def __init__(self):
# The vectorized coordinate functions
self.X = vmap(self._X) # (N x 2) -> N
self.Y = vmap(self._Y) # (N x 2) -> N
self.Z = vmap(self._Z) # (N x 2) -> N
# _T,_N,_B are unvectorized functions that yield the unit tangent, normal
# and bi-normal vectors of the curve at t.
self._T = lambda t: normalize_vector(jnp.array(jacfwd(self._f)(t)))
self._N = lambda t: normalize_vector(jnp.array(jacfwd(self._T)(t)))
self._B = lambda t: normalize_vector(jnp.cross(self._T(t), self._N(t)))
# Vectorized TNB
self.T = vmap(self._T)
self.N = vmap(self._N)
self.B = vmap(self._B)
def _XYZ(self, uv):
""" The CMFs place a wavelength parameter into a space curve (the spectral locus)
multiplying by intensity shifts to a position on a surface (the spectral cone)
"""
intensity, wavelength = uv
x = intensity * CIEXfitSimple(wavelength)
y = intensity * CIEYfitSimple(wavelength)
z = intensity * CIEZfitSimple(wavelength)
return self.XYZ_to_outputspace(jnp.array([x, y, z]))
def _XYZ(self, uv):
# https://math.stackexchange.com/questions/461547/whats-the-equation-of-helix-surface
theta, t = uv
f = self.curve._f
N = self.curve._N
B = self.curve._B
r = self.radius
XYZ = jnp.array(
f(t)) + r * N(t) * jnp.cos(theta) + r * B(t) * jnp.sin(theta)
return XYZ
def _N(uv):
dfdu, dfdv = jnp.array(jacfwd(self._f)(uv)).swapaxes(0, 1)
n = jnp.cross(dfdu, dfdv)
return n / jnp.linalg.norm(n)
def down_right_shifted_conv_transpose(inputs):
out_h, out_w = np.multiply(np.array(inputs.shape[-3:-1]),
np.array(strides or (1, 1)))
inputs = ConvTranspose(out_chan, filter_shape, strides, 'VALID',
**kwargs)(inputs)
return inputs[:, :out_h, :out_w]
# Simple Analytic (Differentiable!) Approximations to the CIE XYZ
# Color Matching Functions
def CIEXfitSimple(wave):
t1 = (wave - 595.8) / 33.33
t2 = (wave - 446.88) / 19.44
return 1.065 * jnp.exp(-0.5 * t1 * t1) + 0.366 * jnp.exp(-0.5 * t2 * t2)
def CIEYfitSimple(wave):
t1 = (jnp.log(wave) - jnp.log(556.3)) / 0.075
return 1.014 * jnp.exp(-0.5 * t1 * t1)
def CIEZfitSimple(wave):
t1 = (jnp.log(wave) - jnp.log(449.8)) / 0.051
return 1.839 * jnp.exp(-0.5 * t1 * t1)
sRGB_primaries = \
jnp.array([
[ 0.41231515, 0.2126, 0.01932727],
[ 0.3576 , 0.7152, 0.1192 ],
[ 0.1805 , 0.0722, 0.95063333]])
def xyz_to_srgb(xyz):
primary_inverse = jnp.linalg.inv(sRGB_primaries)
return xyz.T.dot(primary_inverse)
# visible wavelengths of light
visual_range_nm = [400.0, 700.0]
def __init__(self, r0=[1, 1, 1], v=[1, 0.5, 0]):
self.r0 = jnp.array(r0)
self.v = jnp.array(v)
super().__init__()