def SampleLine(rho1, theta1, pt_min, pt_max):
	def get_intersect(rho2, theta2):
		y = (rho2 - rho1) / (math.tan(theta2) - math.tan(theta1))
		x = rho1 - math.tan(theta1) * y
		return (x, y)

	x0, y0 = pt_min
	x1, y1 = pt_max

	pts  = list()
	pts += [ get_intersect(x0, 0.0) ]
	pts += [ get_intersect(x1, 0.0) ]
	pts += [ get_intersect(y0, math.pi / 2) ]
	pts += [ get_intersect(y1, math.pi / 2) ]
	pts.sort(key=lambda p: math.hypot(p[0], p[1]))

	return pts[0], pts[1]