On 11/29/2016 10:56 PM, clipka wrote:
> Gamut of all theoretically possible surface colours, under D65 (noon
> daylight) illumination, in CIE 1931 xyY space.
>

Is it possible to model the intersection between sRGB, Lab and xyY at 
the same time? I know sRGB is fully contained within the xyY 
chromaticity diagram. But want to know if it is fully contained within 
Lab, and think that visualizing them in this way might be helpful.

Mike

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On 11/29/2016 10:56 PM, clipka wrote:
> Gamut of all theoretically possible surface colours, under D65 (noon
> daylight) illumination, in CIE 1931 xyY space.
>

How did you generate the meshes?

Mike

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Am 11.12.2016 um 00:09 schrieb Mike Horvath:
> On 11/29/2016 10:56 PM, clipka wrote:
>> Gamut of all theoretically possible surface colours, under D65 (noon
>> daylight) illumination, in CIE 1931 xyY space.
>>
> 
> How did you generate the meshes?

"It's complicated."

I struggled quite a while to come up with a reasonably elegant solution,
until at some point I realized that all maximally saturated colours for
any given brightness fall into one of the following two categories:

(A) pigments that exhibit 100% reflectivity across a single (possibly
broad) spectral band, and 0% reflectivity outside that band
(blue-green-yellow-red side of the gamut)

(B) pigments that exhibit 0% reflectivity across a single (possibly
broad) spectral band, and 100% reflectivity outside that band (purple
side of the gamut)

Additionally, it can be noted that by pretending that the range of
visible wavelengths wraps around at the red and blue ends of the
spectrum you can map category (B) to category (A), since the former can
then be interpreted as exhibiting 100% reflectivity across a single
spectral band that straddles the wraparound point.

From these principles a mesh can be computed comparatively easy by
iterating over the "position" of the corresponding spectral band in one
direction (I chose the lower-bound wavelength, but you could just as
well choose the upper-bound wavelength or the center wavelength),
somewhat corresponding to hue, and the width of the band in the other
direction, somewhat corresponding to brightness. The maximum possible
saturation will be a function of the two.

For each mesh vertex you of course still have to compute the XYZ
coordinates of the corresponding spectrum. For this you will need to
perform numerical integration of the CIE Standard Observer table data
over the corresponding range of wavelengths. (Note that this will give
you the equal-energy gamut. For a different illuminant, you need to
multiply each table entry by the illuminant's intensity at the given
wavelength.)

The mesh can be optimized by iterating over the wavelengths in
non-uniform steps, but that seems to be an art of its own, which I
didn't master to the degree I would have liked to.

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Am 11.12.2016 um 01:12 schrieb clipka:
> Am 11.12.2016 um 00:09 schrieb Mike Horvath:
>> On 11/29/2016 10:56 PM, clipka wrote:
>>> Gamut of all theoretically possible surface colours, under D65 (noon
>>> daylight) illumination, in CIE 1931 xyY space.
>>>
>>
>> How did you generate the meshes?
> 
> "It's complicated."

Oh, and of course for the sake of parsing performance I used `#write` to
generate the mesh as a POV-Ray include file, safeguarding the code using
`#if (file_exists(...))`, and then used `#include` to load it.

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On 11/29/2016 10:56 PM, clipka wrote:
> Gamut of all theoretically possible surface colours, under D65 (noon
> daylight) illumination, in CIE 1931 xyY space.
>

Did you use radiosity or emission? I am trying to render the same shape 
but in my scene the shadows are not well defined.


Mike

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Am 19.03.2017 um 03:11 schrieb Mike Horvath:
> On 11/29/2016 10:56 PM, clipka wrote:
>> Gamut of all theoretically possible surface colours, under D65 (noon
>> daylight) illumination, in CIE 1931 xyY space.
>>
> 
> Did you use radiosity or emission? I am trying to render the same shape
> but in my scene the shadows are not well defined.

Radiosity, most surely. I can't stand the look of scenes that don't use it.

I did need some twiddling of the radiosity settings to make it look good
though. I guess I did specify a rather low "maximum_reuse" setting.

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Am 20.03.2017 um 02:21 schrieb Mike Horvath:
> On 11/29/2016 10:56 PM, clipka wrote:
>> Gamut of all theoretically possible surface colours, under D65 (noon
>> daylight) illumination, in CIE 1931 xyY space.
>>
> 
> Here's my version, thanks to clipka and Bruce Lindbloom.

That looks about right now.

You seem to have a gap between the shape and the "black pane" though,
which is particularly noticeable in the yellow and green regions.

I'd therefore recommend investing a bit of extra work to make the shape
extend to the black point -- or, more precisely, the locus of
infinitesimally dark spectral colours.

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On 3/20/2017 8:21 AM, clipka wrote:
> Am 20.03.2017 um 02:21 schrieb Mike Horvath:
>> On 11/29/2016 10:56 PM, clipka wrote:
>>> Gamut of all theoretically possible surface colours, under D65 (noon
>>> daylight) illumination, in CIE 1931 xyY space.
>>>
>>
>> Here's my version, thanks to clipka and Bruce Lindbloom.
>
> That looks about right now.
>
> You seem to have a gap between the shape and the "black pane" though,
> which is particularly noticeable in the yellow and green regions.
>
> I'd therefore recommend investing a bit of extra work to make the shape
> extend to the black point -- or, more precisely, the locus of
> infinitesimally dark spectral colours.
>

I'm not sure what to do with black. It's degenerate in xyY space, isn't 
it? I get divide-by-zero errors when converting from XYZ.


Mike

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Am 20.03.2017 um 14:52 schrieb Mike Horvath:
> On 3/20/2017 8:21 AM, clipka wrote:
>> Am 20.03.2017 um 02:21 schrieb Mike Horvath:
>>> On 11/29/2016 10:56 PM, clipka wrote:
>>>> Gamut of all theoretically possible surface colours, under D65 (noon
>>>> daylight) illumination, in CIE 1931 xyY space.
>>>>
>>>
>>> Here's my version, thanks to clipka and Bruce Lindbloom.
>>
>> That looks about right now.
>>
>> You seem to have a gap between the shape and the "black pane" though,
>> which is particularly noticeable in the yellow and green regions.
>>
>> I'd therefore recommend investing a bit of extra work to make the shape
>> extend to the black point -- or, more precisely, the locus of
>> infinitesimally dark spectral colours.
>>
> 
> I'm not sure what to do with black. It's degenerate in xyY space, isn't
> it? I get divide-by-zero errors when converting from XYZ.

That's why you need to go for infinitesimally dark colours instead: Set
all wavelengths to zero, except for a single wavelength which you set to
a darn small power like, say, 1e-3.

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On 3/20/2017 11:48 AM, clipka wrote:
> Am 20.03.2017 um 14:52 schrieb Mike Horvath:
>> On 3/20/2017 8:21 AM, clipka wrote:
>>> Am 20.03.2017 um 02:21 schrieb Mike Horvath:
>>>> On 11/29/2016 10:56 PM, clipka wrote:
>>>>> Gamut of all theoretically possible surface colours, under D65 (noon
>>>>> daylight) illumination, in CIE 1931 xyY space.
>>>>>
>>>>
>>>> Here's my version, thanks to clipka and Bruce Lindbloom.
>>>
>>> That looks about right now.
>>>
>>> You seem to have a gap between the shape and the "black pane" though,
>>> which is particularly noticeable in the yellow and green regions.
>>>
>>> I'd therefore recommend investing a bit of extra work to make the shape
>>> extend to the black point -- or, more precisely, the locus of
>>> infinitesimally dark spectral colours.
>>>
>>
>> I'm not sure what to do with black. It's degenerate in xyY space, isn't
>> it? I get divide-by-zero errors when converting from XYZ.
>
> That's why you need to go for infinitesimally dark colours instead: Set
> all wavelengths to zero, except for a single wavelength which you set to
> a darn small power like, say, 1e-3.
>

I ended up just replacing that bottom row with the standard 2D xy 
chromaticity diagram, but colored black.

Thanks for catching the issue! I would not have noticed it myself.


Mike

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