计算两条曲线到下一个交点的面积

Question

I have two curves which intersect several times. I don't know where the intersections are. I am trying to get a value for each area between two intersection points without manually setting the boundary.

So far I calcualted the values of each curve and plot them with a green colour in case logifunc is above logifuncsoll and with a red colour if logifunc is below logifuncsoll.

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

Total difference between the two lines is using scipy integrate the absolute value of the difference function.

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)

To find the intersection points, use 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)