> Been thinking about this... This idea may be very mathimatically
intensive, but lets say you did
> the folowing... Use the three points on the triangle and there
relationship to the normal provided
> (assuming you can) and find an area of a real sphere defined by those
points and with same
> real curvature, then use the math for generating spheres to produce those
points within the
> that triangle. This assumes you can calculate based on those point and a
curve what the radius
> would need to be for the sphere, but would in theory produce a true curve,
without the need to
> tessilate the object further. I haven't a clue how myself, but
geometrically it should work. Or so
> I assume...
>

At first thought on this, I don't think it will work.

First of all, the three points and three normals will, in most cases, not be
able to realize a sphere. Any sized sphere large enough to contain all three
points (i.e., can 'rest' on the three points without falling through) can be
defined by these three points, but unless the patch has a spherical
curvature, it can never match all 3 normals.

Secondly, you want each triangle to run smoothly into the next.  Simple
analysis of spheres will tell you that no two spheres of different radii can
be intersected in such a way that their surfaces intersect smoothly.

I don't mean to rain on your parade but I just wanted to point this out
before someone puts a lot of time into trying this only to find it won't
work.  In reality, I don't think there are any simple POV primitives (blobs
and isosurfaces notwithstanding, but I don't even want to think about the
complexity of that) that can define every possible curved triangle.

-tgq

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