3D graphics programmers using Python?

[Bengt Richter]

On Wed, 05 Feb 2003 22:58:33 GMT, "Brandon Van Every" <vanevery at 3DProgrammer.com> wrote:

>Bengt Richter wrote:
>> On Tue, 04 Feb 2003 20:31:46 GMT, "Brandon Van Every"
>> <vanevery at 3DProgrammer.com> wrote: [...]
>>> Breaking up circles is trivial, you're dealing with constant arc
>>> lengths.
>>> Breaking up spheres is much harder, the arc length changes over the
>>> triangular patch.  I've finally finished wrapping my head around the
>>> math of
>>> all of this.  I've solved the problem to the degree it can be.
>> [...]
>> What do you mean by "the arc length changes over the triangular
>> patch"?  Just curious.
>
>Pick 3 distinct points on a sphere.  Call the area they bound a
>"SphereTriangle."  Even if the SphereTriangle is equilateral, great arcs
>traced from a vertex to an opposite edge do *not* have constant length.
>That means when you're trying to compute points on the SphereTriangle, you
>end up having to use arccosines.
>
If you want great circle surface distance, I would have thought arcsine more
likely. I.e., if X ansd Y are on the surface of a sphere with radius r,
(unchecked OTTOMH) isn't the (shorter) surface distance something like
    2.0*r*arcsine( sqrt((Xi-Yi)**2 +(Xj-Yj)**2 + (Xk-Yk)**2)/(2.0*r)
gotta go...

Regards,
Bengt Richter