Ron Parker <ron### [at] povrayorg> wrote in message
news:3885c3c6@news.povray.org...
> On Wed, 19 Jan 2000 11:55:15 +0100, Sigmund Kyrre Aas wrote:
> >Has anybody thought of adding spherical or toroidal coordinate systems
> >to the isosurface patch?
> >Just an idea.
>
> Spherical coordinates are already added, sort of.  As far as I know there
> aren't any usable toroidal coordinate systems, because every point in
> space could be defined in two or more unique ways in such a system.

There are, thought they are odd.

    x =  sinh v cos phi /(cosh v -cos u)
    y =  sinh v sin phi /(cosh v -cos u)
    z =  sin u /(cosh v -cos u)

    The v = const. curves are nested tori filling all of space except for a
circle and its axis of symmetry.  u=const. are the spheres containing that
circle; and phi is the longitude, with phi=const. being halfplanes emanating
from the axis. The coordinate surfaces at any point are all orthogonal.

    Source: Schaum's math tables.

    Why anybody would want them for raytracing I don't know, but I'm sure
somebody will <grin>.

    -Robert Dawson

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