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On 8/4/2018 7:57 AM, Bald Eagle wrote:
> Mike Horvath <mik### [at] gmail com> 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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