Am 05.05.2016 um 15:15 schrieb William F Pokorny:

> I vote for providing access to the citrus shape as an extension to the
> ovus given we have the ovus today - at least as seen by us users.
> Perhaps too we should continue calling it the citrus shape of the ovus
> given it has been introduced as such already. Though certainly other
> names, like those suggested, would be more descriptive for such a shape
> standing apart.

I can only assume that the term "citrus" was introduced as a
description, not a technical term, and I strongly discourage its use in
this sense. As a matter of fact, in mathematics the term "citrus" is
already in use for a different shape.

The proper technical term would be "lemon", while I've been using the
term "spindle" instead, owing to the fact that it is the inside surface
of a "spindle torus".


> When we want:
> 
> 1) the full citrus shape. Would we specify a length directly or do this
> by specifying the distance between the two spheres and both radii as
> zero or nearly zero?

For the full shape, you would simply use

    torus { R1, R2 intersection }

with classic torus parameters for R1 and R2 (with R2>R1). Some
trigonometry may be required to compute these from some other
parameterization such as the distance between the tips and the "equator"
radius.

This syntax will be supported in 3.7.1, and has already been available
in dev releases for quite a while (though I think I didn't make much
noise about it).

> 2) the citrus shape clipped equally on both ends - the barrel shape.
> Would we specify a distance between spheres, both radii the same and
> then to drop both spheres from the result?

That depends on what syntax we eventually end up with ;)

> 3) the citrus shape clipped at one end -an ogive or bullet. We'd do
> something like (2), but be able to drop just the larger sphere while the
> other sphere stays with a near zero radius out at the end of the citrus?

I'm quite sure that would be a special case of 2).

> 4) the citrus shape clipped unequally... Is this doable at all as a
> give-me-the-citrus extension to the ovus? It looks to me like the clip
> to the larger sphere happens perpendicular to the origin of that sphere,
> but the clip to the smaller sphere is somehow calculated & not clear to
> me how?

In the current ovus implementation, the transition between the lower
sphere and the lemon actually does /not/ coincide with the equator of
the lower sphere (except for very specific selections of parameters),
even though /some/ of the sample images seem to imply that.

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