import math

def dist_segment_to_point(Ax, Ay, Bx, By, Cx, Cy):
    """
    return the distance of C
    to the segment [A, B].

    A, B, C are given by Ax, Ay, Bx, By, Cx, Cy
    """

    px, py = Bx - Ax, By - Ay

    dd = px*px + py*py  # dd <- |AB|^2

    if dd == 0:
        # A == B, set P:=A
        Px, Py = Ax, Ay
    else:
        u =  ((Cx - Ax) * px + (Cy - Ay) * py)  # u = AC . AB

        if u < 0:
            # A is the AB segment's closest point to C
            Px, Py = Ax, Ay
        elif u >= dd:
            # B is the AB segment's closest point to C
            Px, Py = Bx, By
        else:
            # P is between points A and B
            u = u/float(dd)
            Px, Py = Ax + u * px, Ay + u * py

    dx, dy = (Cx - Px, Cy - Py)

    return math.sqrt(dx*dx + dy*dy)