def enter(self, ray):
radius = self.radius
# calculate bead center in ray-coordinates
x_bead = self.x
z_bead = self.radius
x_bead_r, z_bead_r = ray_coordinates(ray, x_bead, z_bead)
# use equation-of-a-circle to determine intersect point
bead_thickness_at_intersect = sqrt(radius**2 - x_bead_r**2)
x_intersect_r = 0
z_intersect_r = z_bead_r - bead_thickness_at_intersect
# use first derivative of the equation-of-a-circle and snell's law to
# calculate the ray bending at the surface
theta1_r = atan(x_bead_r/sqrt(radius**2 - x_bead_r**2))
theta2_r = asin(self.n_surround/self.n_bead*sin(theta1_r))
# convert back to standard coordinates
x_intersect, z_intersect = standard_coordinates(ray, x_intersect_r, z_intersect_r)
theta2 = ray.th + theta2_r
ray.x = x_intersect
ray.z += z_intersect
ray.th = theta2
ray.save()
def intersect(self, ray):
x_bead = self.x
z_bead = self.radius
x_bead_r, z_bead_r = ray_coordinates(ray, x_bead, z_bead)
return abs(x_bead_r) < self.radius
