POV-Ray : Newsgroups : povray.general : Ovus : Ovus Server Time
29 Apr 2024 01:46:30 EDT (-0400)
  Ovus  
From: clipka
Date: 2 May 2016 18:37:49
Message: <5727d6bd$1@news.povray.org>
Gerome, this one primarily goes out to you:

I've just come across the documentation of the "ovus" primitive, and am
a bit puzzled.

The parameters of the top and bottom sphere are clear enough.

However, what I don't understand is how the major and minor radii of the
connecting spindle section are determined; theoretically we should have
an infinite number of different spindles to choose from.

This can be easily demonstrated by examining the extreme cases:

- Given any two spheres, there is always (except in pathological cases)
exactly one cone that fully envelopes both spheres and touches each of
them in a circle; connecting the spheres with the cone section between
the circles of contact obviously gives us a shape with continuous slope;
note that any cone can be interpreted as a spindle degenerated to
infinite size.

- Given any two spheres, there is also always (again except in
pathological cases) exactly one sphere that fully envelops both spheres
and touches each of then in a single point; connecting the spheres with
this outer sphere also obviously gives us a shape with continuous slope;
note that any sphere can also be interpreted as a spindle.

Between these two cases lies an infinite spectrum of possible choices
for the spindle. So how is the spindle chosen, and why that particular one?


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