On Fri, 12 Jul 2002 19:08:54 -0400, "TinCanMan" <Tin### [at] hotmailcom> wrote:
> 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


Hadn't thought of that.. I was thinking of a single normal definiing the center of the
triangle and
therefor the curve of the whole thing.. Forgot there where 3. lol However.. What about
an
ellipsoid? That I think would, but kind of creates and even bigger mess figuring it
out. lol May still
not work, but it may be worth the try anyway since if it wasn't possible it should
produce a very
interesting shape, which itself would be very difficult to produce correctly.

Though I agree that in most cases it probably isn't needed, but I kind of get tired of
supposedly
'high-end' models that when rendered require you go back and photoshop the edges
because
you can't smooth out obvious surfaces on the line parallel to the camera view. I don't
care how
good you are with photoshop you miss some and for people like me that are horrible at
it... lol
Additional tessalation is a very poor answer imho. There has got to be a better way
and this one
could produce interesting results in the attempt for anyone with the knowledge to make
the attempt.

First step I think would be to figure out how much to move the points to make them
match a true
sphere, then use that displacement to scale that part to an ellipsiod. Since the
normals would still
be pointing the right way for both that section of the ellipsiod and the intended
curve... Hard to say
without trying, at least for me. Hmm. Though... there may be problems there too, but
only in the sense
of rotation, the needed curve will occure someplace at the right angles on an
ellipsoid, but finding it is
the rub. :p

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