Reimplementation of Specrend.c in Python.
This, (broadly) converts Temperature into and r, g, b value. Or, it gets you close enough that the rest is trivial and is left as an exercise to the reader.
The original is taken from:
specrend.c
And the original website is:
www.fourmilab.ch
Here's some Python:
"""
Colour Rendering of Spectra
by John Walker
http://www.fourmilab.ch/
Last updated: March 9, 2003
Converted to Python by Andrew Hutchins, sometime in early
2011.
This program is in the public domain.
The modifications are also public domain. (AH)
For complete information about the techniques employed in
this program, see the World-Wide Web document:
http://www.fourmilab.ch/documents/specrend/
The xyz_to_rgb() function, which was wrong in the original
version of this program, was corrected by:
Andrew J. S. Hamilton 21 May 1999
Andrew.Hamilton@Colorado.EDU
http://casa.colorado.edu/~ajsh/
who also added the gamma correction facilities and
modified constrain_rgb() to work by desaturating the
colour by adding white.
A program which uses these functions to plot CIE
"tongue" diagrams called "ppmcie" is included in
the Netpbm graphics toolkit:
http://netpbm.sourceforge.net/
(The program was called cietoppm in earlier
versions of Netpbm.)
"""
import math
"""
/* A colour system is defined by the CIE x and y coordinates of
its three primary illuminants and the x and y coordinates of
the white point. */
"""
GAMMA_REC709 = 0
NTSCsystem = {"name": "NTSC",
"xRed": 0.67, "yRed": 0.33,
"xGreen": 0.21, "yGreen": 0.71,
"xBlue": 0.14, "yBlue": 0.08,
"xWhite": 0.3101, "yWhite": 0.3163, "gamma": GAMMA_REC709}
EBUsystem = {"name": "SUBU (PAL/SECAM)",
"xRed": 0.64, "yRed": 0.33,
"xGreen": 0.29, "yGreen": 0.60,
"xBlue": 0.15, "yBlue": 0.06,
"xWhite": 0.3127, "yWhite": 0.3291, "gamma": GAMMA_REC709 }
SMPTEsystem = {"name": "SMPTE",
"xRed": 0.63, "yRed": 0.34,
"xGreen": 0.31, "yGreen": 0.595,
"xBlue": 0.155, "yBlue": 0.07,
"xWhite": 0.3127, "yWhite": 0.3291, "gamma": GAMMA_REC709 }
HDTVsystem = {"name": "HDTV",
"xRed": 0.67, "yRed": 0.33,
"xGreen": 0.21, "yGreen": 0.71,
"xBlue": 0.15, "yBlue": 0.06,
"xWhite": 0.3127, "yWhite": 0.3291, "gamma": GAMMA_REC709 }
CIEsystem = {"name": "CIE",
"xRed": 0.7355, "yRed": 0.2645,
"xGreen": 0.2658, "yGreen": 0.7243,
"xBlue": 0.1669, "yBlue": 0.0085,
"xWhite": 0.3333333333, "yWhite": 0.3333333333, "gamma": GAMMA_REC709 }
Rec709system = {"name": "CIE REC709",
"xRed": 0.64, "yRed": 0.33,
"xGreen": 0.30, "yGreen": 0.60,
"xBlue": 0.15, "yBlue": 0.06,
"xWhite": 0.3127, "yWhite": 0.3291, "gamma": GAMMA_REC709 }
def upvp_to_xy(up, vp):
xc = (9 * up) / ((6 * up) - (16 * vp) + 12)
yc = (4 * vp) / ((6 * up) - (16 * vp) + 12)
return(xc, yc)
def xy_toupvp(xc, yc):
up = (4 * xc) / ((-2 * xc) + (12 * yc) + 3);
vp = (9 * yc) / ((-2 * xc) + (12 * yc) + 3);
return(up, vp)
def xyz_to_rgb(cs, xc, yc, zc):
"""
Given an additive tricolour system CS, defined by the CIE x
and y chromaticities of its three primaries (z is derived
trivially as 1-(x+y)), and a desired chromaticity (XC, YC,
ZC) in CIE space, determine the contribution of each
primary in a linear combination which sums to the desired
chromaticity. If the requested chromaticity falls outside
the Maxwell triangle (colour gamut) formed by the three
primaries, one of the r, g, or b weights will be negative.
Caller can use constrain_rgb() to desaturate an
outside-gamut colour to the closest representation within
the available gamut and/or norm_rgb to normalise the RGB
components so the largest nonzero component has value 1.
"""
xr = cs["xRed"]
yr = cs["yRed"]
zr = 1 - (xr + yr)
xg = cs["xGreen"]
yg = cs["yGreen"]
zg = 1 - (xg + yg)
xb = cs["xBlue"]
yb = cs["yBlue"]
zb = 1 - (xb + yb)
xw = cs["xWhite"]
yw = cs["yWhite"]
zw = 1 - (xw + yw)
rx = (yg * zb) - (yb * zg)
ry = (xb * zg) - (xg * zb)
rz = (xg * yb) - (xb * yg)
gx = (yb * zr) - (yr * zb)
gy = (xr * zb) - (xb * zr)
gz = (xb * yr) - (xr * yb)
bx = (yr * zg) - (yg * zr)
by = (xg * zr) - (xr * zg)
bz = (xr * yg) - (xg * yr)
rw = ((rx * xw) + (ry * yw) + (rz * zw)) / yw
gw = ((gx * xw) + (gy * yw) + (gz * zw)) / yw
bw = ((bx * xw) + (by * yw) + (bz * zw)) / yw
rx = rx / rw; ry = ry / rw; rz = rz / rw
gx = gx / gw; gy = gy / gw; gz = gz / gw
bx = bx / bw; by = by / bw; bz = bz / bw
r = (rx * xc) + (ry * yc) + (rz * zc)
g = (gx * xc) + (gy * yc) + (gz * zc)
b = (bx * xc) + (by * yc) + (bz * zc)
return(r,g,b)
def inside_gamut(r, g, b):
"""
Test whether a requested colour is within the gamut
achievable with the primaries of the current colour
system. This amounts simply to testing whether all the
primary weights are non-negative. */
"""
return (r >= 0) and (g >= 0) and (b >= 0)
def constrain_rgb(r, g, b):
"""
If the requested RGB shade contains a negative weight for
one of the primaries, it lies outside the colour gamut
accessible from the given triple of primaries. Desaturate
it by adding white, equal quantities of R, G, and B, enough
to make RGB all positive. The function returns 1 if the
components were modified, zero otherwise.
"""
# Amount of white needed is w = - min(0, *r, *g, *b)
w = -min([0, r, g, b]) # I think?
# Add just enough white to make r, g, b all positive.
if w > 0:
r += w
g += w
b += w
return(r,g,b)
def gamma_correct(cs, c):
"""
Transform linear RGB values to nonlinear RGB values. Rec.
709 is ITU-R Recommendation BT. 709 (1990) ``Basic
Parameter Values for the HDTV Standard for the Studio and
for International Programme Exchange'', formerly CCIR Rec.
709. For details see
http://www.poynton.com/ColorFAQ.html
http://www.poynton.com/GammaFAQ.html
"""
gamma = cs.gamma
if gamma == GAMMA_REC709:
cc = 0.018
if c < cc:
c = ((1.099 * math.pow(cc, 0.45)) - 0.099) / cc
else:
c = (1.099 * math.pow(c, 0.45)) - 0.099
else:
c = math.pow(c, 1.0 / gamma)
return(c)
def gamma_correct_rgb(cs, r, g, b):
r = gamma_correct(cs, r)
g = gamma_correct(cs, g)
b = gamma_correct(cs, b)
return(r,g,b)
def norm_rgb(r, g, b):
"""
Normalise RGB components so the most intense (unless all
are zero) has a value of 1.
"""
greatest = max([r, g, b])
if greatest > 0:
r /= greatest
g /= greatest
b /= greatest
return(r, g, b)
def spectrum_to_xyz(spec_intens, temp): #spec_intens is a function
"""
Calculate the CIE X, Y, and Z coordinates corresponding to
a light source with spectral distribution given by the
function SPEC_INTENS, which is called with a series of
wavelengths between 380 and 780 nm (the argument is
expressed in meters), which returns emittance at that
wavelength in arbitrary units. The chromaticity
coordinates of the spectrum are returned in the x, y, and z
arguments which respect the identity:
x + y + z = 1.
CIE colour matching functions xBar, yBar, and zBar for
wavelengths from 380 through 780 nanometers, every 5
nanometers. For a wavelength lambda in this range:
cie_colour_match[(lambda - 380) / 5][0] = xBar
cie_colour_match[(lambda - 380) / 5][1] = yBar
cie_colour_match[(lambda - 380) / 5][2] = zBar
AH Note 2011: This next bit is kind of irrelevant on modern
hardware. Unless you are desperate for speed.
In which case don't use the Python version!
To save memory, this table can be declared as floats
rather than doubles; (IEEE) float has enough
significant bits to represent the values. It's declared
as a double here to avoid warnings about "conversion
between floating-point types" from certain persnickety
compilers. */
"""
cie_colour_match = [
[0.0014,0.0000,0.0065], [0.0022,0.0001,0.0105], [0.0042,0.0001,0.0201],
[0.0076,0.0002,0.0362], [0.0143,0.0004,0.0679], [0.0232,0.0006,0.1102],
[0.0435,0.0012,0.2074], [0.0776,0.0022,0.3713], [0.1344,0.0040,0.6456],
[0.2148,0.0073,1.0391], [0.2839,0.0116,1.3856], [0.3285,0.0168,1.6230],
[0.3483,0.0230,1.7471], [0.3481,0.0298,1.7826], [0.3362,0.0380,1.7721],
[0.3187,0.0480,1.7441], [0.2908,0.0600,1.6692], [0.2511,0.0739,1.5281],
[0.1954,0.0910,1.2876], [0.1421,0.1126,1.0419], [0.0956,0.1390,0.8130],
[0.0580,0.1693,0.6162], [0.0320,0.2080,0.4652], [0.0147,0.2586,0.3533],
[0.0049,0.3230,0.2720], [0.0024,0.4073,0.2123], [0.0093,0.5030,0.1582],
[0.0291,0.6082,0.1117], [0.0633,0.7100,0.0782], [0.1096,0.7932,0.0573],
[0.1655,0.8620,0.0422], [0.2257,0.9149,0.0298], [0.2904,0.9540,0.0203],
[0.3597,0.9803,0.0134], [0.4334,0.9950,0.0087], [0.5121,1.0000,0.0057],
[0.5945,0.9950,0.0039], [0.6784,0.9786,0.0027], [0.7621,0.9520,0.0021],
[0.8425,0.9154,0.0018], [0.9163,0.8700,0.0017], [0.9786,0.8163,0.0014],
[1.0263,0.7570,0.0011], [1.0567,0.6949,0.0010], [1.0622,0.6310,0.0008],
[1.0456,0.5668,0.0006], [1.0026,0.5030,0.0003], [0.9384,0.4412,0.0002],
[0.8544,0.3810,0.0002], [0.7514,0.3210,0.0001], [0.6424,0.2650,0.0000],
[0.5419,0.2170,0.0000], [0.4479,0.1750,0.0000], [0.3608,0.1382,0.0000],
[0.2835,0.1070,0.0000], [0.2187,0.0816,0.0000], [0.1649,0.0610,0.0000],
[0.1212,0.0446,0.0000], [0.0874,0.0320,0.0000], [0.0636,0.0232,0.0000],
[0.0468,0.0170,0.0000], [0.0329,0.0119,0.0000], [0.0227,0.0082,0.0000],
[0.0158,0.0057,0.0000], [0.0114,0.0041,0.0000], [0.0081,0.0029,0.0000],
[0.0058,0.0021,0.0000], [0.0041,0.0015,0.0000], [0.0029,0.0010,0.0000],
[0.0020,0.0007,0.0000], [0.0014,0.0005,0.0000], [0.0010,0.0004,0.0000],
[0.0007,0.0002,0.0000], [0.0005,0.0002,0.0000], [0.0003,0.0001,0.0000],
[0.0002,0.0001,0.0000], [0.0002,0.0001,0.0000], [0.0001,0.0000,0.0000],
[0.0001,0.0000,0.0000], [0.0001,0.0000,0.0000], [0.0000,0.0000,0.0000]]
X = 0
Y = 0
Z = 0
for i, lamb in enumerate(range(380, 780, 5)): #lambda = 380; lambda < 780.1; i++, lambda += 5) {
Me = spec_intens(lamb, temp);
X += Me * cie_colour_match[i][0]
Y += Me * cie_colour_match[i][1]
Z += Me * cie_colour_match[i][2]
XYZ = (X + Y + Z)
x = X / XYZ;
y = Y / XYZ;
z = Z / XYZ;
return(x, y, z)
def bb_spectrum(wavelength, bbTemp=5000):
"""
Calculate, by Planck's radiation law, the emittance of a black body
of temperature bbTemp at the given wavelength (in metres). */
"""
wlm = wavelength * 1e-9 # Convert to metres
return (3.74183e-16 * math.pow(wlm, -5.0)) / (math.exp(1.4388e-2 / (wlm * bbTemp)) - 1.0)
""" Built-in test program which displays the x, y, and Z and RGB
values for black body spectra from 1000 to 10000 degrees kelvin.
When run, this program should produce the following output:
Temperature x y z R G B
----------- ------ ------ ------ ----- ----- -----
1000 K 0.6528 0.3444 0.0028 1.000 0.007 0.000 (Approximation)
1500 K 0.5857 0.3931 0.0212 1.000 0.126 0.000 (Approximation)
2000 K 0.5267 0.4133 0.0600 1.000 0.234 0.010
2500 K 0.4770 0.4137 0.1093 1.000 0.349 0.067
3000 K 0.4369 0.4041 0.1590 1.000 0.454 0.151
3500 K 0.4053 0.3907 0.2040 1.000 0.549 0.254
4000 K 0.3805 0.3768 0.2428 1.000 0.635 0.370
4500 K 0.3608 0.3636 0.2756 1.000 0.710 0.493
5000 K 0.3451 0.3516 0.3032 1.000 0.778 0.620
5500 K 0.3325 0.3411 0.3265 1.000 0.837 0.746
6000 K 0.3221 0.3318 0.3461 1.000 0.890 0.869
6500 K 0.3135 0.3237 0.3628 1.000 0.937 0.988
7000 K 0.3064 0.3166 0.3770 0.907 0.888 1.000
7500 K 0.3004 0.3103 0.3893 0.827 0.839 1.000
8000 K 0.2952 0.3048 0.4000 0.762 0.800 1.000
8500 K 0.2908 0.3000 0.4093 0.711 0.766 1.000
9000 K 0.2869 0.2956 0.4174 0.668 0.738 1.000
9500 K 0.2836 0.2918 0.4246 0.632 0.714 1.000
10000 K 0.2807 0.2884 0.4310 0.602 0.693 1.000
"""
if __name__ == "__main__":
print "Temperature x y z R G B\n"
print "----------- ------ ------ ------ ----- ----- -----\n"
for t in range(1000, 10000, 500): # (t = 1000; t <= 10000; t+= 500) {
x, y, z = spectrum_to_xyz(bb_spectrum, t)
r, g, b = xyz_to_rgb(SMPTEsystem, x, y, z)
print " %5.0f K %.4f %.4f %.4f " % (t, x, y, z),
r, g, b = constrain_rgb(r, g, b) # I omit the approximation bit here.
r, g, b = norm_rgb(r, g, b)
print "%.3f %.3f %.3f" % (r, g, b)
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