def find_nearest_points(ray0, ray1):
"""
Find the nearest points on given rays with respect to the other ray.
Parameters
----------
ray0 : ndarray
A ray.
ray1 : ndarray
A ray.
Returns
----------
c0 : ndarray
Closest point on ray0.
c1 : ndarray
Closest point on ray1.
"""
p0 = ray0[0].reshape(3, )
d0 = ray0[1].reshape(3, )
p1 = ray1[0].reshape(3, )
d1 = ray1[1].reshape(3, )
n = np.cross(d0, d1)
if np.all(n) == 0:
point, distances = calculate_intersection_of_two_rays(ray0, ray1)
c0 = c1 = point
else:
n0 = np.cross(d0, n)
n1 = np.cross(d1, n)
c0 = p0 + (np.dot((p1 - p0), n1) / np.dot(d0, n1)) * d0
c1 = p1 + (np.dot((p0 - p1), n0) / np.dot(d1, n0)) * d1
return c0, c1
def linearpolarizer(field, rotation=0):
"""
Definition that represents a linear polarizer.
Parameters
----------
field : ndarray
Polarization vector of an input beam.
rotation : float
Represents rotation of the polarizer along propagation direction in angles (couter-clockwise).
Returns
----------
result : ndarray
Polarization vector of an output beam.
"""
rotation = np.radians(rotation)
rotmat = np.array([[float(np.cos(rotation)),
float(np.sin(rotation))],
[float(-np.sin(rotation)),
float(np.cos(rotation))]])
linearpolarizer = np.array([[1, 0], [0, 0]])
linearpolarizer = np.dot(rotmat.transpose(),
np.dot(linearpolarizer, rotmat))
result = np.dot(linearpolarizer, field)
return result
def closest_point_to_a_ray(point, ray):
"""
Definition to calculate the point on a ray that is closest to given point.
Parameters
----------
point : list
Given point in X,Y,Z.
ray : ndarray
Given ray.
Returns
---------
closest_point : ndarray
Calculated closest point.
"""
from odak.raytracing import propagate_a_ray
if len(ray.shape) == 2:
ray = ray.reshape((1, 2, 3))
p0 = ray[:, 0]
p1 = propagate_a_ray(ray, 1.)
if len(p1.shape) == 2:
p1 = p1.reshape((1, 2, 3))
p1 = p1[:, 0]
p1 = p1.reshape(3)
p0 = p0.reshape(3)
point = point.reshape(3)
closest_distance = -np.dot((p0 - point), (p1 - p0)) / np.sum((p1 - p0)**2)
closest_point = propagate_a_ray(ray, closest_distance)[0]
return closest_point
def same_side(p1, p2, a, b):
"""
Definition to figure which side a point is on with respect to a line and a point. See http://www.blackpawn.com/texts/pointinpoly/ for more. If p1 and p2 are on the sameside, this definition returns True.
Parameters
----------
p1 : list
Point(s) to check.
p2 : list
This is the point check against.
a : list
First point that forms the line.
b : list
Second point that forms the line.
"""
ba = np.subtract(b, a)
p1a = np.subtract(p1, a)
p2a = np.subtract(p2, a)
cp1 = np.cross(ba, p1a)
cp2 = np.cross(ba, p2a)
test = np.dot(cp1, cp2)
if len(p1.shape) > 1:
return test >= 0
if test >= 0:
return True
return False
def calculate_intersection_of_two_rays(ray0, ray1):
"""
Definition to calculate the intersection of two rays.
Parameters
----------
ray0 : ndarray
A ray.
ray1 : ndarray
A ray.
Returns
----------
point : ndarray
Point in X,Y,Z.
distances : ndarray
Distances.
"""
A = np.array([[float(ray0[1][0]), float(ray1[1][0])],
[float(ray0[1][1]), float(ray1[1][1])],
[float(ray0[1][2]), float(ray1[1][2])]])
B = np.array([
ray0[0][0] - ray1[0][0], ray0[0][1] - ray1[0][1],
ray0[0][2] - ray1[0][2]
])
distances = np.linalg.lstsq(A, B)[0]
if np.allclose(np.dot(A, distances), B) == False:
distances = np.array([0, 0])
distances = distances[np.argsort(-distances)]
point = propagate_a_ray(ray0, distances[0])[0]
return point, distances
def intersect_w_surface(ray, points):
"""
Definition to find intersection point inbetween a surface and a ray. For more see: http://geomalgorithms.com/a06-_intersect-2.html
Parameters
----------
ray : ndarray
A vector/ray.
points : ndarray
Set of points in X,Y and Z to define a planar surface.
Returns
----------
normal : ndarray
Surface normal at the point of intersection.
distance : float
Distance in between starting point of a ray with it's intersection with a planar surface.
"""
points = np.asarray(points)
normal = get_triangle_normal(points)
if len(ray.shape) == 2:
ray = ray.reshape((1, 2, 3))
if len(points) == 2:
points = points.reshape((1, 3, 3))
if len(normal.shape) == 2:
normal = normal.reshape((1, 2, 3))
f = normal[:, 0] - ray[:, 0]
distance = np.dot(normal[:, 1], f.T) / np.dot(normal[:, 1], ray[:, 1].T)
n = np.int(np.amax(np.array([ray.shape[0], normal.shape[0]])))
normal = np.zeros((n, 2, 3))
normal[:, 0] = ray[:, 0] + distance.T * ray[:, 1]
distance = np.abs(distance)
if normal.shape[0] == 1:
normal = normal.reshape((2, 3))
distance = distance.reshape((1))
if distance.shape[0] == 1 and len(distance.shape) > 1:
distance = distance.reshape((distance.shape[1]))
return normal, distance
def rotate_point(point,angles=[0,0,0],mode='XYZ',origin=[0,0,0],offset=[0,0,0]):
"""
Definition to rotate a given point. Note that rotation is always with respect to 0,0,0.
Parameters
----------
point : ndarray
A point.
angles : list
Rotation angles in degrees.
mode : str
Rotation mode determines ordering of the rotations at each axis. There are XYZ,YXZ,ZXY and ZYX modes.
origin : list
Reference point for a rotation.
offset : list
Shift with the given offset.
Returns
----------
result : ndarray
Result of the rotation
rotx : ndarray
Rotation matrix along X axis.
roty : ndarray
Rotation matrix along Y axis.
rotz : ndarray
Rotation matrix along Z axis.
"""
point = np.asarray(point)
point -= np.asarray(origin)
rotx = rotmatx(angles[0])
roty = rotmaty(angles[1])
rotz = rotmatz(angles[2])
if mode == 'XYZ':
result = np.dot(rotz,np.dot(roty,np.dot(rotx,point)))
elif mode == 'XZY':
result = np.dot(roty,np.dot(rotz,np.dot(rotx,point)))
elif mode == 'YXZ':
result = np.dot(rotz,np.dot(rotx,np.dot(roty,point)))
elif mode == 'ZXY':
result = np.dot(roty,np.dot(rotx,np.dot(rotz,point)))
elif mode == 'ZYX':
result = np.dot(rotx,np.dot(roty,np.dot(rotz,point)))
result += np.asarray(origin)
result += np.asarray(offset)
return result,rotx,roty,rotz
def rotate_points(points,angles=[0,0,0],mode='XYZ',origin=[0,0,0],offset=[0,0,0]):
"""
Definition to rotate points.
Parameters
----------
points : ndarray
Points.
angles : list
Rotation angles in degrees.
mode : str
Rotation mode determines ordering of the rotations at each axis. There are XYZ,YXZ,ZXY and ZYX modes.
origin : list
Reference point for a rotation.
offset : list
Shift with the given offset.
Returns
----------
result : ndarray
Result of the rotation
"""
points = np.asarray(points)
if angles[0] == 0 and angles[1] == 0 and angles[2] ==0:
result = np.array(offset) + points
return result
points -= np.array(origin)
rotx = rotmatx(angles[0])
roty = rotmaty(angles[1])
rotz = rotmatz(angles[2])
if mode == 'XYZ':
result = np.dot(rotz,np.dot(roty,np.dot(rotx,points.T))).T
elif mode == 'XZY':
result = np.dot(roty,np.dot(rotz,np.dot(rotx,points.T))).T
elif mode == 'YXZ':
result = np.dot(rotz,np.dot(rotx,np.dot(roty,points.T))).T
elif mode == 'ZXY':
result = np.dot(roty,np.dot(rotx,np.dot(rotz,points.T))).T
elif mode == 'ZYX':
result = np.dot(rotx,np.dot(roty,np.dot(rotz,points.T))).T
result += np.array(origin)
result += np.array(offset)
return result