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From: Mike Horvath
Subject: Re: L*C*h(uv) functions
Date: 21 Nov 2016 18:50:38
Message: <5833884e$1@news.povray.org>
On 11/21/2016 4:33 PM, Mike Horvath wrote:
> On 11/21/2016 4:23 PM, clipka wrote:
>>
>> So if I understand you correctly, the shape you want is exactly the
>> volume for which R, G and B are all within the range from 0 to 1.
>>
>
> Yes, exactly!
>
>
>> That sounds like a job for an isosurface to me.
>>
>> Variant A: Create six isosurfaces, each representing one of the
>> boundaries (R<0, G<0, B<0, R>1, G>1, B>1), and intersect them.
>>
>> Variant B: Refactor the functions from variant A, so that they have the
>> same threshold, combine them using max() or min() to achieve the
>> intersection effect, and turn that into a single isosurface.
>>
>
> I don't know how to do either variant. :(
>
> Mike

Forgot to add that I want to use polar coordinates (if that makes a 
difference).

Mike


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From: Mike Horvath
Subject: Re: L*C*h(uv) functions
Date: 21 Nov 2016 19:46:28
Message: <58339564$1@news.povray.org>
On 11/21/2016 4:23 PM, clipka wrote:
> Am 21.11.2016 um 21:56 schrieb Mike Horvath:
>
>>>> Actually, I can create a pigment already. But I don't know how to use
>>>> the functions in a isosurface or a parametric to make the 3D object the
>>>> pigment gets applied to, if possible.
>>>>
>>>> Mike
>>>
>>> Oops! You'll need to know these as well.
>>>
>>> #declare correctRGB1 = function(R,G,B) {min(max(R,0),1)}
>>> #declare correctRGB2 = function(R,G,B) {min(max(G,0),1)}
>>> #declare correctRGB3 = function(R,G,B) {min(max(B,0),1)}
>>>
>>>
>>
>> That is wrong. The RGB values should *not* be corrected. In fact, if any
>> of R, G or B are outside the range of 0 to 1, then the coordinate/color
>> should be discarded. Sorry!
>
> So if I understand you correctly, the shape you want is exactly the
> volume for which R, G and B are all within the range from 0 to 1.
>
> That sounds like a job for an isosurface to me.
>
> Variant A: Create six isosurfaces, each representing one of the
> boundaries (R<0, G<0, B<0, R>1, G>1, B>1), and intersect them.
>
> Variant B: Refactor the functions from variant A, so that they have the
> same threshold, combine them using max() or min() to achieve the
> intersection effect, and turn that into a single isosurface.
>

I am trying random things now.

isosurface
{
	function {max(convertLCH2RGB_R(x,y,z), 1)}
	contained_by
	{
		box {-2,+2}
	}
//	threshold FLOAT_VALUE
	accuracy	0.01
	max_gradient	5
//	[evaluate P0, P1, P2]
//	open
//	[max_trace INTEGER] | [all_intersections]
	pigment {rgb 1}
}

This takes a long time to render, but there's nothing visible happening.

Mike


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From: Mike Horvath
Subject: Re: L*C*h(uv) functions
Date: 21 Nov 2016 23:22:15
Message: <5833c7f7$1@news.povray.org>
I tried this as well.

parametric
{
	function { convertLCH2RGB_R(u,100,v) }
	function { convertLCH2RGB_G(u,100,v) }
	function { convertLCH2RGB_B(u,100,v) }
	<0,0>, <100,360>
	contained_by
	{
		box {-2,+2}
	}
	max_gradient	5
	accuracy	0.01
	precompute	10 x,y,z
	pigment {rgb 1}
}

The render is too slow. The pps is below 100 and still dropping.

Mike


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From: clipka
Subject: Re: L*C*h(uv) functions
Date: 22 Nov 2016 02:30:45
Message: <5833f425$1@news.povray.org>
Am 22.11.2016 um 01:46 schrieb Mike Horvath:

> I am trying random things now.
> 
> isosurface
> {
>     function {max(convertLCH2RGB_R(x,y,z), 1)}

throw away the max() function, and take care of the polar-ish coordinate
system by replacing:

    convertLCH2RGB_R(x,y,z)

with:

    convertLCH2RGB_R(y*200-100,sqrt(x*x+z*z)*100,atan2(x/z)*pi/180)

(presuming you want L up and I got the math right)

>     contained_by
>     {
>         box {-2,+2}
>     }
> //    threshold FLOAT_VALUE

... and use threshold 1. That should give you something visible.

>     accuracy    0.01
>     max_gradient    5
> //    [evaluate P0, P1, P2]
> //    open
> //    [max_trace INTEGER] | [all_intersections]
>     pigment {rgb 1}
> }
> 
> This takes a long time to render, but there's nothing visible happening.
> 
> Mike


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From: Mike Horvath
Subject: Re: L*C*h(uv) functions
Date: 22 Nov 2016 02:33:02
Message: <5833f4ae$1@news.povray.org>
On 11/22/2016 2:30 AM, clipka wrote:
> Am 22.11.2016 um 01:46 schrieb Mike Horvath:
>
>> I am trying random things now.
>>
>> isosurface
>> {
>>     function {max(convertLCH2RGB_R(x,y,z), 1)}
>
> throw away the max() function, and take care of the polar-ish coordinate
> system by replacing:
>
>     convertLCH2RGB_R(x,y,z)
>
> with:
>
>     convertLCH2RGB_R(y*200-100,sqrt(x*x+z*z)*100,atan2(x/z)*pi/180)
>
> (presuming you want L up and I got the math right)
>
>>     contained_by
>>     {
>>         box {-2,+2}
>>     }
>> //    threshold FLOAT_VALUE
>
> ... and use threshold 1. That should give you something visible.
>
>>     accuracy    0.01
>>     max_gradient    5
>> //    [evaluate P0, P1, P2]
>> //    open
>> //    [max_trace INTEGER] | [all_intersections]
>>     pigment {rgb 1}
>> }
>>
>> This takes a long time to render, but there's nothing visible happening.
>>
>> Mike
>

THANK YOU!!

However atan2 requires two parameters and your math only has one.

Mike


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From: clipka
Subject: Re: L*C*h(uv) functions
Date: 22 Nov 2016 02:44:13
Message: <5833f74d@news.povray.org>
Am 22.11.2016 um 08:33 schrieb Mike Horvath:

>>     convertLCH2RGB_R(y*200-100,sqrt(x*x+z*z)*100,atan2(x/z)*pi/180)

> THANK YOU!!
> 
> However atan2 requires two parameters and your math only has one.

Sorry, try atan2(x,z).


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From: Mike Horvath
Subject: Re: L*C*h(uv) functions
Date: 22 Nov 2016 02:45:52
Message: <5833f7b0$1@news.povray.org>
On 11/22/2016 2:44 AM, clipka wrote:
> Am 22.11.2016 um 08:33 schrieb Mike Horvath:
>
>>>     convertLCH2RGB_R(y*200-100,sqrt(x*x+z*z)*100,atan2(x/z)*pi/180)
>
>> THANK YOU!!
>>
>> However atan2 requires two parameters and your math only has one.
>
> Sorry, try atan2(x,z).
>

Here is the whole file again with your changes. The shape I get when I 
render is that of a pointy cap. I don't know if that's correct or not.


Mike


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From: clipka
Subject: Re: L*C*h(uv) functions
Date: 22 Nov 2016 03:31:26
Message: <5834025e$1@news.povray.org>
Am 22.11.2016 um 08:45 schrieb Mike Horvath:
> On 11/22/2016 2:44 AM, clipka wrote:
>> Am 22.11.2016 um 08:33 schrieb Mike Horvath:
>>
>>>>     convertLCH2RGB_R(y*200-100,sqrt(x*x+z*z)*100,atan2(x/z)*pi/180)
>>
>>> THANK YOU!!
>>>
>>> However atan2 requires two parameters and your math only has one.
>>
>> Sorry, try atan2(x,z).
>>
> 
> Here is the whole file again with your changes. The shape I get when I
> render is that of a pointy cap. I don't know if that's correct or not.

How would I know -- I'm not familiar with that colour model.

Now you need to intersect that shape with the five others -- or use the
combined function:

    min(
      convertLCH2RGB_R(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
      convertLCH2RGB_G(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
      convertLCH2RGB_B(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
      1-convertLCH2RGB_R(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
      1-convertLCH2RGB_G(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
      1-convertLCH2RGB_B(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180)
    )

should do the job, I think.


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From: Mike Horvath
Subject: Re: L*C*h(uv) functions
Date: 22 Nov 2016 03:43:51
Message: <58340547$1@news.povray.org>
On 11/22/2016 3:31 AM, clipka wrote:
>     min(
>       convertLCH2RGB_R(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
>       convertLCH2RGB_G(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
>       convertLCH2RGB_B(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
>       1-convertLCH2RGB_R(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
>       1-convertLCH2RGB_G(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
>       1-convertLCH2RGB_B(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180)
>     )

I think the last parameter should be atan2(x,z)*180/pi because atan2 
returns radians and convertLCH2RGB_R expects degrees.

Also, here's a rough approximation of what the surface should look like.

https://commons.wikimedia.org/wiki/File:Cielch_color_solid_cylinder.png

But with smooth curves instead of blocky sections.

Mike


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From: Mike Horvath
Subject: Re: L*C*h(uv) functions
Date: 22 Nov 2016 03:44:21
Message: <58340565$1@news.povray.org>
On 11/22/2016 3:31 AM, clipka wrote:
>     min(
>       convertLCH2RGB_R(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
>       convertLCH2RGB_G(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
>       convertLCH2RGB_B(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
>       1-convertLCH2RGB_R(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
>       1-convertLCH2RGB_G(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180),
>       1-convertLCH2RGB_B(y*200-100,sqrt(x*x+z*z)*100,atan2(x,z)*pi/180)
>     )


Forgot to say that the above just results in a cube.

Mike


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