计算两条曲线到下一个交点的面积

Question

我有两条相交多次的曲线。我不知道十字路口在哪里。我试图在不手动设置边界的情况下为两个交点之间的每个区域获取一个值。

到目前为止，我计算了每条曲线的值，如果 logifunc 高于 logifuncsoll，则用绿色绘制它们，如果 logifunc 低于 logifuncsoll，则用红色绘制。

E701077['logifuncsoll'] = 1811.7/ (1 + 769.67 * np.exp(-0.704566*(xsoll)))+14.5212
E701077['logifunc'] = 1847.28 / (1 + 312.09 * np.exp(-0.606454*(x701077)))-8.16471


plt.figure(dpi=300)
plt.plot(x701077, E701077['logifuncsoll'],'r',markersize=np.sqrt(1), label ="soll",color='red' )
plt.plot(x701077, E701077['logifunc'],'r',markersize=np.sqrt(1), label ="E701077",color='purple' )
plt.legend
fig, ax = plt.subplots(1, 1, sharex=True)
ax.plot(x701077, E701077['logifunc'],linewidth=1 , label='logifunc', color= 'purple')
ax.plot(x701077, E701077['logifuncsoll'],linewidth=1, label='logifuncsoll', color='black') 
ax.fill_between(x701077, E701077['logifuncsoll'], E701077['logifunc'], where=E701077['logifunc'] >= E701077['logifuncsoll'], facecolor='green', interpolate=True)
ax.fill_between(x701077, E701077['logifuncsoll'], E701077['logifunc'], where=E701077['logifunc'] <= E701077['logifuncsoll'], facecolor='red', interpolate=True)
ax.legend(loc='upper left', frameon=False)

Answer 1

两行总差是用scipy求差函数的绝对值积分。

import scipy.integrate
left_lim = 0
right_lim = 27
func = lambda x: abs( (1811.7/ (1 + 769.67 * np.exp(-0.704566*(x)))+14.5212)-
(1847.28 / (1 + 312.09 * np.exp(-0.606454*(x)))-8.16471) )

area = scipy.integrate.quad(func, left_lim, right_lim)

要查找交点，请使用 Shapely。

import shapely
from shapely.geometry import LineString, Point

line1 = LineString(E701077['logifuncsoll'].values)
line2 = LineString(E701077['logifunc'].values)

int_pt = line1.intersection(line2)
point_of_intersection = int_pt.x, int_pt.y

print(point_of_intersection)