #格式:path = [[-6, 9], [8, -7], [8, 3], [-6, 9]]    def __init__(self, path):        if (path[-1] != path[0]):            path.append(path[0]);        self.path = path;        #顶点数量        self.vertNum = len(self.path)-1;        self.vertex = [];        self.edge = [];        self.vertexCalc();        self.edgeCalc();    def vertexCalc(self):        for i in range(self.vertNum):            self.vertex.append(Point(self.path[i]));    def getVertex(self):        return self.vertex;    def edgeCalc(self):        for i in range(self.vertNum):            self.edge.append(SegLine(self.path[i], self.path[i+1]));    def getEdge(self):        return self.edge;    #传入的是[x, y]格式的对象    def pointInPolygon(self, point):        #测试点左右两边截多边形的各边，得到的交点数都为奇数，说明测试点在多边形内        #反之在外面        oddNodes = False;        #点在多边形的边上        if (Point(point) in self.vertex):            return 0;        x, y = point[0], point[1];        j = self.vertNum - 1;        for i in range(self.vertNum):            p1 = self.vertex[i].value();            p2 = self.vertex[j].value();            px1, py1 = p1[0], p1[1];            px2, py2 = p2[0], p2[1];                        if (((py1 < y and py2 >= y) or (py2 < y and py1 >= y)) and \               (px1 <= x or px2 <= x)):                if ((px1+(y-py1)/(py2-py1)*(px2-px1)) < x):                    oddNodes = not oddNodes;            j = i;        if (oddNodes == False):            #点不在多边形内            return -1;        else:            #点在多边形内            return 1;    #两个多边形的交集区域    def intersection(self, other):        vlist_1 = self.vertex;        vlist_2 = other.vertex;                commonVert = set();        for i in range(len(vlist_1)):            #点在多边形外部是-1, 在边上是0, 在内部是1            if other.pointInPolygon(vlist_1[i].value()) != -1:                commonVert.add(vlist_1[i]);        for i in range(len(vlist_2)):            if self.pointInPolygon(vlist_2[i].value()) != -1:                commonVert.add(vlist_2[i]);        commonVert = list(commonVert);        for i in range(len(commonVert)):            commonVert[i] = commonVert[i].value();        #返回顶点序列        return commonVert;            #把给定的坐标点阵列数组[x, y],...按照距离它们的中心点的角度进行排列    #是为了把无序排列的闭合曲线上的点进行有序排列，后续可再经过连线形成    #可填充的闭合曲线    def angularSort(self, array):        len0 = len(array);        len1 = len(array[0]);        if (len0 <= 0 or len1 != 2):            return array;        xTotal = yTotal = xCenter = yCenter = 0;        for i in range(len0):            xTotal += array[i][0];            yTotal += array[i][1];        xCenter = xTotal/len0;        yCenter = yTotal/len0;        x = y = xdiff = ydiff = 0;        arrayB = [];                for i in range(len0):            x = array[i][0];            y = array[i][1];            xdiff = x - xCenter;            ydiff = y - yCenter;            if (abs(xdiff) < 1e-4):                if (ydiff > 0):                    arrayB.append([x, y, math.pi/2]);                else:                    arrayB.append([x, y, math.pi/2*3]);            elif (xdiff >= 0 and ydiff > 0):                #第一象限                arrayB.append([x, y, math.atan(abs(ydiff/xdiff))]);            elif (xdiff < 0 and ydiff >= 0):                #第二象限                arrayB.append([x, y, math.pi-math.atan(abs(ydiff/xdiff))]);            elif (xdiff <= 0 and ydiff < 0):                #第三象限                arrayB.append([x, y, math.pi+math.atan(abs(ydiff/xdiff))]);            else:                #第四象限                arrayB.append([x, y, math.pi*2-math.atan(abs(ydiff/xdiff))]);        arrayB = sorted(arrayB, key = lambda a:(a[2], (a[0]-xCenter)**2+(a[1]-yCenter)**2));        retArray = [];        for i in range(len(arrayB)):            retArray.append(arrayB[i][:-1]);        return retArray;>>> 20[][[4, -1], [3.56, -0.67], [6, -3]][[4, -1], [3.6, -0.6], [3.56, -0.67]][][][][[4, -1], [3.6, -0.6]][[4, -1], [3.6, -0.6]][[4, -1], [3.6, -0.6]][[4, -1], [1.5, 1.5], [3.6, -0.6]][[4, -1], [1.5, 1.5], [3.6, -0.6]][[4, -1], [1.5, 1.5], [3.6, -0.6]][[4, -1]][[4, -1], [3.08, -1.38], [3.33, -1.67], [3.56, -0.67]][[4, -1], [3.56, -0.67], [1.33, 1]][[3.56, -0.67], [1.5, 1.5], [3.6, -0.6]][[4, -1], [1.33, 1], [3.56, -0.67]][[1.33, 1], [3.56, -0.67]][][[3.56, -0.67]]20[[], [[4, -1], [3.56, -0.67], [6, -3]], [[4, -1], [3.6, -0.6], [3.56, -0.67]], [], [], [], [[4, -1], [3.6, -0.6]], [[4, -1], [3.6, -0.6]], [[4, -1], [3.6, -0.6]], [[4, -1], [1.5, 1.5], [3.6, -0.6]], [[4, -1], [1.5, 1.5], [3.6, -0.6]], [[4, -1], [1.5, 1.5], [3.6, -0.6]], [[4, -1]], [[4, -1], [3.08, -1.38], [3.33, -1.67], [3.56, -0.67]], [[4, -1], [3.56, -0.67], [1.33, 1]], [[3.56, -0.67], [1.5, 1.5], [3.6, -0.6]], [[4, -1], [1.33, 1], [3.56, -0.67]], [[1.33, 1], [3.56, -0.67]], [], [[3.56, -0.67]]]---[[], [[4, -1], [3.56, -0.67], [6, -3]], [[3.6, -0.6], [3.56, -0.67], [4, -1]], [], [], [], [[4, -1], [3.6, -0.6]], [[4, -1], [3.6, -0.6]], [[4, -1], [3.6, -0.6]], [[1.5, 1.5], [3.6, -0.6], [4, -1]], [[1.5, 1.5], [3.6, -0.6], [4, -1]], [[1.5, 1.5], [3.6, -0.6], [4, -1]], [[4, -1]], [[4, -1], [3.56, -0.67], [3.08, -1.38], [3.33, -1.67]], [[1.33, 1], [4, -1], [3.56, -0.67]], [[1.5, 1.5], [3.56, -0.67], [3.6, -0.6]], [[1.33, 1], [4, -1], [3.56, -0.67]], [[1.33, 1], [3.56, -0.67]], [], [[3.56, -0.67]]]>>> def tmp15():    #两组路径    path1 = a6=[[[2, -3], [3.33, -1.67], [5.09, -3.68], [2, -6], [1.2, -6.6], [-0.86, -5.57], [-0.4, -4.2], [1, 0], [2, -3]], [[2, -3], [3.33, -1.67], [5.09, -3.68], [5.56, -3.33], [6, -3], [4, -1], [3.56, -0.67], [3.08, -1.38], [2, -3]], [[2, -3], [3.33, -1.67], [5.09, -3.68], [5.56, -3.33], [4, -1], [3.6, -0.6], [3.56, -0.67], [3.08, -1.38], [2, -3]], [[2, -3], [3.33, -1.67], [3.08, -1.38], [1.24, 0.72], [1.33, 1], [0.44, 1.67], [0.46, 1.62], [1, 0], [2, -3]], [[2, -3], [3.33, -1.67], [3.08, -1.38], [3.56, -0.67], [1.33, 1], [1.24, 0.72], [0.46, 1.62], [1, 0], [2, -3]], [[2, -3], [3.33, -1.67], [3.08, -1.38], [3.56, -0.67], [1.33, 1], [0.44, 1.67], [0.46, 1.62], [1, 0], [2, -3]], [[2, -3], [3.33, -1.67], [4, -1], [3.6, -0.6], [3.56, -0.67], [3.08, -1.38], [1.24, 0.72], [1, 0], [2, -3]], [[2, -3], [3.33, -1.67], [4, -1], [3.6, -0.6], [3.56, -0.67], [1.33, 1], [1.24, 0.72], [1, 0], [2, -3]], [[2, -3], [3.33, -1.67], [4, -1], [3.6, -0.6], [3.56, -0.67], [1.33, 1], [1.24, 0.72], [3.08, -1.38], [2, -3]], [[2, -3], [3.33, -1.67], [4, -1], [3.6, -0.6], [1.5, 1.5], [1.33, 1], [1.24, 0.72], [1, 0], [2, -3]], [[2, -3], [3.33, -1.67], [4, -1], [3.6, -0.6], [1.5, 1.5], [1.33, 1], [1.24, 0.72], [3.08, -1.38], [2, -3]], [[2, -3], [3.33, -1.67], [4, -1], [3.6, -0.6], [1.5, 1.5], [1.33, 1], [3.56, -0.67], [3.08, -1.38], [2, -3]], [[2, -3], [3.33, -1.67], [4, -1], [3.56, -0.67], [3.08, -1.38], [1.24, 0.72], [0.46, 1.62], [1, 0], [2, -3]], [[2, -3], [3.33, -1.67], [4, -1], [3.56, -0.67], [1.33, 1], [1.24, 0.72], [0.46, 1.62], [1, 0], [2, -3]], [[2, -3], [3.33, -1.67], [4, -1], [3.56, -0.67], [1.33, 1], [0.44, 1.67], [0.46, 1.62], [1, 0], [2, -3]], [[2, -3], [1, 0], [1.24, 0.72], [1.33, 1], [1.5, 1.5], [3.6, -0.6], [3.56, -0.67], [3.08, -1.38], [2, -3]], [[2, -3], [1, 0], [1.24, 0.72], [1.33, 1], [3.56, -0.67], [4, -1], [3.33, -1.67], [3.08, -1.38], [2, -3]], [[2, -3], [1, 0], [1.24, 0.72], [0.46, 1.62], [0.44, 1.67], [1.33, 1], [3.56, -0.67], [3.08, -1.38], [2, -3]], [[2, -3], [1, 0], [0.46, 1.62], [0.36, 1.73], [0.44, 1.67], [1.33, 1], [1.24, 0.72], [3.08, -1.38], [2, -3]], [[2, -3], [1, 0], [0.46, 1.62], [0.36, 1.73], [0.44, 1.67], [1.33, 1], [3.56, -0.67], [3.08, -1.38], [2, -3]]]    path2 = a8=[[[4, -1], [6, -3], [6, 3], [4.29, 0.43], [3.67, -0.5], [1.78, 2.33], [1.5, 1.5], [3.6, -0.6], [4, -1]], [[4, -1], [6, -3], [6, 3], [2, 3], [1.78, 2.33], [1.5, 1.5], [1.33, 1], [3.56, -0.67], [4, -1]], [[4, -1], [6, -3], [6, 3], [2, 3], [1.78, 2.33], [1.5, 1.5], [3.6, -0.6], [3.56, -0.67], [4, -1]], [[4, -1], [6, -3], [6, 3], [2, 3], [1.78, 2.33], [3.67, -0.5], [3.6, -0.6], [3.56, -0.67], [4, -1]], [[4, -1], [6, -3], [6, 3], [2, 3], [1.33, 3], [1.78, 2.33], [1.5, 1.5], [3.6, -0.6], [4, -1]], [[4, -1], [6, -3], [6, 3], [2, 3], [1.33, 3], [1.78, 2.33], [3.67, -0.5], [3.6, -0.6], [4, -1]], [[4, -1], [6, -3], [6, 3], [2, 3], [1.33, 3], [0, 3], [1.5, 1.5], [3.6, -0.6], [4, -1]], [[4, -1], [3.6, -0.6], [3.67, -0.5], [1.78, 2.33], [2, 3], [6, 3], [4.29, 0.43], [4.5, 0], [4, -1]], [[4, -1], [3.6, -0.6], [3.67, -0.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [4.5, 0], [4, -1]], [[4, -1], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [2, 3], [6, 3], [4.29, 0.43], [4.5, 0], [4, -1]], [[4, -1], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [3.67, -0.5], [4.29, 0.43], [6, 3], [4.5, 0], [4, -1]], [[4, -1], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [4.5, 0], [4, -1]], [[4, -1], [3.6, -0.6], [1.5, 1.5], [0, 3], [1.33, 3], [2, 3], [6, 3], [4.5, 0], [4, -1]], [[4, -1], [4.5, 0], [6, -3], [5.56, -3.33], [5.09, -3.68], [3.33, -1.67], [3.08, -1.38], [3.56, -0.67], [4, -1]], [[4, -1], [4.5, 0], [4.29, 0.43], [3.67, -0.5], [1.78, 2.33], [1.5, 1.5], [1.33, 1], [3.56, -0.67], [4, -1]], [[4, -1], [4.5, 0], [4.29, 0.43], [3.67, -0.5], [1.78, 2.33], [1.5, 1.5], [3.6, -0.6], [3.56, -0.67], [4, -1]], [[4, -1], [4.5, 0], [4.29, 0.43], [3.67, -0.5], [3.6, -0.6], [1.5, 1.5], [1.33, 1], [3.56, -0.67], [4, -1]], [[4, -1], [4.5, 0], [6, 3], [2, 3], [1.78, 2.33], [1.5, 1.5], [1.33, 1], [3.56, -0.67], [4, -1]], [[4, -1], [4.5, 0], [6, 3], [2, 3], [1.78, 2.33], [1.5, 1.5], [3.6, -0.6], [3.56, -0.67], [4, -1]], [[4, -1], [4.5, 0], [6, 3], [2, 3], [1.78, 2.33], [3.67, -0.5], [3.6, -0.6], [3.56, -0.67], [4, -1]]]    len_ = min(len(path1), len(path2));    print(len_);    interPath = [];    for i in range(len_):        poly1 = Polygon(path1[i]);        poly2 = Polygon(path2[i]);        interPath.append(poly1.intersection(poly2));    print(len(interPath));    print(interPath);        #调用geo的几何变形类    transform = geo.Transform();            result = [];    for i in range(len(interPath)):        if (len(interPath[i]) > 3):            result.append(transform.angularSort(interPath[i]));        else:            result.append(interPath[i]);    print('---');    print(result);#</span>

<span style="font-size:18px;">//$path1 = a7=[[[6, -3], [8, -7], [5.35, -3.97], [5.09, -3.68], [5.56, -3.33], [4, -1], [4.5, 0], [6, 3], [6, -3]], [[6, -3], [8, -7], [5.35, -3.97], [5.09, -3.68], [3.33, -1.67], [3.08, -1.38], [3.56, -0.67], [4, -1], [6, -3]], [[6, -3], [8, -7], [5.35, -3.97], [5.09, -3.68], [3.33, -1.67], [4, -1], [4.5, 0], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4.29, 0.43], [3.67, -0.5], [1.78, 2.33], [1.5, 1.5], [3.6, -0.6], [4, -1], [6, -3]], [[6, -3], [4.5, 0], [4.29, 0.43], [3.67, -0.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4.29, 0.43], [6, 3], [2, 3], [1.78, 2.33], [3.67, -0.5], [4, -1], [6, -3]], [[6, -3], [4.5, 0], [4, -1], [3.67, -0.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4, -1], [3.6, -0.6], [3.67, -0.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4, -1], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4, -1], [3.56, -0.67], [3.6, -0.6], [3.67, -0.5], [4.29, 0.43], [6, 3], [6, -3]], [[6, -3], [4, -1], [5.56, -3.33], [5.67, -3.5], [8, -7], [8, 3], [6, 3.86], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.67, -0.5], [1.78, 2.33], [2, 3], [3.33, 5], [6, 3.86], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.67, -0.5], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.6, -0.6], [3.67, -0.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [3.67, -0.5], [4.29, 0.43], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.6, -0.6], [1.5, 1.5], [0, 3], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.56, -0.67], [3.6, -0.6], [3.67, -0.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.56, -0.67], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.56, -0.67], [1.33, 1], [1.5, 1.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]]]$path2 = [[[6, 9], [2.4, 5.4], [0.8, 3.8], [1.33, 3], [2, 3], [6, 3], [6, 3.86], [3.33, 5], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [1.33, 3], [2, 3], [3.33, 5], [6, 3.86], [8, 3], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [0, 3], [1.5, 1.5], [1.78, 2.33], [2, 3], [3.33, 5], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [0, 3], [1.33, 3], [1.78, 2.33], [2, 3], [3.33, 5], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [0, 3], [1.33, 3], [2, 3], [6, 3], [6, 3.86], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [0, 3], [1.33, 3], [2, 3], [3.33, 5], [6, 3.86], [6, 9]], [[6, 9], [2.4, 5.4], [3.33, 5], [2, 3], [6, 3], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [2.4, 5.4], [3.33, 5], [6, 3.86], [6, 3], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [2.4, 5.4], [-6, 9], [-0.37, 2.56], [0, 3], [1.33, 3], [2, 3], [3.33, 5], [6, 9]], [[6, 9], [3.33, 5], [2, 3], [1.78, 2.33], [3.67, -0.5], [4.29, 0.43], [6, 3], [6, 3.86], [6, 9]], [[6, 9], [3.33, 5], [2, 3], [6, 3], [6, -3], [5.67, -3.5], [8, -7], [8, 3], [6, 9]], [[6, 9], [3.33, 5], [2, 3], [6, 3], [6, -3], [8, -7], [8, 3], [6, 3.86], [6, 9]], [[6, 9], [3.33, 5], [2, 3], [6, 3], [4.5, 0], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [3.33, 5], [6, 3.86], [6, 3], [6, -3], [5.67, -3.5], [8, -7], [8, 3], [6, 9]], [[6, 9], [3.33, 5], [6, 3.86], [6, 3], [4.5, 0], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [4.29, 0.43], [4.5, 0], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [6, -3], [5.56, -3.33], [5.67, -3.5], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [6, -3], [5.67, -3.5], [5.35, -3.97], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [4.5, 0], [6, -3], [5.67, -3.5], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [4.5, 0], [4, -1], [6, -3], [8, -7], [8, 3], [6, 9]]]//交集$inter = [[[6, 3]], [], [], [[1.78, 2.33]], [[6, 3], [2, 3], [1.33, 3]], [[2, 3]], [[6, -3], [6, 3], [2, 3]], [[6, -3], [6, 3]], [[2, 3]], [[3.67, -0.5], [4.29, 0.43], [6, 3]], [[8, 3], [6, 3.86], [6, 3], [5.67, -3.5], [6, -3], [8, -7]], [[6, 3], [6, 3.86], [3.33, 5], [2, 3], [6, -3]], [[6, 3], [2, 3], [4.5, 0], [6, -3]], [[6, -3], [6, 3]], [[6, -3], [6, 3], [4.5, 0]], [[6, 3], [4.29, 0.43], [4.5, 0], [6, -3]], [[6, -3], [6, 3]], [[6, -3], [6, 3]], [[6, -3], [6, 3], [4.5, 0]], [[6, 3], [4.5, 0], [4, -1], [6, -3]]]if (1) {var r = 20;              config.setSector(1,1,1,1);                config.graphPaper2D(0, 0, r);              config.axis2D(0, 0, 250, 1.2);   //坐标轴设定                var scaleX = 2*r, scaleY = 2*r;                  var spaceX = 2, spaceY = 2;                   var xS = -10, xE = 10;                  var yS = -10, yE = 10;                  config.axisSpacing(xS, xE, spaceX, scaleX, 'X');                    config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');                                        var transform = new Transform();    //顶点var a = [];for (var i = 0; i < $vertex.length; i++) {a.push($vertex[i][0]);}//显示变换                if (a.length > 0) {                    a = transform.scale(transform.translate(a, 0, 0), scaleX/spaceX, scaleY/spaceY);}var lable = [];for (var i = 0; i < 100; i++) {lable.push(i.toFixed(0));}/*//边集var b = [];for (var i = 0; i < $seg.length; i++) {b.push([a[$seg[i][0]], a[$seg[i][1]]]);}var edges = b.length;for (var i = 0; i < edges; i++) {shape.multiLineDraw([].concat(b[i]), 'red');}*/var colorArray = ['red', 'orange', 'yellow', 'green', 'cyan', 'blue', 'purple', ];var seg = [];var nSeg = $divideSeg.length;plot.setLineWidth(2);for (var i = 0; i < nSeg; i++) {seg = transform.scale(transform.translate($divideSeg[i], 0, 0), scaleX/spaceX, scaleY/spaceY);shape.multiLineDraw([].concat(seg), 'pink');}var nPath = $inter.length;i = xGlobal;//路径var path1 = transform.scale(transform.translate($path1[i%nPath], 0, 0), scaleX/spaceX, scaleY/spaceY);plot.setLineWidth(8);shape.multiLineDraw([].concat(path1), colorArray[4]);var path2 = transform.scale(transform.translate($path2[i%nPath], 0, 0), scaleX/spaceX, scaleY/spaceY);plot.setLineWidth(6);shape.multiLineDraw([].concat(path2), colorArray[3]);//主要顶点shape.pointDraw([].concat(a), 'blue', 1, 1, lable);var interPoints = $inter[i%nPath].length;if (interPoints > 0) {var interpath = transform.scale(transform.translate($inter[i%nPath], 0, 0), scaleX/spaceX, scaleY/spaceY);if (interPoints >= 2) {plot.setLineWidth(4);shape.strokeDraw([].concat(interpath), colorArray[0]);}else {shape.pointDraw([].concat(interpath), 'red');}}}//</span>

这样会有一些成功的图，比如：

但更多的会像这样：

记录顶点然后不论采取何种排序方式，都可能会排出很奇怪的边来，这些边并不是原多边形的边。

所以还是直接记录所有的相交边，内部边好了。

<span style="font-size:18px;">#class Polygon():    #格式:path = [[-6, 9], [8, -7], [8, 3], [-6, 9]]    def __init__(self, path):        if (path[-1] != path[0]):            path.append(path[0]);        self.path = path;        #顶点数量        self.vertNum = len(self.path)-1;        self.vertex = [];        self.edge = [];        self.vertexCalc();        self.edgeCalc();    def vertexCalc(self):        for i in range(self.vertNum):            self.vertex.append(Point(self.path[i]));    def getVertex(self):        return self.vertex;    def edgeCalc(self):        for i in range(self.vertNum):            self.edge.append(SegLine(self.path[i], self.path[i+1]));    def getEdge(self):        return self.edge;    #传入的是[x, y]格式的对象    def pointInPolygon(self, point):        #测试点左右两边截多边形的各边，得到的交点数都为奇数，说明测试点在多边形内        #反之在外面        oddNodes = False;        #点在多边形的边上        if (Point(point) in self.vertex):            return 0;        x, y = point[0], point[1];        j = self.vertNum - 1;        for i in range(self.vertNum):            p1 = self.vertex[i].value();            p2 = self.vertex[j].value();            px1, py1 = p1[0], p1[1];            px2, py2 = p2[0], p2[1];                        if (((py1 < y and py2 >= y) or (py2 < y and py1 >= y)) and \               (px1 <= x or px2 <= x)):                if ((px1+(y-py1)/(py2-py1)*(px2-px1)) < x):                    oddNodes = not oddNodes;            j = i;        if (oddNodes == False):            #点不在多边形内            return -1;        else:            #点在多边形内            return 1;    #线段是否在多边形内的判断，传入[[x1, y1], [x2, y2]]    def segInPolygon(self, seg):        p1, p2 = seg[0], seg[1];        #组成线段的两个端点都不在多边形外部，认为它是在多边形内部（或边上）        if self.pointInPolygon(p1) >= 0 and self.pointInPolygon(p2) >= 0:            return True;        return False;            #两个多边形的交集区域    #返回内部点的集合并不能准确生成相交多边形区域，但有时也会用到    def intersection(self, other):        vlist_1 = self.vertex;        vlist_2 = other.vertex;                commonVert = set();        for i in range(len(vlist_1)):            #点在多边形外部是-1, 在边上是0, 在内部是1            if other.pointInPolygon(vlist_1[i].value()) != -1:                commonVert.add(vlist_1[i]);        for i in range(len(vlist_2)):            if self.pointInPolygon(vlist_2[i].value()) != -1:                commonVert.add(vlist_2[i]);        commonVert = list(commonVert);        for i in range(len(commonVert)):            commonVert[i] = commonVert[i].value();        #返回顶点序列        return commonVert;    def intersection_seg(self, other):        elist_1 = self.edge;        elist_2 = other.edge;        interEdge = set();        for i in range(len(elist_1)):            if other.segInPolygon(elist_1[i].value()) == True:                interEdge.add(elist_1[i]);        for i in range(len(elist_2)):            if self.segInPolygon(elist_2[i].value()) == True:                interEdge.add(elist_2[i]);        interEdge = list(interEdge);        return interEdge;#</span>

<span style="font-size:18px;">#>>> 2020[][][][][SegLine([1.33, 3], [2, 3]), SegLine([2, 3], [6, 3])][][SegLine([6, -3], [6, 3]), SegLine([2, 3], [6, 3])][SegLine([6, -3], [6, 3])][][SegLine([4.29, 0.43], [6, 3]), SegLine([3.67, -0.5], [4.29, 0.43])][SegLine([8, -7], [8, 3]), SegLine([8, -7], [5.67, -3.5]), SegLine([6, -3], [6, 3]), SegLine([5.67, -3.5], [6, -3]), SegLine([8, 3], [6, 3.86]), SegLine([6, 3], [6, 3.86])][SegLine([2, 3], [6, 3]), SegLine([6, 3.86], [3.33, 5]), SegLine([2, 3], [3.33, 5]), SegLine([6, 3], [6, 3.86]), SegLine([6, -3], [6, 3])][SegLine([4.5, 0], [6, 3]), SegLine([6, -3], [6, 3]), SegLine([6, -3], [4.5, 0]), SegLine([2, 3], [6, 3])][SegLine([6, -3], [6, 3])][SegLine([4.5, 0], [6, 3]), SegLine([6, -3], [4.5, 0]), SegLine([6, -3], [6, 3])][SegLine([4.5, 0], [4.29, 0.43]), SegLine([4.29, 0.43], [6, 3]), SegLine([6, -3], [4.5, 0]), SegLine([6, -3], [6, 3])][SegLine([6, -3], [6, 3])][SegLine([6, -3], [6, 3])][SegLine([4.5, 0], [6, 3]), SegLine([6, -3], [4.5, 0]), SegLine([6, -3], [6, 3])][SegLine([4.5, 0], [6, 3]), SegLine([6, -3], [4, -1]), SegLine([4, -1], [4.5, 0]), SegLine([6, -3], [6, 3])]>>> def tmp15():    #两组路径    path1 = a7=[[[6, -3], [8, -7], [5.35, -3.97], [5.09, -3.68], [5.56, -3.33], [4, -1], [4.5, 0], [6, 3], [6, -3]], [[6, -3], [8, -7], [5.35, -3.97], [5.09, -3.68], [3.33, -1.67], [3.08, -1.38], [3.56, -0.67], [4, -1], [6, -3]], [[6, -3], [8, -7], [5.35, -3.97], [5.09, -3.68], [3.33, -1.67], [4, -1], [4.5, 0], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4.29, 0.43], [3.67, -0.5], [1.78, 2.33], [1.5, 1.5], [3.6, -0.6], [4, -1], [6, -3]], [[6, -3], [4.5, 0], [4.29, 0.43], [3.67, -0.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4.29, 0.43], [6, 3], [2, 3], [1.78, 2.33], [3.67, -0.5], [4, -1], [6, -3]], [[6, -3], [4.5, 0], [4, -1], [3.67, -0.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4, -1], [3.6, -0.6], [3.67, -0.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4, -1], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4, -1], [3.56, -0.67], [3.6, -0.6], [3.67, -0.5], [4.29, 0.43], [6, 3], [6, -3]], [[6, -3], [4, -1], [5.56, -3.33], [5.67, -3.5], [8, -7], [8, 3], [6, 3.86], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.67, -0.5], [1.78, 2.33], [2, 3], [3.33, 5], [6, 3.86], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.67, -0.5], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.6, -0.6], [3.67, -0.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [3.67, -0.5], [4.29, 0.43], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.6, -0.6], [1.5, 1.5], [0, 3], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.56, -0.67], [3.6, -0.6], [3.67, -0.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.56, -0.67], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.56, -0.67], [1.33, 1], [1.5, 1.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]]]    path2 = a17=[[[6, 9], [2.4, 5.4], [0.8, 3.8], [1.33, 3], [2, 3], [6, 3], [6, 3.86], [3.33, 5], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [1.33, 3], [2, 3], [3.33, 5], [6, 3.86], [8, 3], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [0, 3], [1.5, 1.5], [1.78, 2.33], [2, 3], [3.33, 5], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [0, 3], [1.33, 3], [1.78, 2.33], [2, 3], [3.33, 5], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [0, 3], [1.33, 3], [2, 3], [6, 3], [6, 3.86], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [0, 3], [1.33, 3], [2, 3], [3.33, 5], [6, 3.86], [6, 9]], [[6, 9], [2.4, 5.4], [3.33, 5], [2, 3], [6, 3], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [2.4, 5.4], [3.33, 5], [6, 3.86], [6, 3], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [2.4, 5.4], [-6, 9], [-0.37, 2.56], [0, 3], [1.33, 3], [2, 3], [3.33, 5], [6, 9]], [[6, 9], [3.33, 5], [2, 3], [1.78, 2.33], [3.67, -0.5], [4.29, 0.43], [6, 3], [6, 3.86], [6, 9]], [[6, 9], [3.33, 5], [2, 3], [6, 3], [6, -3], [5.67, -3.5], [8, -7], [8, 3], [6, 9]], [[6, 9], [3.33, 5], [2, 3], [6, 3], [6, -3], [8, -7], [8, 3], [6, 3.86], [6, 9]], [[6, 9], [3.33, 5], [2, 3], [6, 3], [4.5, 0], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [3.33, 5], [6, 3.86], [6, 3], [6, -3], [5.67, -3.5], [8, -7], [8, 3], [6, 9]], [[6, 9], [3.33, 5], [6, 3.86], [6, 3], [4.5, 0], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [4.29, 0.43], [4.5, 0], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [6, -3], [5.56, -3.33], [5.67, -3.5], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [6, -3], [5.67, -3.5], [5.35, -3.97], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [4.5, 0], [6, -3], [5.67, -3.5], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [4.5, 0], [4, -1], [6, -3], [8, -7], [8, 3], [6, 9]]]    len_ = min(len(path1), len(path2));    print(len_);    interPath = [];    for i in range(len_):        poly1 = Polygon(path1[i]);        poly2 = Polygon(path2[i]);        interPath.append(poly1.intersection_seg(poly2));    print(len(interPath));    for i in range(len(interPath)):        print(interPath[i]);#</span>

如果直接按线段来显示，肯定会得到满意的图像，当然，阿伟是选择画蛇添足了一下。想让它们生成路径。

<span style="font-size:18px;">#共处理路径（条）： 20路径： []路径： []路径： []路径： []路径： [SegLine([1.33, 3], [2, 3]), SegLine([2, 3], [6, 3])]顶点数： 3连通： [[1.33, 3], [2, 3], [6, 3]]路径： []路径： [SegLine([2, 3], [6, 3]), SegLine([6, -3], [6, 3])]顶点数： 3连通： [[6, -3], [6, 3], [2, 3]]路径： [SegLine([6, -3], [6, 3])]路径： []路径： [SegLine([4.29, 0.43], [6, 3]), SegLine([3.67, -0.5], [4.29, 0.43])]顶点数： 3连通： [[3.67, -0.5], [4.29, 0.43], [6, 3]]路径： [SegLine([6, 3], [6, 3.86]), SegLine([5.67, -3.5], [6, -3]), SegLine([8, -7], [5.67, -3.5]), SegLine([8, 3], [6, 3.86]), SegLine([8, -7], [8, 3]), SegLine([6, -3], [6, 3])]顶点数： 6连通： [[8, -7], [5.67, -3.5], [6, -3], [6, 3], [6, 3.86], [8, 3], [8, -7]]路径： [SegLine([2, 3], [6, 3]), SegLine([6, 3.86], [3.33, 5]), SegLine([6, -3], [6, 3]), SegLine([6, 3], [6, 3.86]), SegLine([2, 3], [3.33, 5])]顶点数： 5连通： [[6, -3], [6, 3], [2, 3], [3.33, 5], [6, 3.86], [6, 3]]路径： [SegLine([6, -3], [4.5, 0]), SegLine([4.5, 0], [6, 3]), SegLine([2, 3], [6, 3]), SegLine([6, -3], [6, 3])]顶点数： 4连通： [[6, -3], [4.5, 0], [6, 3], [2, 3]]路径： [SegLine([6, -3], [6, 3])]路径： [SegLine([4.5, 0], [6, 3]), SegLine([6, -3], [4.5, 0]), SegLine([6, -3], [6, 3])]顶点数： 3连通： [[6, -3], [6, 3], [4.5, 0], [6, -3]]路径： [SegLine([4.29, 0.43], [6, 3]), SegLine([6, -3], [4.5, 0]), SegLine([4.5, 0], [4.29, 0.43]), SegLine([6, -3], [6, 3])]顶点数： 4连通： [[6, -3], [4.5, 0], [4.29, 0.43], [6, 3], [6, -3]]路径： [SegLine([6, -3], [6, 3])]路径： [SegLine([6, -3], [6, 3])]路径： [SegLine([4.5, 0], [6, 3]), SegLine([6, -3], [4.5, 0]), SegLine([6, -3], [6, 3])]顶点数： 3连通： [[6, -3], [6, 3], [4.5, 0], [6, -3]]路径： [SegLine([6, -3], [4, -1]), SegLine([4, -1], [4.5, 0]), SegLine([4.5, 0], [6, 3]), SegLine([6, -3], [6, 3])]顶点数： 4连通： [[6, -3], [4, -1], [4.5, 0], [6, 3], [6, -3]]***result:***[[], [], [], [], [[1.33, 3], [2, 3], [6, 3]], [], [[6, -3], [6, 3], [2, 3]], [[[6, -3], [6, 3]]], [], [[3.67, -0.5], [4.29, 0.43], [6, 3]], [[8, -7], [5.67, -3.5], [6, -3], [6, 3], [6, 3.86], [8, 3], [8, -7]], [[6, -3], [6, 3], [2, 3], [3.33, 5], [6, 3.86], [6, 3]], [[6, -3], [4.5, 0], [6, 3], [2, 3]], [[[6, -3], [6, 3]]], [[6, -3], [6, 3], [4.5, 0], [6, -3]], [[6, -3], [4.5, 0], [4.29, 0.43], [6, 3], [6, -3]], [[[6, -3], [6, 3]]], [[[6, -3], [6, 3]]], [[6, -3], [6, 3], [4.5, 0], [6, -3]], [[6, -3], [4, -1], [4.5, 0], [6, 3], [6, -3]]]#</span>

<span style="font-size:18px;">#def tmp15():    #两组路径    path1 = a7=[[[6, -3], [8, -7], [5.35, -3.97], [5.09, -3.68], [5.56, -3.33], [4, -1], [4.5, 0], [6, 3], [6, -3]], [[6, -3], [8, -7], [5.35, -3.97], [5.09, -3.68], [3.33, -1.67], [3.08, -1.38], [3.56, -0.67], [4, -1], [6, -3]], [[6, -3], [8, -7], [5.35, -3.97], [5.09, -3.68], [3.33, -1.67], [4, -1], [4.5, 0], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4.29, 0.43], [3.67, -0.5], [1.78, 2.33], [1.5, 1.5], [3.6, -0.6], [4, -1], [6, -3]], [[6, -3], [4.5, 0], [4.29, 0.43], [3.67, -0.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4.29, 0.43], [6, 3], [2, 3], [1.78, 2.33], [3.67, -0.5], [4, -1], [6, -3]], [[6, -3], [4.5, 0], [4, -1], [3.67, -0.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4, -1], [3.6, -0.6], [3.67, -0.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4, -1], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4.5, 0], [4, -1], [3.56, -0.67], [3.6, -0.6], [3.67, -0.5], [4.29, 0.43], [6, 3], [6, -3]], [[6, -3], [4, -1], [5.56, -3.33], [5.67, -3.5], [8, -7], [8, 3], [6, 3.86], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.67, -0.5], [1.78, 2.33], [2, 3], [3.33, 5], [6, 3.86], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.67, -0.5], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.6, -0.6], [3.67, -0.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [3.67, -0.5], [4.29, 0.43], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.6, -0.6], [1.5, 1.5], [0, 3], [1.33, 3], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.56, -0.67], [3.6, -0.6], [3.67, -0.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.56, -0.67], [3.6, -0.6], [1.5, 1.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]], [[6, -3], [4, -1], [3.56, -0.67], [1.33, 1], [1.5, 1.5], [1.78, 2.33], [2, 3], [6, 3], [6, -3]]]    path2 = a17=[[[6, 9], [2.4, 5.4], [0.8, 3.8], [1.33, 3], [2, 3], [6, 3], [6, 3.86], [3.33, 5], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [1.33, 3], [2, 3], [3.33, 5], [6, 3.86], [8, 3], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [0, 3], [1.5, 1.5], [1.78, 2.33], [2, 3], [3.33, 5], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [0, 3], [1.33, 3], [1.78, 2.33], [2, 3], [3.33, 5], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [0, 3], [1.33, 3], [2, 3], [6, 3], [6, 3.86], [6, 9]], [[6, 9], [2.4, 5.4], [0.8, 3.8], [0, 3], [1.33, 3], [2, 3], [3.33, 5], [6, 3.86], [6, 9]], [[6, 9], [2.4, 5.4], [3.33, 5], [2, 3], [6, 3], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [2.4, 5.4], [3.33, 5], [6, 3.86], [6, 3], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [2.4, 5.4], [-6, 9], [-0.37, 2.56], [0, 3], [1.33, 3], [2, 3], [3.33, 5], [6, 9]], [[6, 9], [3.33, 5], [2, 3], [1.78, 2.33], [3.67, -0.5], [4.29, 0.43], [6, 3], [6, 3.86], [6, 9]], [[6, 9], [3.33, 5], [2, 3], [6, 3], [6, -3], [5.67, -3.5], [8, -7], [8, 3], [6, 9]], [[6, 9], [3.33, 5], [2, 3], [6, 3], [6, -3], [8, -7], [8, 3], [6, 3.86], [6, 9]], [[6, 9], [3.33, 5], [2, 3], [6, 3], [4.5, 0], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [3.33, 5], [6, 3.86], [6, 3], [6, -3], [5.67, -3.5], [8, -7], [8, 3], [6, 9]], [[6, 9], [3.33, 5], [6, 3.86], [6, 3], [4.5, 0], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [4.29, 0.43], [4.5, 0], [6, -3], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [6, -3], [5.56, -3.33], [5.67, -3.5], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [6, -3], [5.67, -3.5], [5.35, -3.97], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [4.5, 0], [6, -3], [5.67, -3.5], [8, -7], [8, 3], [6, 9]], [[6, 9], [6, 3.86], [6, 3], [4.5, 0], [4, -1], [6, -3], [8, -7], [8, 3], [6, 9]]]    len_ = min(len(path1), len(path2));    print('共处理路径（条）：', len_);    interPath = [];    result = [];    for i in range(len_):        poly1 = Polygon(path1[i]);        poly2 = Polygon(path2[i]);        interPath.append(poly1.intersection_seg(poly2));    for i in range(len(interPath)):        print('路径：',interPath[i]);        len_path = len(interPath[i]);        if (len_path == 0):            result.append(interPath[i]);        elif (len_path < 2): #路径中包含的线段数小于2            print('No:', i);            val = [];            for j in range(len_path):                val_ = interPath[i][j].value();                val.append(val_[0]);                val.append(val_[1]);            result.append(val);            print(val);        else:            result.append(connectSeg(interPath[i]));    print('***result:***');    print(result);            #处理每个顶点最多连接两条线段的#线段集的路径连接问题。def connectSeg(seg):    #seg = [SegLine([8, -7], [8, 3]), SegLine([8, -7], [5.67, -3.5]), SegLine([6, -3], [6, 3]), SegLine([5.67, -3.5], [6, -3]), SegLine([8, 3], [6, 3.86]), SegLine([6, 3], [6, 3.86])];    #去除重复线段    seg = list(set(seg));    len_seg = len(seg);        d = dict();      path = [];    #构造顶点集    vertex = set();    for i in range(len_seg):        seg_ = seg[i].value();        vertex.add(Point(seg_[0]));        vertex.add(Point(seg_[1]));    print('顶点数：', len(vertex));    #这里的排序相当重要，一定要从所有顶点中最小的那个开始找    vertex = sorted(list(vertex));    len_vert = len(vertex);    #构造边集字典    for i in range(len_vert):        d[vertex[i]] = [];    for i in range(len_seg):        seg_ = seg[i].value();        d[Point(seg_[0])].append(Point(seg_[1]));        d[Point(seg_[1])].append(Point(seg_[0]));    #选择起始点    start = curVert = vertex[0];    path.append(curVert);        while len_vert > 0:        #从字典中移除相应线段的记录        if (len(d[curVert]) == 0):            break;        choice = d[curVert].pop(0);        d[choice].remove(curVert);        #处理下一个点        curVert = choice;        if (curVert in vertex):            vertex.remove(curVert);            path.append(curVert);            len_vert = len(vertex);        else:            path.append(curVert);            break;    for i in range(len(path)):        path[i] = path[i].value();    print('连通：', path);    return path;#</span>

由于有很多种情况，所以下面的一些图就会暴露出问题，但这些问题已经仅仅是存在于最后一步了。

最后这张图的点7和点12本来应该连接成区域的，这里是暴露出了路径连通算法的缺陷，这个在上节提过了。

但如果严格认为两个多边形共用的边不是交集，这张图的结果就会正确，当然，上一张图就没有交集了。

还是根据需要的应用场景去选择好了。

本节到此结束，欲知后事如何，请看下回分解。