Le 03/05/2016 00:37, clipka a écrit :
> 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.
>

The minor radius of the spindle is twice the biggest radius of the 
circles. (in code : ConnectingRadius).

The major radius of the spindle is implicit, as only the position of the 
center of the circle of the torus is computed. (in 2D)

The choice of the minor radius (biggest circle x 2) is so that when the 
smaller radius would disappear (aka be near 0), the remaining sphere and 
the spindle would merge. (well, in fact, the visible part of the spindle 
would also disappears, without discontinuity)

> 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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