蒙特卡洛方法求四边形面积以及两个四边形相重叠的面积_randomSeed.zip

# 撒币算法 import random # 解二元一次方程 def binary_equation(point1, point2): w = (point1[1] - point2[1]) / (point1[0] - point2[0]) b = point1[1] - w * point1[0] return w, b # 四个flag，全true点才在范围内 def single_random_point(x, y, w1, w2, w3, w4, b1, b2, b3, b4): flag1 = (y < (w1 * x + b1)) if w2 is not None: if w2 < 0: flag2 = (y < (w2 * x + b2)) else: flag2 = (y > (w2 * x + b2)) else: flag2 = (x < b2) flag3 = (y > (w3 * x + b3)) if w4 is not None: if w4 < 0: flag4 = (y > (w4 * x + b4)) else: flag4 = (y < (w4 * x + b4)) else: flag4 = (x > b4) return [flag1, flag2, flag3, flag4] # 求四边形在大图中所占比重 # 输入样例：四个坐标，[300,300] def single_area_ratio(s, size_l): w1, w2, w3, w4, b1, b2, b3, b4 = for_w_b(s) k = 0 n = 2000000 for i in range(n): x = random.uniform(0, size_l[0]) y = random.uniform(0, size_l[1]) flag = single_random_point(x, y, w1, w2, w3, w4, b1, b2, b3, b4) if flag[0] and flag[1] and flag[2] and flag[3]: k += 1 return float(k) / float(n) # 求四边形四个边的一次方程参数 def for_w_b(s): if s[0][0] != s[1][0]: w1, b1 = binary_equation(s[0], s[1]) else: w1 = None b1 = s[0][0] if s[1][0] != s[2][0]: w2, b2 = binary_equation(s[1], s[2]) else: w2 = None b2 = s[1][0] if s[2][0] != s[3][0]: w3, b3 = binary_equation(s[2], s[3]) else: w3 = None b3 = s[2][0] if s[3][0] != s[0][0]: w4, b4 = binary_equation(s[3], s[0]) else: w4 = None b4 = s[0][0] return w1, w2, w3, w4, b1, b2, b3, b4 # 求两个四边形相交区域面积 def double_area_ratio(s1, size_l, s2): # one shape w1, w2, w3, w4, b1, b2, b3, b4 = for_w_b(s1) # another one w1_1, w1_2, w1_3, w1_4, b1_1, b1_2, b1_3, b1_4 = for_w_b(s2) k = 0 n = 2000000 for i in range(n): x = random.uniform(0, size_l[0]) y = random.uniform(0, size_l[1]) flag = single_random_point(x, y, w1, w2, w3, w4, b1, b2, b3, b4) flag1 = single_random_point(x, y, w1_1, w1_2, w1_3, w1_4, b1_1, b1_2, b1_3, b1_4) if flag[0] and flag[1] and flag[2] and flag[3] \ and flag1[0] and flag1[1] and flag1[2] and flag1[3]: k += 1 return float(k) / float(n) shape1 = [[0, 150], [150, 150], [150, 0], [0, 0]] shape2 = [[50, 200], [200, 200], [200, 50], [50, 50]] # print(double_area_ratio(shape1, [200, 200], shape2)) # r1 = double_area_ratio(shape1, [200, 200], shape2) / single_area_ratio(shape1, [200, 200]) # r2 = double_area_ratio(shape1, [200, 200], shape2) / single_area_ratio(shape2, [200, 200]) # # print('两图相交面积与shape1的比：' + str(int(float(r1) * 100)) + '%') # print('两图相交面积与shape2的比：' + str(int(float(r2) * 100)) + '%') print(single_area_ratio(shape1, [200, 200])) print(double_area_ratio(shape1, [200, 200], shape2))