问题
I have written a lib for working with colours and stuck trying to calculate Tc(k). From what I have read working in the CIE 1931 XYZ colour space is the way to go and it can be obtained using xyY.
So far I have got everything correct to the point of figuring out the correct x and y from :
X Y
x = ____________ y = ____________
( X + Y + Z) ( X + Y + Z)
The numbers much up to the chart, but cant find anything that details how you go from x and y to Tc(K)
eg: For #FF0000 I get the following.
x: 0.64007449945677
y: 0.32997051063169
I have read a number of papers on the topic and litterally all the wikipedia articles. All the questions I have come across on SO simply link to a wiki article on colours, not seen one that has the actual formula for calculating Tc(k)
回答1:
If I understand you correctly please see this pdf where a number of methods (briefly :( ) described. From this PDF:
[CCT1] Calculations are performed using CIE 1960 uniform color space coordinates u and v. Coordinates u and v are derived from x and y using the formulae: u = 4x/(12y-2x+3) and v = 6y/(12y-2x+3) The correlated color temperature is defined as the temperature of a blackbody that lies closest to the u,v coordinates of the test source. Two separate methods provide results: one is an iterative method based on the definition, and the other is the commonly used Robertson’s method involving interpolation based on a table of 30 pre-calculated u, v and inverse-slope parameters. Iteration If uS and vS are the values for a test source, and uT and vT are the blackbody values at temperature T, the correlated color temperature is the value of T where:
sqrt( (uS - uT)^2 + (vS - vT)^2 )
is minimized. Adjusting the temperature T to obtain the minimum of this function was done using spreadsheets (Quattro Pro 8 and Excel 97). Both spreadsheets gave identical values.
Don't know if it actually helps you.
回答2:
Based on the Wikipedia article I entered the approximated formula for Color Temperature calculation into Excel as
=(-449*((R1-0,332)/(S1-0,1858))^3)+(3525*((R1-0,332)/(S1-0,1858))^2)-(6823,3*((R1-0,332)/(S1-0,1858)))+(5520,33)
R1 is color space x coordinate from 0 to 1
S1 is color space y coordinate from 0 to 1
Works fine!
回答3:
I done some digging in some open source apps and found something in UFRaw. I have not quite figured out what is going on exactly.
Also found a paper that seems to cover the topic quite well.
Converted to php and this is what I have so far:
$temp = array(9500, 7000, 5500, 3750, 3000, 2700, 2250, 1800, 1500);
$hex = array('9DBEFF', 'E4EEFF', 'FFE4BE', 'FFA04C', 'FF7A26', 'FF6A19', 'FF500B', 'FF3403', 'FF2300');
echo '<h3>K -> RGB</h3>';
foreach ($temp as $k) {
$rgb = ColourConverter::temperature2rgb($k);
echo sprintf('<div style="background-color:rgb(%s); text-align: center; width: 100px; height: 25px; clear: both;">%s</div>', implode(', ', $rgb), $k);
}
echo '<h3>RGB -> K</h3>';
foreach ($hex as $v) {
$rgb = array_values(ColourConverter::hex2rgb($v));
$k = round(ColourConverter::rgb2temperature($rgb[0], $rgb[1], $rgb[2]));
echo sprintf('<div style="background-color:rgb(%s); text-align: center; width: 100px; height: 25px; clear: both;">%s</div>', implode(', ', $rgb), $k);
}
My output:
Pretty close but not 100% yet. (Found a bug in my code and it is now almost perfect)
- The colours are slightly off going from k -> rgb
- It does not work doing k -> rgb -> k. You don't get back to the same value.
Code
UFRaw line 246-294
void Temperature_to_RGB(double T, double RGB[3])
{
int c;
double xD, yD, X, Y, Z, max;
// Fit for CIE Daylight illuminant
if (T <= 4000) {
xD = 0.27475e9 / (T * T * T) - 0.98598e6 / (T * T) + 1.17444e3 / T + 0.145986;
} else if (T <= 7000) {
xD = -4.6070e9 / (T * T * T) + 2.9678e6 / (T * T) + 0.09911e3 / T + 0.244063;
} else {
xD = -2.0064e9 / (T * T * T) + 1.9018e6 / (T * T) + 0.24748e3 / T + 0.237040;
}
yD = -3 * xD * xD + 2.87 * xD - 0.275;
// Fit for Blackbody using CIE standard observer function at 2 degrees
//xD = -1.8596e9/(T*T*T) + 1.37686e6/(T*T) + 0.360496e3/T + 0.232632;
//yD = -2.6046*xD*xD + 2.6106*xD - 0.239156;
// Fit for Blackbody using CIE standard observer function at 10 degrees
//xD = -1.98883e9/(T*T*T) + 1.45155e6/(T*T) + 0.364774e3/T + 0.231136;
//yD = -2.35563*xD*xD + 2.39688*xD - 0.196035;
X = xD / yD;
Y = 1;
Z = (1 - xD - yD) / yD;
max = 0;
for (c = 0; c < 3; c++) {
RGB[c] = X * XYZ_to_RGB[0][c] + Y * XYZ_to_RGB[1][c] + Z * XYZ_to_RGB[2][c];
if (RGB[c] > max) max = RGB[c];
}
for (c = 0; c < 3; c++) RGB[c] = RGB[c] / max;
}
void RGB_to_Temperature(double RGB[3], double *T, double *Green)
{
double Tmax, Tmin, testRGB[3];
Tmin = 2000;
Tmax = 23000;
for (*T = (Tmax + Tmin) / 2; Tmax - Tmin > 0.1; *T = (Tmax + Tmin) / 2) {
Temperature_to_RGB(*T, testRGB);
if (testRGB[2] / testRGB[0] > RGB[2] / RGB[0])
Tmax = *T;
else
Tmin = *T;
}
*Green = (testRGB[1] / testRGB[0]) / (RGB[1] / RGB[0]);
if (*Green < 0.2) *Green = 0.2;
if (*Green > 2.5) *Green = 2.5;
}
回答4:
The Wikipedia states that the color temperature is calculated by considering the u-v chromaticities, not x-y, so you have to perform a translation. That said, I recommend using an approximation (also explained in the Wikipedia) as suggested by @sixlettervariables.
The real question is, what are you trying to find the color temperature of?. I see a reference (#FF0000) to RGB colors, which are meaningless without stating a color space. Supposing you are in sRGB (so I can point you at Wikipedia again), you have to first obtain the linear RGB co-ordinates before proceeding to XYZ.
回答5:
I realize this is an old question, but I was struggling to find an answer as well. I finally came across this nifty calculator that also posts the formula as follows:
n = (x-0.3320)/(0.1858-y)
CCT = 437*n^3 + 3601*n^2 + 6861*n + 5517
Hope this helps anyone else who's still looking.
回答6:
Found the Temperature to RGB solution written in JavaScript and converted it into PHP.
<?php
function colorTemperatureToRGB($kelvin)
{
$temp = $kelvin / 100;
$red = null;
$green = null;
$blue = null;
if ($temp <= 66)
{
$red = 255;
$green = $temp;
$green = 99.4708025861 * log($green) - 161.1195681661;
if ($temp <= 19)
{
$blue = 0;
}
else
{
$blue = $temp - 10;
$blue = 138.5177312231 * log($blue) - 305.0447927307;
}
}
else
{
$red = $temp - 60;
$red = 329.698727446 * pow($red, -0.1332047592);
$green = $temp - 60;
$green = 288.1221695283 * pow($green, -0.0755148492);
$blue = 255;
}
return [
'r' => clamp($red, 0, 255),
'g' => clamp($green, 0, 255),
'b' => clamp($blue, 0, 255)
];
}
function clamp($x, $min, $max)
{
if ($x < $min)
return $min;
if ($x > $max)
return $max;
return $x;
}
var_dump(colorTemperatureToRGB(7000));
来源：https://stackoverflow.com/questions/13975917/calculate-colour-temperature-in-k