寻找直线和轮廓之间的交点

问题描述

我试图找到直线（红色虚线）与等高线以红色突出显示的交点（请参见图）。我在第二个绘图中使用.get_paths将所述轮廓线与其他轮廓线隔离（第二个绘图）。

I am trying to find the intersection point of a straight(dashed red) with the contour-line highlighted in red(see plot). I used .get_paths in the second plot to isolate said contour line form the others(second plot).

我看过轮廓交点问题，，并尝试将其用作基础但无法复制任何有用的内容。

I have looked at a contour intersection problem, How to find all the intersection points between two contour-set in an efficient way, and have tried to use it as a base but have not been able to reproduce anything useful.

有人有什么想法吗？

用于重新创建图的相关函数，

relevant functions to recreate plot,

可以找到交点，而不是使用该点作为 fsolve（）的初始猜测值找到真正的解决方案：

Use shapely can find the intersection point, than use the point as the init guess value for fsolve() to find the real solution:
#for contour
def p_0(num,t) :
    esc_p = np.sum((((-1)**n)*(np.exp(t)**n)*((math.factorial(n)*((n+1)**0.5))**-1)) for n in range(1,num,1))
    return esc_p+1

tau = np.arange(-2,3,0.1)

x,y= np.meshgrid(tau,tau)
cs = plt.contour(x, y, np.log(p_0(51, y)/p_0(51, x)),[0.2],colors='k')

p=0.75
logp = (np.log(p*np.exp(tau)))
plt.plot(tau,logp)

from shapely.geometry import LineString
v1 = cs.collections[0].get_paths()[0].vertices

ls1 = LineString(v1)
ls2 = LineString(np.c_[tau, logp])
points = ls1.intersection(ls2)
x, y = points.x, points.y

from scipy import optimize

def f(p):
    x, y = p
    e1 = np.log(0.75*np.exp(x)) - y
    e2 = np.log(p_0(51, y)/p_0(51, x)) - 0.2
    return e1, e2

x2, y2 = optimize.fsolve(f, (x, y))

plt.plot(x, y, "ro")
plt.plot(x2, y2, "gx")

print x, y
print x2, y2
这是输出：
0.273616328952 -0.0140657435002
0.275317387697 -0.0123646847549
和情节：
                        
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