def getFaceNormal(self, face):
points = []
for v in face:
points.append(Point(v[0], v[1], v[2]))
vecA = Vector.from_points(points[0], points[1])
vecB = Vector.from_points(points[0], points[2])
vecResult = Vector.cross(vecA, vecB)
return vecResult
def getUVFaceNormal( facepath ): uvs = getWindingOrder(facepath) if len(uvs) < 3: return (1,0,0) #if there are less than 3 uvs we have no uv area so bail #get edge vectors and cross them to get the uv face normal uvAPos = cmd.polyEditUV(uvs[0], query=True, uValue=True, vValue=True) uvBPos = cmd.polyEditUV(uvs[1], query=True, uValue=True, vValue=True) uvCPos = cmd.polyEditUV(uvs[2], query=True, uValue=True, vValue=True) uvAB = Vector( [uvBPos[0]-uvAPos[0], uvBPos[1]-uvAPos[1], 0] ) uvBC = Vector( [uvCPos[0]-uvBPos[0], uvCPos[1]-uvBPos[1], 0] ) uvNormal = uvAB.cross( uvBC ).normalize() return uvNormal
def getUVFaceNormal( facepath ): uvs = getWindingOrder(facepath) if len(uvs) < 3: return (1,0,0) #if there are less than 3 uvs we have no uv area so bail #get edge vectors and cross them to get the uv face normal uvAPos = cmd.polyEditUV(uvs[0], query=True, uValue=True, vValue=True) uvBPos = cmd.polyEditUV(uvs[1], query=True, uValue=True, vValue=True) uvCPos = cmd.polyEditUV(uvs[2], query=True, uValue=True, vValue=True) uvAB = Vector( [uvBPos[0]-uvAPos[0], uvBPos[1]-uvAPos[1], 0] ) uvBC = Vector( [uvCPos[0]-uvBPos[0], uvCPos[1]-uvBPos[1], 0] ) uvNormal = uvAB.cross( uvBC ).normalize() return uvNormal
def add_slab_vectorial(self, n1, thickness, alpha):
"""
Calculates the effect of the slab, using vectorial theory, considering s and p polarizations.
n1: refractive index of the slab
thickness: thickness
alpha: angle from the xy plane, conventionally from the y axis
"""
n0 = self.n
k = self.k
k1 = n1 / n0 * k
kx = self.kx
ky = self.ky
kz = self.kz
# k vector
vk = Vector(kx, ky, kz)
uk = vk.norm
ux = Vector(1, 0, 0).to_size_like(vk)
uy = Vector(0, 1, 0).to_size_like(vk)
uz = Vector(0, 0, 1).to_size_like(vk)
# normal to the surface
u = Vector(0, np.sin(alpha), np.cos(alpha)).to_size_like(vk)
us = (uk.cross(u)).norm
up = us.cross(uk)
E0 = ux # assume initial polarization along x
E = uk.cross(-uz.cross(E0))
E = E / E.mag
Es = E.dot(us)
Ep = E.dot(up)
print(E)
# incidence angle, relative to the slab surface
#phi0 = np.arccos(uk.cross(u).mag())
phi0 = np.arcsin(np.abs(uk.dot(u)))
#Snell's law:
phi1 = np.arcsin(n0 / n1 * np.sin(phi0))
beta = phi0 - phi1
#uk1 = uk * np.cos(beta) - up * np.sin(beta)
with np.errstate(invalid='ignore'):
theta0 = np.arcsin(ky / k)
theta1 = np.arcsin(n0 / n1 * np.sin(theta0 + alpha)) - alpha
ky1 = k1 * np.sin(theta1)
k_rho1 = np.sqrt(kx**2 + ky1**2)
kz1 = np.sqrt(k1**2 - k_rho1**2)
# additional phase due to propagation in the slab
phase = (kz1 - kz) * 2 * np.pi * thickness / np.cos(alpha)
# Fresnel law of refraction
Ts01 = 2 * n0 * np.cos(theta0) / (n0 * np.cos(theta0) +
n1 * np.cos(theta1))
Tp01 = 2 * n0 * np.cos(theta0) / (n0 * np.cos(theta1) +
n1 * np.cos(theta0))
Ts10 = 2 * n1 * np.cos(theta1) / (n1 * np.cos(theta1) +
n0 * np.cos(theta0))
Tp10 = 2 * n1 * np.cos(theta1) / (n1 * np.cos(theta0) +
n0 * np.cos(theta1))
transmittance = (Es * Ts01 * Ts10 + Ep * Tp01 * Tp10
) # assuming equal s and p polarization components
#bprint(transmittance)
self.amplitude *= transmittance
self.phase += phase
self.thickness = thickness
self.alpha = alpha
self.n1 = n1
self.correct_slab_defocus()
import numpy as np from vectors import Point, Vector import functools v1 = Vector(1, 2, 3) v2 = Vector(10, 20, 30) print(v1.add(10)) print(v1.sum(v2)) # displays <1 22 33> print(v1.magnitude()) #We can multiply a vector by a real number. print(v2.multiply(4)) #=> Vector(4.0, 8.0, 12.0) print(v1.dot(v2)) print(v1.dot(v2, 180)) print(v1.cross(v2)) print(v1.angle(v2)) print(v1.parallel(v2)) print(v1.perpendicular(v2)) #print(v1.non_parallel(v2))
