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From: Mike Horvath
Subject: Spherical isosurface
Date: 28 Nov 2016 23:42:34
Message: <583cc0ea$1@news.povray.org>
Clipka gave me these formulas to generate a cylindrical isosurface.

#declare fL = function(x,y,z) {y*100}
#declare fC = function(x,y,z) {sqrt(x*x+z*z)*128}
#declare fH = function(x,y,z) {atan2d(x,z)}

What would be a formula for a sphere? L should be latitude, H longitude, 
and C radius.

Thanks.


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From: Mike Horvath
Subject: Re: Spherical isosurface
Date: 29 Nov 2016 06:19:51
Message: <583d1e07$1@news.povray.org>
On 11/28/2016 6:42 PM, Mike Horvath wrote:
> Clipka gave me these formulas to generate a cylindrical isosurface.
>
> #declare fL = function(x,y,z) {y*100}
> #declare fC = function(x,y,z) {sqrt(x*x+z*z)*128}
> #declare fH = function(x,y,z) {atan2d(x,z)}
>
> What would be a formula for a sphere? L should be latitude, H longitude,
> and C radius.
>
> Thanks.

Would I use atan(x,y) for L? This produces values between -90..90 
degrees, correct? Or should it be atan(z,y)?

Thanks.

Mike


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From: omniverse
Subject: Re: Spherical isosurface
Date: 29 Nov 2016 11:10:00
Message: <web.583d615dc3db15af9c5d6c810@news.povray.org>
Mike Horvath <mik### [at] gmailcom> wrote:
> On 11/28/2016 6:42 PM, Mike Horvath wrote:
> > Clipka gave me these formulas to generate a cylindrical isosurface.
> >
> > #declare fL = function(x,y,z) {y*100}
> > #declare fC = function(x,y,z) {sqrt(x*x+z*z)*128}
> > #declare fH = function(x,y,z) {atan2d(x,z)}
> >
> > What would be a formula for a sphere? L should be latitude, H longitude,
> > and C radius.
> >
> > Thanks.
>
> Would I use atan(x,y) for L? This produces values between -90..90
> degrees, correct? Or should it be atan(z,y)?

I sure don't know enough to tell you much of anything, the sphere equation is
something like:

function(x,y,z,r) {(pow(x,2)+pow(y,2)+pow(z,2))-pow(r,2)}

There's also the inbuilt function called internal (61) used by functions.inc for
its f_sphere(x,y,z,r) where r is radius. Hopefully I got this right, please
don't count on it!

Bob

P.S. I was trying, rather clumsily, to get the idea of what you might have been
trying to make and only succeeded in creating strange isosurface shapes. Some
were a partial sphere with both a vertical and horizontal cut across it,
thinking I changed to atan(y) and atan2(x,z) but I got lost in the fascination
of new shapes.


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From: Bald Eagle
Subject: Re: Spherical isosurface
Date: 29 Nov 2016 12:55:00
Message: <web.583d7a91c3db15afc437ac910@news.povray.org>
Mike Horvath <mik### [at] gmailcom> wrote:

> What would be a formula for a sphere?

I always start here:

http://www.econym.demon.co.uk/isotut/

whenever I have any questions about isosurfaces.

Like Christoph said, it takes a certain "way" of thinking to successfully play
with isosurfaces.

I'd also be aware that you may use code and equations that successfully yield a
visible isosurface in a render.  That surface may or may not be correct - so I'd
also be thinking about placing visible markers, sending numeric results to the
debug stream, overlaying the isosurface onto your stacked-block model, or some
other way of performing sanity and accuracy checks.

Aside from that, as Christoph said, "don't listen to that man"
I use this
https://www.maxiaids.com/Media/Thumbs/0008/0008988-big-keys-lx-color-abc-300.jpg
to write my SDL code, and when I'm down in the basement POVving, my mom makes me
wear a special helmet so I don't injure myself when trying to visualize 3D
vectors or do Big Boy math.  ;)

:D


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From: Mike Horvath
Subject: Re: Spherical isosurface
Date: 29 Nov 2016 16:58:01
Message: <583db399$1@news.povray.org>
On 11/29/2016 6:07 AM, omniverse wrote:
> Mike Horvath <mik### [at] gmailcom> wrote:
>> On 11/28/2016 6:42 PM, Mike Horvath wrote:
>>> Clipka gave me these formulas to generate a cylindrical isosurface.
>>>
>>> #declare fL = function(x,y,z) {y*100}
>>> #declare fC = function(x,y,z) {sqrt(x*x+z*z)*128}
>>> #declare fH = function(x,y,z) {atan2d(x,z)}
>>>
>>> What would be a formula for a sphere? L should be latitude, H longitude,
>>> and C radius.
>>>
>>> Thanks.
>>
>> Would I use atan(x,y) for L? This produces values between -90..90
>> degrees, correct? Or should it be atan(z,y)?
>
> I sure don't know enough to tell you much of anything, the sphere equation is
> something like:
>
> function(x,y,z,r) {(pow(x,2)+pow(y,2)+pow(z,2))-pow(r,2)}
>
> There's also the inbuilt function called internal (61) used by functions.inc for
> its f_sphere(x,y,z,r) where r is radius. Hopefully I got this right, please
> don't count on it!
>
> Bob
>
> P.S. I was trying, rather clumsily, to get the idea of what you might have been
> trying to make and only succeeded in creating strange isosurface shapes. Some
> were a partial sphere with both a vertical and horizontal cut across it,
> thinking I changed to atan(y) and atan2(x,z) but I got lost in the fascination
> of new shapes.
>
>

Thanks for trying, at least.

:)

Mike


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From: Mike Horvath
Subject: Re: Spherical isosurface
Date: 29 Nov 2016 17:03:27
Message: <583db4df$1@news.povray.org>
On 11/29/2016 7:54 AM, Bald Eagle wrote:
> Mike Horvath <mik### [at] gmailcom> wrote:
>
>> What would be a formula for a sphere?
>
> I always start here:
>
> http://www.econym.demon.co.uk/isotut/
>
> whenever I have any questions about isosurfaces.

That tutorial only gives a single function for a sphere. I need separate 
functions for latitude, longitude and radius, that get combined later 
using an additional function.

Like this:

#declare fD = function(C) {abs(C-0.5)-0.5}
#declare fDist = function(Dr,Dg,Db) {max(Dr,Dg,Db)}
#declare fR = function(L,C,H) {convertLCH2RGBa1(L,C,H)}
#declare fG = function(L,C,H) {convertLCH2RGBa2(L,C,H)}
#declare fB = function(L,C,H) {convertLCH2RGBa3(L,C,H)}
#declare fL = function(x,y,z) {90+atand(x/y)}			// wrong!
#declare fC = function(x,y,z) {sqrt(x*x+z*z)*128}
#declare fH = function(x,y,z) {atan2d(x,z)}

#declare fFinal = function(L,C,H)
{
	fDist
	(
		fD(fR(L,C,H)),
		fD(fG(L,C,H)),
		fD(fB(L,C,H))
	)
}

Mike


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From: Mike Horvath
Subject: Re: Spherical isosurface
Date: 29 Nov 2016 17:59:05
Message: <583dc1e9$1@news.povray.org>
On 11/28/2016 6:42 PM, Mike Horvath wrote:
> Clipka gave me these formulas to generate a cylindrical isosurface.
>
> #declare fL = function(x,y,z) {y*100}
> #declare fC = function(x,y,z) {sqrt(x*x+z*z)*128}
> #declare fH = function(x,y,z) {atan2d(x,z)}
>
> What would be a formula for a sphere? L should be latitude, H longitude,
> and C radius.
>
> Thanks.

Maybe this?

#declare fL = function(x,y,z) {90+atand(sqrt(x*x+z*z)*128/y*100)}

Problem: L ranges from 0..100, and C ranges from 0..128, and I want to 
avoid generating a flattened ellipsoid.

Mike


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From: Bald Eagle
Subject: Re: Spherical isosurface
Date: 29 Nov 2016 20:05:00
Message: <web.583ddf60c3db15afc437ac910@news.povray.org>
Mike Horvath <mik### [at] gmailcom> wrote:

> > What would be a formula for a sphere? L should be latitude, H longitude,
> > and C radius.

https://en.wikipedia.org/wiki/Spherical_coordinate_system
Conversely, the Cartesian coordinates may be retrieved from the spherical
coordinates
https://wikimedia.org/api/rest_v1/media/math/render/svg/d7bcd516d317c31ac48ed36e2ead9537a5f16e2e

> Problem: L ranges from 0..100, and C ranges from 0..128, and I want to
> avoid generating a flattened ellipsoid.
>
> Mike

#declare C = C*(100/128);


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From: clipka
Subject: Re: Spherical isosurface
Date: 29 Nov 2016 20:26:51
Message: <583de48b$1@news.povray.org>
Am 29.11.2016 um 00:42 schrieb Mike Horvath:
> Clipka gave me these formulas to generate a cylindrical isosurface.
> 
> #declare fL = function(x,y,z) {y*100}
> #declare fC = function(x,y,z) {sqrt(x*x+z*z)*128}
> #declare fH = function(x,y,z) {atan2d(x,z)}
> 
> What would be a formula for a sphere? L should be latitude, H longitude,
> and C radius.

What you need is _not_ "formulas to generate a [spherical] isosurface".

What you need is formulas to convert from a point in cartesian space to
a colour in the spherical (as oppsed to cylindrical) LCh model.

This is just a small building block in your isosurface function, and in
and of itself has no special relation to isosurfaces whatsoever. (You'll
need to use the same formula to eventually compute an RGB colour pigment.)


If Chroma (C) is to be (spherical) radius, that part is easy:

    #declare fC = function(x,y,z) { sqrt(x*x+y*y+z*z)*CONST }

Hue (H) should be unchanged:

    #declare fH = function(x,y,z) { atan2(x,z)*CONST }

Luminance gets a bit more complicated: You have to use an atan-based
formula to get an angle, but you must plug in the y coordinate and the
distance between the y axis; the latter is equal to sqrt(x*x+z*z), so
this gives you:

    #declare fL = function(x,y,z) { atan2(sqrt(x*x+z*z),y)*CONST }

Choose CONST values as needed; atan2()*CONST may happen to be replacable
by atan2d() again.


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From: Mike Horvath
Subject: Re: Spherical isosurface
Date: 29 Nov 2016 20:59:10
Message: <583dec1e@news.povray.org>
On 11/29/2016 3:04 PM, Bald Eagle wrote:
> Mike Horvath <mik### [at] gmailcom> wrote:
>
>>> What would be a formula for a sphere? L should be latitude, H longitude,
>>> and C radius.
>
> https://en.wikipedia.org/wiki/Spherical_coordinate_system
> Conversely, the Cartesian coordinates may be retrieved from the spherical
> coordinates
>
https://wikimedia.org/api/rest_v1/media/math/render/svg/d7bcd516d317c31ac48ed36e2ead9537a5f16e2e
>
>> Problem: L ranges from 0..100, and C ranges from 0..128, and I want to
>> avoid generating a flattened ellipsoid.
>>
>> Mike
>
> #declare C = C*(100/128);
>
>

THANK YOU!!

This had what I needed:

https://en.wikipedia.org/wiki/Spherical_coordinate_system#Cartesian_coordinates


I'm not sure I'm 100% correct, but here are my calculations:

#declare fD = function(C) {abs(C-0.5)-0.5}
#declare fDist = function(Dr,Dg,Db) {max(Dr,Dg,Db)}
#declare fR = function(L,C,H) {convertLCH2RGBa1(L,C,H)}
#declare fG = function(L,C,H) {convertLCH2RGBa2(L,C,H)}
#declare fB = function(L,C,H) {convertLCH2RGBa3(L,C,H)}
#declare fL = function(x,y,z) {acosd(y/sqrt(x*x+y*y+z*z))/180*100}
#declare fC = function(x,y,z) {sqrt(x*x+y*y+z*z)*128}
#declare fH = function(x,y,z) {atan2d(z,x)}

#declare fFinal = function(L,C,H)
{
	fDist
	(
		fD(fR(L,C,H)),
		fD(fG(L,C,H)),
		fD(fB(L,C,H))
	)
}


I just wish the results were more interesting.


Mike


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Attachments:
Download 'cielch_color_solid_sphere_isosurface_light.png' (61 KB)

Preview of image 'cielch_color_solid_sphere_isosurface_light.png'
cielch_color_solid_sphere_isosurface_light.png


 

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