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cmfxyz.m
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%CMFXYZ Color matching function
%
% The color matching function is the XYZ tristimulus required to match a
% particular wavelength excitation.
%
% XYZ = CMFXYZ(LAMBDA) is the CIE XYZ color matching function (Nx3) for
% illumination at wavelength LAMBDA (Nx1) [m]. If LAMBDA is a vector then
% each row of XYZ is the color matching function of the corresponding
% element of LAMBDA.
%
% XYZ = CMFXYZ(LAMBDA, E) is the CIE XYZ color matching (1x3) function for
% an illumination spectrum E (Nx1) defined at corresponding wavelengths
% LAMBDA (Nx1).
%
% Note::
% - CIE 1931 2-deg XYZ CMFs from cvrl.ioo.ucl.ac.uk
%
% References::
% - Robotics, Vision & Control, Section 14.3,
% P. Corke, Springer 2011.
%
% See also CMFRGB, CCXYZ.
% Copyright 2022-2023 Peter Corke, Witold Jachimczyk, Remo Pillat
function XYZ = cmfxyz(lambda, spect)
if true
ciedat = [
0 0 0 0
% CIE 1931 2-deg XYZ CMFs from cvrl.ioo.ucl.ac.uk
360,0.000129900000,0.000003917000,0.000606100000
365,0.000232100000,0.000006965000,0.001086000000
370,0.000414900000,0.000012390000,0.001946000000
375,0.000741600000,0.000022020000,0.003486000000
380,0.001368000000,0.000039000000,0.006450001000
385,0.002236000000,0.000064000000,0.010549990000
390,0.004243000000,0.000120000000,0.020050010000
395,0.007650000000,0.000217000000,0.036210000000
400,0.014310000000,0.000396000000,0.067850010000
405,0.023190000000,0.000640000000,0.110200000000
410,0.043510000000,0.001210000000,0.207400000000
415,0.077630000000,0.002180000000,0.371300000000
420,0.134380000000,0.004000000000,0.645600000000
425,0.214770000000,0.007300000000,1.039050100000
430,0.283900000000,0.011600000000,1.385600000000
435,0.328500000000,0.016840000000,1.622960000000
440,0.348280000000,0.023000000000,1.747060000000
445,0.348060000000,0.029800000000,1.782600000000
450,0.336200000000,0.038000000000,1.772110000000
455,0.318700000000,0.048000000000,1.744100000000
460,0.290800000000,0.060000000000,1.669200000000
465,0.251100000000,0.073900000000,1.528100000000
470,0.195360000000,0.090980000000,1.287640000000
475,0.142100000000,0.112600000000,1.041900000000
480,0.095640000000,0.139020000000,0.812950100000
485,0.057950010000,0.169300000000,0.616200000000
490,0.032010000000,0.208020000000,0.465180000000
495,0.014700000000,0.258600000000,0.353300000000
500,0.004900000000,0.323000000000,0.272000000000
505,0.002400000000,0.407300000000,0.212300000000
510,0.009300000000,0.503000000000,0.158200000000
515,0.029100000000,0.608200000000,0.111700000000
520,0.063270000000,0.710000000000,0.078249990000
525,0.109600000000,0.793200000000,0.057250010000
530,0.165500000000,0.862000000000,0.042160000000
535,0.225749900000,0.914850100000,0.029840000000
540,0.290400000000,0.954000000000,0.020300000000
545,0.359700000000,0.980300000000,0.013400000000
550,0.433449900000,0.994950100000,0.008749999000
555,0.512050100000,1.000000000000,0.005749999000
560,0.594500000000,0.995000000000,0.003900000000
565,0.678400000000,0.978600000000,0.002749999000
570,0.762100000000,0.952000000000,0.002100000000
575,0.842500000000,0.915400000000,0.001800000000
580,0.916300000000,0.870000000000,0.001650001000
585,0.978600000000,0.816300000000,0.001400000000
590,1.026300000000,0.757000000000,0.001100000000
595,1.056700000000,0.694900000000,0.001000000000
600,1.062200000000,0.631000000000,0.000800000000
605,1.045600000000,0.566800000000,0.000600000000
610,1.002600000000,0.503000000000,0.000340000000
615,0.938400000000,0.441200000000,0.000240000000
620,0.854449900000,0.381000000000,0.000190000000
625,0.751400000000,0.321000000000,0.000100000000
630,0.642400000000,0.265000000000,0.000049999990
635,0.541900000000,0.217000000000,0.000030000000
640,0.447900000000,0.175000000000,0.000020000000
645,0.360800000000,0.138200000000,0.000010000000
650,0.283500000000,0.107000000000,0.000000000000
655,0.218700000000,0.081600000000,0.000000000000
660,0.164900000000,0.061000000000,0.000000000000
665,0.121200000000,0.044580000000,0.000000000000
670,0.087400000000,0.032000000000,0.000000000000
675,0.063600000000,0.023200000000,0.000000000000
680,0.046770000000,0.017000000000,0.000000000000
685,0.032900000000,0.011920000000,0.000000000000
690,0.022700000000,0.008210000000,0.000000000000
695,0.015840000000,0.005723000000,0.000000000000
700,0.011359160000,0.004102000000,0.000000000000
705,0.008110916000,0.002929000000,0.000000000000
710,0.005790346000,0.002091000000,0.000000000000
715,0.004109457000,0.001484000000,0.000000000000
720,0.002899327000,0.001047000000,0.000000000000
725,0.002049190000,0.000740000000,0.000000000000
730,0.001439971000,0.000520000000,0.000000000000
735,0.000999949300,0.000361100000,0.000000000000
740,0.000690078600,0.000249200000,0.000000000000
745,0.000476021300,0.000171900000,0.000000000000
750,0.000332301100,0.000120000000,0.000000000000
755,0.000234826100,0.000084800000,0.000000000000
760,0.000166150500,0.000060000000,0.000000000000
765,0.000117413000,0.000042400000,0.000000000000
770,0.000083075270,0.000030000000,0.000000000000
775,0.000058706520,0.000021200000,0.000000000000
780,0.000041509940,0.000014990000,0.000000000000
785,0.000029353260,0.000010600000,0.000000000000
790,0.000020673830,0.000007465700,0.000000000000
795,0.000014559770,0.000005257800,0.000000000000
800,0.000010253980,0.000003702900,0.000000000000
805,0.000007221456,0.000002607800,0.000000000000
810,0.000005085868,0.000001836600,0.000000000000
815,0.000003581652,0.000001293400,0.000000000000
820,0.000002522525,0.000000910930,0.000000000000
825,0.000001776509,0.000000641530,0.000000000000
830,0.000001251141,0.000000451810,0.000000000000
1e9 0 0 0];
else
ciedat = [
0 0 0 0
360.000000000000,0.000000122200,0.000000013398,0.000000535027
365.000000000000,0.000000919270,0.000000100650,0.000004028300
370.000000000000,0.000005958600,0.000000651100,0.000026143700
375.000000000000,0.000033266000,0.000003625000,0.000146220000
380.000000000000,0.000159952000,0.000017364000,0.000704776000
385.000000000000,0.000662440000,0.000071560000,0.002927800000
390.000000000000,0.002361600000,0.000253400000,0.010482200000
395.000000000000,0.007242300000,0.000768500000,0.032344000000
400.000000000000,0.019109700000,0.002004400000,0.086010900000
405.000000000000,0.043400000000,0.004509000000,0.197120000000
410.000000000000,0.084736000000,0.008756000000,0.389366000000
415.000000000000,0.140638000000,0.014456000000,0.656760000000
420.000000000000,0.204492000000,0.021391000000,0.972542000000
425.000000000000,0.264737000000,0.029497000000,1.282500000000
430.000000000000,0.314679000000,0.038676000000,1.553480000000
435.000000000000,0.357719000000,0.049602000000,1.798500000000
440.000000000000,0.383734000000,0.062077000000,1.967280000000
445.000000000000,0.386726000000,0.074704000000,2.027300000000
450.000000000000,0.370702000000,0.089456000000,1.994800000000
455.000000000000,0.342957000000,0.106256000000,1.900700000000
460.000000000000,0.302273000000,0.128201000000,1.745370000000
465.000000000000,0.254085000000,0.152761000000,1.554900000000
470.000000000000,0.195618000000,0.185190000000,1.317560000000
475.000000000000,0.132349000000,0.219940000000,1.030200000000
480.000000000000,0.080507000000,0.253589000000,0.772125000000
485.000000000000,0.041072000000,0.297665000000,0.570060000000
490.000000000000,0.016172000000,0.339133000000,0.415254000000
495.000000000000,0.005132000000,0.395379000000,0.302356000000
500.000000000000,0.003816000000,0.460777000000,0.218502000000
505.000000000000,0.015444000000,0.531360000000,0.159249000000
510.000000000000,0.037465000000,0.606741000000,0.112044000000
515.000000000000,0.071358000000,0.685660000000,0.082248000000
520.000000000000,0.117749000000,0.761757000000,0.060709000000
525.000000000000,0.172953000000,0.823330000000,0.043050000000
530.000000000000,0.236491000000,0.875211000000,0.030451000000
535.000000000000,0.304213000000,0.923810000000,0.020584000000
540.000000000000,0.376772000000,0.961988000000,0.013676000000
545.000000000000,0.451584000000,0.982200000000,0.007918000000
550.000000000000,0.529826000000,0.991761000000,0.003988000000
555.000000000000,0.616053000000,0.999110000000,0.001091000000
560.000000000000,0.705224000000,0.997340000000,0.000000000000
565.000000000000,0.793832000000,0.982380000000,0.000000000000
570.000000000000,0.878655000000,0.955552000000,0.000000000000
575.000000000000,0.951162000000,0.915175000000,0.000000000000
580.000000000000,1.014160000000,0.868934000000,0.000000000000
585.000000000000,1.074300000000,0.825623000000,0.000000000000
590.000000000000,1.118520000000,0.777405000000,0.000000000000
595.000000000000,1.134300000000,0.720353000000,0.000000000000
600.000000000000,1.123990000000,0.658341000000,0.000000000000
605.000000000000,1.089100000000,0.593878000000,0.000000000000
610.000000000000,1.030480000000,0.527963000000,0.000000000000
615.000000000000,0.950740000000,0.461834000000,0.000000000000
620.000000000000,0.856297000000,0.398057000000,0.000000000000
625.000000000000,0.754930000000,0.339554000000,0.000000000000
630.000000000000,0.647467000000,0.283493000000,0.000000000000
635.000000000000,0.535110000000,0.228254000000,0.000000000000
640.000000000000,0.431567000000,0.179828000000,0.000000000000
645.000000000000,0.343690000000,0.140211000000,0.000000000000
650.000000000000,0.268329000000,0.107633000000,0.000000000000
655.000000000000,0.204300000000,0.081187000000,0.000000000000
660.000000000000,0.152568000000,0.060281000000,0.000000000000
665.000000000000,0.112210000000,0.044096000000,0.000000000000
670.000000000000,0.081260600000,0.031800400000,0.000000000000
675.000000000000,0.057930000000,0.022601700000,0.000000000000
680.000000000000,0.040850800000,0.015905100000,0.000000000000
685.000000000000,0.028623000000,0.011130300000,0.000000000000
690.000000000000,0.019941300000,0.007748800000,0.000000000000
695.000000000000,0.013842000000,0.005375100000,0.000000000000
700.000000000000,0.009576880000,0.003717740000,0.000000000000
705.000000000000,0.006605200000,0.002564560000,0.000000000000
710.000000000000,0.004552630000,0.001768470000,0.000000000000
715.000000000000,0.003144700000,0.001222390000,0.000000000000
720.000000000000,0.002174960000,0.000846190000,0.000000000000
725.000000000000,0.001505700000,0.000586440000,0.000000000000
730.000000000000,0.001044760000,0.000407410000,0.000000000000
735.000000000000,0.000727450000,0.000284041000,0.000000000000
740.000000000000,0.000508258000,0.000198730000,0.000000000000
745.000000000000,0.000356380000,0.000139550000,0.000000000000
750.000000000000,0.000250969000,0.000098428000,0.000000000000
755.000000000000,0.000177730000,0.000069819000,0.000000000000
760.000000000000,0.000126390000,0.000049737000,0.000000000000
765.000000000000,0.000090151000,0.000035540500,0.000000000000
770.000000000000,0.000064525800,0.000025486000,0.000000000000
775.000000000000,0.000046339000,0.000018338400,0.000000000000
780.000000000000,0.000033411700,0.000013249000,0.000000000000
785.000000000000,0.000024209000,0.000009619600,0.000000000000
790.000000000000,0.000017611500,0.000007012800,0.000000000000
795.000000000000,0.000012855000,0.000005129800,0.000000000000
800.000000000000,0.000009413630,0.000003764730,0.000000000000
805.000000000000,0.000006913000,0.000002770810,0.000000000000
810.000000000000,0.000005093470,0.000002046130,0.000000000000
815.000000000000,0.000003767100,0.000001516770,0.000000000000
820.000000000000,0.000002795310,0.000001128090,0.000000000000
825.000000000000,0.000002082000,0.000000842160,0.000000000000
830.000000000000,0.000001553140,0.000000629700,0.000000000000
1e9 0 0 0];
end
XYZ = interp1(ciedat(:,1)*1e-9, ciedat(:,2:4), lambda, 'pchip', 0);
if nargin == 2
% approximate rectangular integration
dlambda = lambda(2) - lambda(1);
XYZ = spect(:)' * XYZ * dlambda;
end