|
|
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?
Post a reply to this message
|
|