Finding The Intersection Point Between Line And Piecewise Linear Curves

I have two curves, one is a line, for example y = x/4 and another one is the set of points which I connect with line segments (for example : x = [1, 2.5, 3.4, 5.8, 6], y = [2, 4, 5

Solution 1:

There is no reason that there should be exactly one intersection point. For your example, if you had taken $y = 1$, you would have three intersections, if you had taken $y = -2$, you would have none, and if had taken $y = 0$, you would have infinitely many.

To find them all, one way to proceed would be to consider each of the line segments connecting elements from x and y, and for which you have already found the slopes and intersects, and extend the line segment to be defined on the real line. Now, using for instance one of the procedures in this question find the intersections between your given line and the extended one. If there are 0 intersections, then the original unextended line segment also has 0 intersections, if there is 1 intersection, the unextended one will have 1 intersection if the x-value lies within the range of x-values defining the line segment (and 0 otherwise), and if there are infinitely many intersections, then every point on the line segment will lie in the intersection. Repeat the process for each of your line segments.

defget_intersection(line1, line2):
    """Returns the intersection, if any, between two lines, None if the lines are equal, and
    the empty array if the lines are parallel.

    Args:
        line1 (numpy.array): [slope, intercept] of the first line.
        line2 (numpy.array): [slope, intercept] of the second line.

    Taken from https://stackoverflow.com/a/42727584/5085211.
    """if (np.array_equal(line1, line2)):
        returnNoneif line1[0] == line2[0]:
        return np.empty(0)
    l1 = np.insert(line1, 1, -1)
    l2 = np.insert(line2, 1, -1)
    x, y, z = np.cross(l1, l2)
    return np.hstack([x, y]) / z

line_of_interest = [0.25, 0]  # y = x/4for i inrange(len(x)-1):
    p = get_intersection(a[i], line_of_interest)
    if np.array_equal(p, []):
        continueelif np.array_equal(p, None):
        print('Entire line segment between {0} and {1}'.format(x[i], x[i+1]))
    elif x[i] <= p[0] and p[0] < x[i+1]:
        print(p)

# Prints:# [ 0.  0.]# [ 1.09090909  0.27272727]# [ 3.11111111  0.77777778]# [ 5.6  1.4]