[从头学数学] 第267节 [计算几何] 路径规划

<span style="font-size:18px;"># >>> 28 [Point([⑴0,⑼]),Point([⑵,Point([2,Point([-0.71,⑺.45]),Point([0.29,⑺.29]),⑺]),Point([8,Point([-0.18,⑹.82]),⑸]),⑶]),Point([6,Point([4.3,⑴.44]),Point([4.58,⑴.11]),Point([4,⑴]),1]),Point([2.0,2.33]),Point([0,3]),Point([1.5,Point([4.57,3.29]),Point([0.71,4.06]),Point([⑷,5]),Point([⑹,9]),9])] >>> #生成结点表 def tmp10(): divideSeg = [[[⑴0,⑼],[-0.71,⑺.45]],[[-0.71,⑺.45],[0.29,⑺.29]],[[0.29,⑺.29],[2,⑺]],[[⑵,[-0.18,⑹.82]],[[-0.18,⑹.82],[4.3,⑴.44]],[[4.3,⑴.44],[4.58,⑴.11]],[[4.58,⑴.11],[8,3]],[[2,[⑵,⑸]],[[8,⑺],[4,⑴]],⑶],[2.0,2.33]],[[2.0,2.33],3],[[6,[1.5,[[1.5,[0.71,4.06]],[[0.71,4.06],[0,5]],[[4,1],[4.57,3.29]],[[4.57,3.29],[6,9]],[[0,[⑷,5],[⑹,9]]]; vertex = set(); for i in range(len(divideSeg)): vertex.add(Point(divideSeg[i][0])); vertex.add(Point(divideSeg[i][1])); vertexArray = sorted(list(vertex)); print(len(vertexArray)); print(vertexArray); #</span>

<span style="font-size:18px;"># >>> [(0,3,9.42),(3,4,1.01),(4,5,1.73),(1,2.02),7,0.82),(7,11,7.0),(11,12,0.43),(12,21,5.35),(2,2.42),0.66),8,2.57),(6,6.68),13,0.53),(9,15,5.33),(15,18,0.67),(18,19,0.0),(10,2.36),4.3),17,0.84),(17,23,1.32),(23,25,1.18),(14,22,(22,27,5.89),(16,1.5),0.5),(20,1.46),3.94),24,4.8),(25,26,7.21)] >>> >>> 选择的线路是： [⑴0,⑼]-->[-0.71,⑺.45]-->[-0.18,⑹.82]-->[4.3,⑴.44]-->[4.58,⑴.11]-->[2.0,2.33]-->[1.5,3]-->[0.71,4.06]-->[4.57,3.29]-->[6,9] ，这条线路总长为33.96米 >>> >>> 选择的线路是： [⑴0,9] ，这条线路总长为33.96米 [[0,[3,7],[7,11],[11,12],[12,15],[15,17],[17,23],[23,22],[22,27]] [[[⑴0,9]]] >>> #生成结点表 def tmp10(): debug = 0; #主端点 mainVert = [[[⑴0,0],2],4],⑸],6],⑴],8],9],10],13],[[⑷,14],[[⑹,16],17]]; #分线段 divideSeg = [[[⑴0,9]]]; vertex = set(); for i in range(len(divideSeg)): vertex.add(Point(divideSeg[i][0])); vertex.add(Point(divideSeg[i][1])); #顶点列表 vertexArray = sorted(list(vertex)); if (debug): print(len(vertexArray)); #print(vertexArray); #顶点字典 vertexDict = dict(); for i in range(len(vertexArray)): vertexDict[vertexArray[i]] = i; #node_list #格式[(序号1,序号2,距离),(...),...] node_list = []; for i in range(len(divideSeg)): point_1 = divideSeg[i][0]; point_2 = divideSeg[i][1]; idx1 = vertexDict[Point(point_1)]; idx2 = vertexDict[Point(point_2)]; d = round(geo.distance2D(point_1,point_2),2); node_list.append((idx1,idx2,d)); #print(node_list); node = list(range(len(vertexArray))); #节点数量的平方 node_map = [[0 for val in range(len(node))] for val in range(len(node))]; node_map = Dijk.set_node_map(node_map,node,node_list); #任务 from_node = vertexDict[Point(mainVert[0][0])]; #改动2维数组的第1个下标 to_node = vertexDict[Point(mainVert[17][0])]; #注意不要超过主顶点的阵列个数 #路径描写 addressString = vertexArray; #求取路径 dijkstrapath = Dijk.DijkstraPath(node_map); #路径字符串 dijkstrapath(from_node,to_node); print(dijkstrapath.pathString(addressString)); path = dijkstrapath.path(); #用顶点序号显示 #print(path); for i in range(len(path)): path[i][0] = vertexArray[path[i][0]].point; path[i][1] = vertexArray[path[i][1]].point; #用顶点值显示 print(path); #</span>

<span style="font-size:18px;"># ### # @usage 求两个给定地点，所有路径中的最短值 # @author mw # @date 2016年01月13日 星期3 09:50:23 # @param # @return # ### class DijkstraPath(): #初始化 def __init__(self,node_map): self.node_map = node_map; self.node_length = len(node_map); self.used_node_list = []; self.collected_node_dict = {}; self.step = 0; #调用函数 def __call__(self,from_node,to_node): self.from_node = from_node; self.to_node = to_node; self._init_dijkstra(); return self._format_path(); def _init_dijkstra(self): self.used_node_list.append(self.from_node); self.collected_node_dict[self.from_node] = [0,⑴]; for index1,node1 in enumerate(self.node_map[self.from_node]): if node1: self.collected_node_dict[index1] = [node1,self.from_node]; self._foreach_dijkstra(); def _foreach_dijkstra(self): #保证每一个点最多只到1次 if len(self.used_node_list) == self.node_length - 1: return; #由于items()方法会改变原字典内容，所以此处拷贝副本 collected_node_dict = dict(self.collected_node_dict); # 遍历已有权值节点 for key,val in collected_node_dict.items(): if key not in self.used_node_list and key != self.to_node: self.used_node_list.append(key); else: continue; # 对节点进行遍历 for index1,node1 in enumerate(self.node_map[key]): # 如果节点在权值节点中并且权值大于新权值 if node1 and index1 in self.collected_node_dict \ and self.collected_node_dict[index1][0] > node1 + val[0]: # 更新权值 self.collected_node_dict[index1][0] = node1 + val[0] self.collected_node_dict[index1][1] = key; elif node1 and index1 not in self.collected_node_dict: self.collected_node_dict[index1] = [node1 + val[0],key]; self.step += 1; if self.step > self.node_length*10: #print('步数太多'); return; #递归 self._foreach_dijkstra(); def _format_path(self): node_list = []; temp_node = self.to_node; node_list.append((temp_node,self.collected_node_dict[temp_node][0])); while self.collected_node_dict[temp_node][1] != ⑴: temp_node = self.collected_node_dict[temp_node][1]; node_list.append((temp_node,self.collected_node_dict[temp_node][0])); node_list.reverse(); return node_list; def path(self): node_list = self._format_path(); size = len(node_list); result = []; for i in range(size⑴): result.append([node_list[i][0],node_list[i+1][0]]); return result; def pathString(self,node): node_list = self._format_path(); size = len(node_list); s = '选择的线路是：\n'; for i in range(size): if i < size⑴: s += str(node[node_list[i][0]])+'-->'; else: s += str(node[node_list[i][0]]); s+= ' ，这条线路总长为{0}米'.format(round(node_list[size⑴][1],2)); return s; def set_node_map(node_map,node_list): for x,y,val in node_list: node_map[node.index(x)][node.index(y)] = node_map[node.index(y)][node.index(x)] = val return node_map; #</span>

<span style="font-size:18px;">// $vertex = [[[⑴0,17]]; $seg = [[10,2.0],16,7.211],5.657],[1,15.62],10.0],12.166],6.0],[9,8.246],14,10.198]]; $divideSeg = [[[⑴0,9]]]; $path = [[[⑴0,9]]]; if (1) { var r = 20; config.setSector(1,1,1); config.graPHPaper2D(0,r); config.axis2D(0,250,1.2); //坐标轴设定 var scaleX = 2*r,scaleY = 2*r; var spaceX = 2,spaceY = 2; var xS = ⑴0,xE = 10; var yS = ⑴0,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),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 = $divideSeg.length; for (var i = 0; i < nSeg; i++) { seg = transform.scale(transform.translate($divideSeg[i],scaleY/spaceY); shape.multiLineDraw([].concat(seg),colorArray[i%7]); } nSeg = $path.length; plot.setLineWidth(5); for (var i = 0; i < nSeg; i++) { seg = transform.scale(transform.translate($path[i],'pink'); } shape.pointDraw([].concat(a),lable); } //</span>