[vslist] Results of dominant wavelength/excitation purity
help request
Andrew Watson
andrew.b.watson@nasa.gov
Tue Nov 16 12:36:01 2004
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The following is a Mathematica routine I wrote some years ago. The
code is no doubt incomprehensible, but the idea is simple. First,
from a table of the spectrum locus defined by {x,y} chromaticity
coordinates vs wavelength, create an interpolating function that
returns {x,y} for an arbitrary wavelength. Then find the angle of the
line between the white point and the point in question. Then, find
the point along the spectrum locus for which the line from the white
point has (nearly) the same angle.
The bit at the end generates a plot of the situation. I attach an
example below.
The code for Excitation purity follows in a straightforward way.
DominantWavelength[xy_, xyw_:{0.33, 0.33},
chromaticity_:CIE1931Chromaticity, plot_:False] :=
Module[{sign = 1, LambdaToxy, x, angle, AngleFromWhite,
PositiveAngle, dw, xyl},
LambdaToxy[lambda_] := (#[lambda] &) /@
(WaveTableInterpolation[chromaticity][[{1, 2}]]);
AngleFromWhite[xy0_] := ArcTan @@ (xy0 - xyw);
PositiveAngle[xy1_] :=
If[# < 0, # + 2 \[Pi], #, #] &[AngleFromWhite[xy1] -
AngleFromWhite[LambdaToxy[700]]];
angle = PositiveAngle[xy];
If[angle > PositiveAngle[LambdaToxy[400]], (angle = angle - Pi;
sign = -1)];
dw = (FindRoot[angle - PositiveAngle[LambdaToxy[lambda]] == 0,
{lambda, 500, 400,700}][[1, 2]]) ;
If[plot, xyl = LambdaToxy[dw];
ChromaticityDiagram[NMLabels -> {400, 500, 560, 700}
, Epilog -> {RGBColor @@ NearestRGB[dw, xyw],
Line[{xy, xyw}], Line[{xyl, xyw}], PointSize[.04],
GrayLevel[.6],
Point[xyw], Point[xyl], GrayLevel[0], Point[xy]}]];
dw sign ]
ExcitationPurity[xy_, xyw_:{.33,.33}, chromaticity_:CIE1931Chromaticity] :=
If[xy == xyw, 0, Divide @@ ((First /@
{xy, WaveTableValue[chromaticity,
DominantWavelength[xy,xyw,chromaticity]]}) - xyw[[1]])]
Here we evaluate an example, with plot.
DominantWavelength[{.3, .5},{.33,.33}, CIE1931Chromaticity,True]
--
Andrew B. Watson
MS 262-2
NASA Ames Research Center
Moffett Field, CA 94035-1000
(650) 604-5419 (650) 604-0255 fax
andrew.b.watson@nasa.gov http://vision.arc.nasa.gov/
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<html><head><style type="text/css"><!--
blockquote, dl, ul, ol, li { padding-top: 0 ; padding-bottom: 0 }
--></style><title>Re: [vslist] Results of dominant
wavelength/excitation pur</title></head><body>
<div>The following is a Mathematica routine I wrote some years ago.
The code is no doubt incomprehensible, but the idea is simple. First,
from a table of the spectrum locus defined by {x,y} chromaticity
coordinates vs wavelength, create an interpolating function that
returns {x,y} for an arbitrary wavelength. Then find the angle of the
line between the white point and the point in question. Then, find the
point along the spectrum locus for which the line from the white point
has (nearly) the same angle.</div>
<div><br></div>
<div>The bit at the end generates a plot of the situation. I attach an
example below.</div>
<div><br></div>
<div>The code for Excitation purity follows in a straightforward
way.</div>
<div><br></div>
<div>DominantWavelength[xy_, xyw_:{0.33, 0.33},
chromaticity_:CIE1931Chromaticity, plot_:False] :=</div>
<div> Module[{sign = 1, LambdaToxy, x, angle,
AngleFromWhite, PositiveAngle, dw, xyl},</div>
<div> LambdaToxy[lambda_] := (#[lambda] &) /@
(WaveTableInterpolation[chromaticity][[{1, 2}]]);</div>
<div> AngleFromWhite[xy0_] := ArcTan @@ (xy0 -
xyw);</div>
<div> PositiveAngle[xy1_] :=</div>
<div> If[# < 0, # + 2 \[Pi], #, #]
&[AngleFromWhite[xy1] - AngleFromWhite[LambdaToxy[700]]];</div>
<div> angle = PositiveAngle[xy];</div>
<div> If[angle > PositiveAngle[LambdaToxy[400]],
(angle = angle - Pi; sign = -1)];</div>
<div> dw = (FindRoot[angle -
PositiveAngle[LambdaToxy[lambda]] == 0, {lambda, 500, 400,700}][[1,
2]]) ;</div>
<div> If[plot, xyl =
LambdaToxy[dw];</div>
<div> <x-tab>
</x-tab>ChromaticityDiagram[NMLabels -> {400, 500, 560, 700}</div>
<div> <x-tab> </x-tab>,
Epilog -> {RGBColor @@ NearestRGB[dw, xyw],</div>
<div> <x-tab
> </x-tab>Line[{xy, xyw}], Line[{xyl,
xyw}], PointSize[.04], GrayLevel[.6],</div>
<div> <x-tab
> </x-tab>Point[xyw], Point[xyl],
GrayLevel[0], Point[xy]}]];</div>
<div> dw sign ]</div>
<div><br></div>
<div>ExcitationPurity[xy_, xyw_:{.33,.33},
chromaticity_:CIE1931Chromaticity] :=</div>
<div> If[xy == xyw, 0, Divide @@ ((First /@</div>
<div> {xy, WaveTableValue[chromaticity,</div>
<div> DominantWavelength[xy,xyw,chromaticity]]}) -
xyw[[1]])]</div>
<div><br></div>
<div><br></div>
<div>Here we evaluate an example, with plot.</div>
<div><br></div>
<div><font face="MC" color="#000000"><b>DominantWavelength[{.3,
.5},{.33,.33}, CIE1931Chromaticity,True]</b></font></div>
<div><br></div>
<div><img src="cid:p06200704bdc0054a902d@[143.232.72.120].1.0"></div>
<x-sigsep><pre>--
</pre></x-sigsep>
<div><br>
Andrew B. Watson<br>
MS 262-2<br>
NASA Ames Research Center<br>
Moffett Field, CA 94035-1000<br>
(650) 604-5419<x-tab> </x-tab>(650) 604-0255
fax<br>
andrew.b.watson@nasa.gov<x-tab>
</x-tab>http://vision.arc.nasa.gov/</div>
</body>
</html>
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