def refract(self, ray):
"""
Calculates the new direction of the ray incident to the refracting
surface using Snell's law in vector form.
"""
n = self._n0 / self._n1
intercept = self.intersect(ray)
if intercept is None:
return None
k1_ray = ray.k()
normal = nk.normalise((intercept - self._O) * (np.sign(k1_ray[2]) *
np.sign(self._curv)))
c = np.dot(-normal, k1_ray)
sin_t1_sq = 1 - c*c
if sin_t1_sq > 1./(n*n):
return None
k2_ray = nk.normalise(n*k1_ray + (n*c - np.sqrt(1-n*n*(1-c*c)))*normal)
return k2_ray
def reflect(self, ray):
"""
Calculates the reflected direction of the ray incident to the surface.
"""
intercept = self.intersect(ray)
if intercept is None:
return None
k1_ray = ray.k()
normal = nk.normalise((intercept - self._O) * (np.sign(k1_ray[2]) *
np.sign(self._curv)))
cos_t = - np.dot(normal, k1_ray)
k2_ray = k1_ray + 2*cos_t*normal
return k2_ray
def append(self, r, k):
"""
Appends new point and direction to the ray usually after interaction
with optical element.
r, k can be numpy arrays or lists of floats and/or integers.
Appended points and directions are numpy arrays of floats.
Directions are normalised.
"""
if len(r) != 3 or len(k) != 3:
raise Exception('3D vector size')
r = np.array(r, dtype=float)
k = nk.normalise(np.array(k, dtype=float))
self._vertices.append(r)
self._directions.append(k)
def __init__(self, r=[0, 0, 0], k=[0, 0, 1], wavelength = 0):
"""
Instantiates an optical ray at a starting position r with initial
(normalised) direction k. Coordinates are in the x,y,z Cartesian form.
r and k can be numpy arrays or lists of integers and/or floats.
wavelength is a float (measured in nanometres).
"""
if len(r) != 3 or len(k) != 3:
raise Exception('3D vector size')
self._r = np.array(r, dtype=float)
self._k = nk.normalise(np.array(k, dtype=float))
if wavelength == 0:
self._wavelength = None
self._wavelength = float(wavelength)
# __vertices and __directions are lists of all segment endpoints and
# directions of the ray. They are useful for plotting but not useful
# for the user.
self._vertices = [self._r]
self._directions = [self._k]
