没有理由应该恰好有一个交点。以您的示例为例，如果您采用了$​​ y = 1 $，则将有三个交集；如果您采用了$​​ y = -2 $，则将不会有交集；如果您采用了$​​ y = 0 $，则将无穷大。许多。

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.

要找到全部，一种方法是考虑连接 x $ c $中的元素的每个线段c>和 y ，并且已经找到了它们的斜率和相交点，并扩展了要在实线上定义的线段。现在，使用此问题中的过程之一，查找给定线与扩展的。如果有0个交集，则原始未扩展线段也有0个交集；如果有1个交集，则如果x值位于定义该线段的x值范围内，则未扩展的那个线段将具有1个交集。否则），并且如果有无限多个相交，则线段上的每个点都将位于相交处。对每个线段重复该过程。

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.

def get_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://***.com/a/42727584/5085211.
    """
    if (np.array_equal(line1, line2)):
        return None
    if 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/4

for i in range(len(x)-1):
    p = get_intersection(a[i], line_of_interest)
    if np.array_equal(p, []):
        continue
    elif 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]