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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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