考虑了切线的k为负的情况

main.py

@@ -26,7 +26,7 @@ class Draw:
         msp.add_circle((dgc, h_cav), rc, dxfattribs={"color": color})
         msp.add_line((dgc, 0), (dgc, h_cav))  # 导线
         msp.add_line((0, h_gav), (dgc, h_cav))
-        msp.add_line((0, rg), (200, rg), dxfattribs={"color": color})
+        msp.add_line((0, rg), (2000, rg), dxfattribs={"color": color})
         # 计算圆交点
         # circle_intersection = solve_circle_intersection(rs, rc, h_gav, h_cav, dgc)
         # msp.add_line((0, h_gav), circle_intersection)  # 地线
@@ -42,8 +42,8 @@ class Draw:
 # 圆交点
 def solve_circle_intersection(rs, rc, hgav, hcav, dgc):
     # 用牛顿法求解
-    x = 300
+    x = rc  # 初始值
-    y = 300
+    y = rc  # 初始值
     for bar in range(0, 10):
         A = [[-2 * x, -2 * (y - hgav)], [-2 * (x - dgc), -2 * (y - hcav)]]
         b = [
@@ -79,7 +79,7 @@ def thunder_density(i):  # l雷电流幅值密度函数
 
 
 def angel_density(angle):  # 入射角密度函数 angle单位是弧度
-    r = 0.75 * (math.cos(angle) ** 3)
+    r = 0.75 * (math.cos(angle - math.pi / 2) ** 3)
     return r
 
 
@@ -110,6 +110,8 @@ def intersection_angle(dgc, h_gav, h_cav, i_curt, u_ph):  # 暴露弧的角度
         rc, rg, h_cav, dgc
     )  # 暴露圆和补雷线的交点
     np_circle_intersection = np.array(circle_intersection)
+    if not circle_intersection:
+        abc = 123
     theta2_line = np_circle_intersection - np.array([dgc, h_cav])
     theta2 = math.atan(theta2_line[1] / theta2_line[0])
     np_circle_line_intersection = np.array(circle_line_intersection)
@@ -127,39 +129,83 @@ def distance_point_line(point_x, point_y, line_x, line_y, k):
     return d
 
 
-def bd_area(i_curt, u_ph, dgc, h_gav, h_cav):  # 暴露弧的投影面积
+def fun_calculus_pw(theta, max_w):
-    theta1, theta2 = intersection_angle(dgc, h_gav, h_cav, i_curt, u_ph)
+    w_fineness = 0.01
-    rc = rc_fun(i_curt, u_ph)
+    r_pw = 0
-    rs = rs_fun(i_curt)
+    if int(max_w / w_fineness) < 0:
-    rg = rg_fun(i_curt, h_cav)
+        abc = 123
+        pass
+    w_samples, d_w = np.linspace(0, max_w, int(max_w / w_fineness) + 1, retstep=True)
+    for cal_w in w_samples:
+        r_pw += (
+            (
+                abs(angel_density(cal_w)) * math.sin(theta - cal_w + math.pi)
+                + abs(angel_density(cal_w + d_w))
+                * math.sin(theta - cal_w + math.pi - d_w)
+            )
+            / 2
+        ) * d_w
+    return r_pw
+
+
+def cal_bd(theta, rc, rs, rg, dgc, h_cav, h_gav):
     # 求暴露弧上一点的切线
-    line_x = math.cos(theta1) * rc + dgc
+    line_x = math.cos(theta) * rc + dgc
-    line_y = math.sin(theta1) * rc + h_cav
+    line_y = math.sin(theta) * rc + h_cav
-    max_w = 0  # 入射角
+    max_w = theta + math.pi / 2  # 入射角
-    if theta1 < 0:
-        max_w = theta1 + math.pi / 2
     k = math.tan(max_w)
     # 求保护弧到直线的距离，判断是否相交
     d_to_rs = distance_point_line(0, h_gav, line_x, line_y, k)
     if d_to_rs < rs:  # 相交
         # 要用过直线上一点到暴露弧的切线
         new_k = tangent_line_k(line_x, line_y, 0, h_gav, rs, init_k=k)
+        if not new_k:
+            a = 12
+            tangent_line_k(line_x, line_y, 0, h_gav, rs, init_k=k)
+        if new_k >= 0:
             max_w = math.atan(new_k)  # 用于保护弧相切的角度
-            intersection_angle(dgc, h_gav, h_cav, i_curt, u_ph)
+        elif new_k < 0:
-            gMSP.add_circle((0, h_gav), rs)
+            max_w = math.atan(new_k) + math.pi
-            gMSP.add_circle((dgc, h_cav), rc)
+        if max_w < 0:
-            gMSP.add_line((dgc, h_cav), (line_x, line_y))
+            abc = 123
-            gMSP.add_line(
+            tangent_line_k(line_x, line_y, 0, h_gav, rs, init_k=k)
-                (-500, k * (-500 - line_x) + line_y), (500, k * (500 - line_x) + line_y)
+            # intersection_angle(dgc, h_gav, h_cav, i_curt, u_ph)
-            )
+            # gMSP.add_circle((0, h_gav), rs)
-            gMSP.add_line((0, rg), (1000, rg))
+            # gMSP.add_circle((dgc, h_cav), rc)
-            gCAD.save()
+            # gMSP.add_line((dgc, h_cav), (line_x, line_y))
-            pass
+            # gMSP.add_line(
+            #     (-500, k * (-500 - line_x) + line_y), (500, k * (500 - line_x) + line_y)
+            # )
+            # gMSP.add_line((0, rg), (1000, rg))
+            # gCAD.save()
+            tangent_line_k(line_x, line_y, 0, h_gav, rs, init_k=k)
 
-    # k=tangent_line_k(point_x, point_y, dgc, h_cav,rc)
+        pass
-    # 暂时不考虑雷电入射角的影响
+    r = rc / math.cos(theta) * fun_calculus_pw(theta, max_w)
-    r = (math.cos(theta1) - math.cos(theta2)) * rc
     return r
+
+
+def bd_area(i_curt, u_ph, dgc, h_gav, h_cav):  # 暴露弧的投影面积
+    theta1, theta2 = intersection_angle(dgc, h_gav, h_cav, i_curt, u_ph)
+    theta_fineness = 0.01
+    rc = rc_fun(i_curt, u_ph)
+    rs = rs_fun(i_curt)
+    rg = rg_fun(i_curt, h_cav)
+    r_bd = 0
+    theta_sample, d_theta = np.linspace(
+        theta1, theta2, int((theta2 - theta1) / theta_fineness) + 1, retstep=True
+    )
+    for cal_theta in theta_sample[:-1]:
+        r_bd += (
+            (
+                cal_bd(cal_theta, rc, rs, rg, dgc, h_cav, h_gav)
+                + cal_bd(cal_theta + d_theta, rc, rs, rg, dgc, h_cav, h_gav)
+            )
+            / 2
+            * d_theta
+        )
+    return r_bd
+
     # r1=rc*(-math.cos(thyta2)+math.cos(thyta1))
     # 入射角密度函数积分
     # arrival_angle_fineness=0.0001
@@ -170,15 +216,20 @@ def tangent_line_k(line_x, line_y, center_x, center_y, radius, init_k=10.0):
     # 直线方程为 y-y0=k(x-x0)，x0和y0为经过直线的任意一点
     # 牛顿法求解k
     # f(k)=(k*x1-y1-k*x0+y0)**2-R**2*(k**2+1) x1,y1是圆心
-    # TODO:应该找到两个角度值后再比较
+    # TODO:需要检验k值不存在的情况
-    k = init_k
+    k_candidate = [-100, 100]
+    for ind, k_cdi in enumerate(list(k_candidate)):
+        k = k_candidate[ind]
+        k_candidate[ind] = None
         for bar in range(0, 30):
-        fk = (k * center_x - center_y - k * line_x + line_y) ** 2 - (radius ** 2) * (
+            fk = (k * center_x - center_y - k * line_x + line_y) ** 2 - (
-            k ** 2 + 1
+                radius ** 2
-        )
+            ) * (k ** 2 + 1)
 
             d_fk = (
-            2 * (k * center_x - center_y - k * line_x + line_y) * (center_x - line_x)
+                2
+                * (k * center_x - center_y - k * line_x + line_y)
+                * (center_x - line_x)
                 - 2 * (radius ** 2) * k
             )
             d_k = -fk / d_fk
@@ -186,34 +237,46 @@ def tangent_line_k(line_x, line_y, center_x, center_y, radius, init_k=10.0):
             if abs(d_k) < 1e-5:
                 dd = distance_point_line(center_x, center_y, line_x, line_y, k)
                 if abs(dd - radius) < 1e-5:
-                return k
+                    k_candidate[ind] = k
-    return None
+                    break
+    # 把k转化成相应的角度，从x开始，逆时针为正
+    k_angle = []
+    for kk in k_candidate:
+        if kk >= 0:
+            k_angle.append(math.atan(kk))
+        if kk < 0:
+            k_angle.append(math.pi + math.atan(kk))
+    # 返回相对x轴最大的角度k
+    return np.array(k_candidate)[np.max(k_angle) == k_angle].tolist()[-1]
 
 
 def egm():
-    u_ph = 750 / 1.732  # 运行相电压
+    for u_bar in range(1):
-    h_cav = 160  # 导线对地平均高
+        u_ph = math.sqrt(2) * 750 * math.cos(2 * math.pi / 6 * 0) / 1.732  # 运行相电压
+        h_cav = 90  # 导线对地平均高
         h_gav = h_cav + 9.5 + 2.7
-    dgc = -2  # 导地线水平距离
+        dgc = 2.9  # 导地线水平距离
         # 迭代法计算最大电流
         i_max = 0
         _min_i = 20  # 尝试的最小电流
-    _max_i = 80  # 尝试的最大电流
+        _max_i = 300  # 尝试的最大电流
-    for i_bar in np.linspace(_min_i, _max_i, int((_max_i - _min_i) / 0.01)):  # 雷电流
+        for i_bar in np.linspace(_min_i, _max_i, int((_max_i - _min_i) / 0.1)):  # 雷电流
             print(f"尝试计算电流为{i_bar:.2f}")
             rs = rs_fun(i_bar)
-        if not np.isreal(rs):
+            # if not np.isreal(rs):
-            continue
+            #     continue
             rc = rc_fun(i_bar, u_ph)
-        if not np.isreal(rc):
+            # if not np.isreal(rc):
-            continue
+            #     continue
             rg = rg_fun(i_bar, h_cav)
-        if not np.isreal(rg):
+            # if not np.isreal(rg):
-            continue
+            #     continue
             circle_intersection = solve_circle_intersection(rs, rc, h_gav, h_cav, dgc)
             if not circle_intersection:  # if circle_intersection is []
                 continue
-        circle_line_intersection = solve_circle_line_intersection(rc, rg, h_cav, dgc)
+            circle_line_intersection = solve_circle_line_intersection(
+                rc, rg, h_cav, dgc
+            )
             min_distance_intersection = (
                 np.sum(
                     (np.array(circle_intersection) - np.array(circle_line_intersection))
@@ -224,7 +287,7 @@ def egm():
             i_max = i_bar
             if min_distance_intersection < 0.1:
                 break
-    i_min = min_i(6.78, 750 / 1.732)
+        i_min = min_i(6.78, u_ph / 1.732)
         cad = Draw()
         cad.draw(i_min, u_ph, h_gav, h_cav, dgc, 2)
         cad.draw(i_max, u_ph, h_gav, h_cav, dgc, 6)
@@ -235,14 +298,16 @@ def egm():
             print(f"最大电流设置为自然界最大电流{i_max}kA")
         print(f"最大电流为{i_max:.2f}")
         print(f"最小电流为{i_min:.2f}")
-    if i_min > i_max:
+        curt_fineness = 0.1  # 电流积分细度
+        if i_min > i_max or abs(i_min - i_max) < curt_fineness:
             print("最大电流小于最小电流，没有暴露弧，程序结束。")
             return
         # 开始积分
-    curt_fineness = 0.1  # 电流积分细度
         curt_segment_n = int((i_max - i_min) / curt_fineness)  # 分成多少份
         calculus = 0
-    i_curt_samples, d_curt = np.linspace(i_min, i_max, curt_segment_n + 1, retstep=True)
+        i_curt_samples, d_curt = np.linspace(
+            i_min, i_max, curt_segment_n + 1, retstep=True
+        )
         for i_curt in i_curt_samples:
             cal_bd_first = bd_area(i_curt, u_ph, dgc, h_gav, h_cav)
             cal_bd_second = bd_area(i_curt + d_curt, u_ph, dgc, h_gav, h_cav)