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/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 15.04.0 ] */
/* [wxMaxima: input start ] */
/* Authors: Alexei Boronine, Bastien Dejean */
/* References:
https://gist.github.com/baskerville/8297428
http://www.brucelindbloom.com/ */
/* The following values are taken directly from matrix.wxm */
refX: 3127/3290;
refY: 1;
refZ: 3583/3290;
M_RGB_XYZ: matrix(
[506752/1228815, 87881/245763, 12673/70218],
[87098/409605, 175762/245763, 12673/175545],
[7918/409605, 87881/737289, 1001167/1053270]);
M_XYZ_RGB: invert(M_RGB_XYZ);
/* Note that the standard defines these constants as decimals
and is incorrect. We are using the correct non-standard values.
See: http://www.brucelindbloom.com/index.html?LContinuity.html */
epsilon: (6 / 29) ^ 3;
kappa: (29 / 3) ^ 3;
refU: (4 * refX) / (refX + (15 * refY) + (3 * refZ));
refV: (9 * refY) / (refX + (15 * refY) + (3 * refZ));
/* Not used, see linearRGBChannelFromLUV */
fromLinear(c):= if (c<=0.0031308)
then 12.92 * c
else 1.055 * c ^ (1 / 2.4) - 0.055;
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
f_inv(t) := if (t ^ 3 > epsilon)
then t ^ 3
else (116 * t - 16) / kappa;
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
/* Returns the value of a linear sRGB channel specified by its matrix
values. Note that this is not the final sRGB value since gamma correction
is not applied, however, the value happens to be correct in two cases:
0 and 1. (Solve fromLinear above to see for yourself). As it happens, the
only use for this function is to solve it for 0 and 1, which means
fromLinear won't be necessary.
*/
linearRGBChannelFromLUV(L, U, V, m1, m2, m3) := block(
[varY, varU, varV, Y, X, Z],
varY : f_inv((L + 16) / 116),
varU : U / (13 * L) + refU,
varV : V / (13 * L) + refV,
Y : varY * refY,
X : 0 - (9 * Y * varU) / ((varU - 4) * varV - varU * varV),
Z : (9 * Y - (15 * varV * Y) - (varV * X)) / (3 * varV),
[X, Y, Z] . [m1, m2, m3]
);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
/* Given L, U, RGB channel and limit t (0 or 1), return the V value
that will push the CIE LUV color outside the sRGB gamut for the given
channel and the given limit. */
solve(linearRGBChannelFromLUV(L, U, V, m1, m2, m3) = t, V);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
/* Bounding function generator */
bound(L, m1, m2, m3, t) := solve(linearRGBChannelFromLUV(L, x, y, m1, m2, m3) = t, y)[1];
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
/* Generate bounding function that draws a line on CIE LUV space, stepping
outside of which will push the red RGB value below 0 */
bound(50, M_XYZ_RGB[1][1], M_XYZ_RGB[1][2], M_XYZ_RGB[1][3], 0);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
block(
[L],
L: 50,
plot2d([
rhs(bound(L, M_XYZ_RGB[1][1], M_XYZ_RGB[1][2], M_XYZ_RGB[1][3], 0)),
rhs(bound(L, M_XYZ_RGB[1][1], M_XYZ_RGB[1][2], M_XYZ_RGB[1][3], 1)),
rhs(bound(L, M_XYZ_RGB[2][1], M_XYZ_RGB[2][2], M_XYZ_RGB[2][3], 0)),
rhs(bound(L, M_XYZ_RGB[2][1], M_XYZ_RGB[2][2], M_XYZ_RGB[2][3], 1)),
rhs(bound(L, M_XYZ_RGB[3][1], M_XYZ_RGB[3][2], M_XYZ_RGB[3][3], 0)),
rhs(bound(L, M_XYZ_RGB[3][1], M_XYZ_RGB[3][2], M_XYZ_RGB[3][3], 1))
], [x,-400,400], [y,-400,400], [
legend,
"red = 0",
"red = 1",
"green = 0",
"green = 1",
"blue = 0",
"blue = 1"
], [
xlabel,
"hue"
], [
ylabel,
"chroma"
])
);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
fpprec: 17;
bfloat(M_XYZ_RGB);
bfloat(M_RGB_XYZ);
bfloat(refX);
bfloat(refY);
bfloat(refZ);
bfloat(refU);
bfloat(refV);
bfloat(kappa);
bfloat(epsilon);
/* [wxMaxima: input end ] */
/* Maxima can't load/batch files which end with a comment! */
"Created with wxMaxima"$
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