POV-Ray : Newsgroups : povray.general : Offset surface Server Time: 19 Jan 2019 05:06:20 GMT
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From: Mike Horvath
Subject: Re: Offset surface
Date: 2 Aug 2018 22:26:42
Message: <5b638522$1@news.povray.org>
Are there isosurface functions for the hyperboloid? Both the saddle and 
hourglass versions. Thanks!


Mike


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From: Mike Horvath
Subject: Re: Offset surface
Date: 2 Aug 2018 22:37:01
Message: <5b63878d$1@news.povray.org>
On 8/2/2018 6:26 PM, Mike Horvath wrote:
> Are there isosurface functions for the hyperboloid? Both the saddle and 
> hourglass versions. Thanks!
> 
> 
> Mike

I need to create confocal ellipsoids and hyperboloids, with a cross 
section like in this image

https://commons.wikimedia.org/wiki/File:Elliptical_coordinates_grid.svg

Is this possible with isosurfaces? The parametric formulas are easier to 
deal with, but I don't think you can do offset curves with the 
parametrics. Am I wrong?


Mike


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From: Bald Eagle
Subject: Re: Offset surface
Date: 3 Aug 2018 00:20:01
Message: <web.5b639e8ea78a3750458c7afe0@news.povray.org>
Mike Horvath <mik### [at] gmailcom> wrote:
> On 8/2/2018 6:26 PM, Mike Horvath wrote:
> > Are there isosurface functions for the hyperboloid? Both the saddle and
> > hourglass versions.

I would probably have to say - of course there are.

> I need to create confocal ellipsoids and hyperboloids, with a cross
> section like in this image
>
> https://commons.wikimedia.org/wiki/File:Elliptical_coordinates_grid.svg

Looks pretty straightforward:
https://en.wikipedia.org/wiki/Confocal_conic_sections

> Is this possible with isosurfaces? The parametric formulas are easier to
> deal with, but I don't think you can do offset curves with the
> parametrics. Am I wrong?

Isosurfaces and (conventionally portrayed) parametrics are infinitely thin
shells of a surface.

to make lines , you'd need sphere-sweeps or similar.

But if you're looking to make nested shells (which I think is actually where
you're going with this, then you're going to want are the 3D shapes.

Presumably you want the ones that come standard with POV-Ray:
shapes.old
Insert menu:
Shapes2
Special shapes
http://www.f-lohmueller.de/pov_tut/addon/00_Basic_Templates/22_Shapes2/__index.htm

 f_ellipsoid(x,y,z, P0, P1, P2). f_ellipsoid generates spheres and ellipsoids.
Needs "threshold 1".
Setting these scaling parameters to 1/n gives exactly the same effect as
performing a scale operation to increase the scaling by n in the corresponding
direction.

    P0 : X scale (inverse)
    P1 : Y scale (inverse)
    P2 : Z scale (inverse)


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From: Bald Eagle
Subject: Re: Offset surface
Date: 3 Aug 2018 00:40:01
Message: <web.5b63a3cba78a3750458c7afe0@news.povray.org>
I haven't had to dig into this, but it's possible to make the hyperboloid while
specifying the foci, so I can't imagine the ellipsoid is any more difficult:

http://news.povray.org/povray.binaries.images/message/%3Cweb.591d8c269364765ac437ac910%40news.povray.org%3E/#%3Cweb.591
d8c269364765ac437ac910%40news.povray.org%3E


Looks like a Two-fer:
https://theinnerframe.wordpress.com/2016/08/01/quadrics/


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From: Mike Horvath
Subject: Re: Offset surface
Date: 4 Aug 2018 01:16:08
Message: <5b64fe58$1@news.povray.org>
On 8/2/2018 8:37 PM, Bald Eagle wrote:
> I haven't had to dig into this, but it's possible to make the hyperboloid while
> specifying the foci, so I can't imagine the ellipsoid is any more difficult:
> 
>
http://news.povray.org/povray.binaries.images/message/%3Cweb.591d8c269364765ac437ac910%40news.povray.org%3E/#%3Cweb.591
> d8c269364765ac437ac910%40news.povray.org%3E
> 
> 
> Looks like a Two-fer:
> https://theinnerframe.wordpress.com/2016/08/01/quadrics/
> 
> 
> 
> 

Since I'm trying to model ellipsoidal coordinate system, the formulas 
need to be parametric, so that I can make proper grid lines at the 
correct intervals and angles and so forth. You and Tor Olav did a great 
job of figuring out the method of creating offset surfaces of implicit 
functions. Would you mind trying the same for parametrics? Thanks.


Mike


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From: Bald Eagle
Subject: Re: Offset surface
Date: 4 Aug 2018 12:00:01
Message: <web.5b6594b7a78a3750458c7afe0@news.povray.org>
Mike Horvath <mik### [at] gmailcom> wrote:

> Since I'm trying to model ellipsoidal coordinate system, the formulas
> need to be parametric, so that I can make proper grid lines at the
> correct intervals and angles and so forth. You and Tor Olav did a great
> job of figuring out the method of creating offset surfaces of implicit
> functions. Would you mind trying the same for parametrics? Thanks.

Surely I'm missing something.
(It's likely - as it's Saturday morning, and I'm only 1 cup into it)

You, Mike Horvath, are mikh2161, posfan12 as well as (but not limited to)
SharkD.
The elliptic and hyperbolic curves in the Geogebra file were made by you.
(10 years ago)
When you click on the Geogebra file link, you get the drawing on the right, and
the formulas on the left.

So all you need to do is make the same thing in 3D - a series of nested shells
(with thickness)

Those shells are proportional, not constant-thickness, correct?
So they're just scaled versions of each other.
And ellipsoids are just scaled spheres.

Do you want the GRID, or do you want to be able to place "points" on the grid?
Are you using standard elliptic math, or some specialized geodectic system with
an equation that only you have worked out and know the form of?

Because you can mix isosurface shells and parametrically placed points.
The solution of the implicit and parametric equations are exactly the same.
They give you exactly the same set of points in space.


I have a hard time (efficiently) programming using a ouijaboard instead of a
keyboard, and the only chicken I have is in the freezer.
If I'm lucky, I likely have another 15 minutes free before RL starts pulling me
away.
Ready... set.... GO!

Fully stating the exact goal in no uncertain terms helps define what needs to be
done, so that the solution is the one desired, not one that's close, but still
completely useless.  You probably can't use a 2015 Toyota starter in a 1958
Ford, but it would take the same amount of effort to deliver you either part.

Perhaps you could freely share some completed SDL that's implementing the
solutions already given to you to shed some light on the mystery.
"I need to get from HERE to THERE, in order to do exactly THIS (and NOT _that_)"

Please, and Thank You.


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From: Mike Horvath
Subject: Re: Offset surface
Date: 4 Aug 2018 14:31:46
Message: <5b65b8d2$1@news.povray.org>
On 8/4/2018 7:57 AM, Bald Eagle wrote:
> Mike Horvath <mik### [at] gmailcom> wrote:
> 
>> Since I'm trying to model ellipsoidal coordinate system, the formulas
>> need to be parametric, so that I can make proper grid lines at the
>> correct intervals and angles and so forth. You and Tor Olav did a great
>> job of figuring out the method of creating offset surfaces of implicit
>> functions. Would you mind trying the same for parametrics? Thanks.
> 
> Surely I'm missing something.
> (It's likely - as it's Saturday morning, and I'm only 1 cup into it)
> 
> You, Mike Horvath, are mikh2161, posfan12 as well as (but not limited to)
> SharkD.

Correct.

> The elliptic and hyperbolic curves in the Geogebra file were made by you.
> (10 years ago)
> When you click on the Geogebra file link, you get the drawing on the right, and
> the formulas on the left.
> 
> So all you need to do is make the same thing in 3D - a series of nested shells
> (with thickness)
> 
> Those shells are proportional, not constant-thickness, correct?
> So they're just scaled versions of each other.
> And ellipsoids are just scaled spheres.
> 
> Do you want the GRID, or do you want to be able to place "points" on the grid?
> Are you using standard elliptic math, or some specialized geodectic system with
> an equation that only you have worked out and know the form of?
> 

I just want the grid. So, thin lines/curves of constant thickness, like 
the curves in this collection.

http://lib.povray.org/searchcollection/index2.php?objectName=ShapeGrid&version=1.12&contributorTag=SharkD

I may expand the collection to include more shapes, and simplify some of 
the existing ones; and the parametric object formulas are a natural 
(albeit slow) fit for this purpose.




> Because you can mix isosurface shells and parametrically placed points.
> The solution of the implicit and parametric equations are exactly the same.
> They give you exactly the same set of points in space.
> 
> 

Yes, placing points parametrically is not hard.


Thanks.

Mike


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From: Stephen
Subject: Re: Offset surface
Date: 4 Aug 2018 16:53:59
Message: <5b65da27$1@news.povray.org>
On 04/08/2018 12:57, Bald Eagle wrote:
> Surely I'm missing something.
> (It's likely - as it's Saturday morning, and I'm only 1 cup into it)

Never mind America's opioid problem. Someone seems to have a caffeine 
problem. ;)



-- 

Regards
     Stephen


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From: Mike Horvath
Subject: Re: Offset surface
Date: 4 Aug 2018 22:43:44
Message: <5b662c20$1@news.povray.org>
Stop!

I just remembered parametric objects are not solid. So they are of no 
use to me. Sorry.


Mike


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From: Mike Horvath
Subject: Re: Offset surface
Date: 5 Aug 2018 00:46:08
Message: <5b6648d0$1@news.povray.org>
Everything is hunky-dory. Thanks, all, for the help!


Mike


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