Shay, when you say 'dividing a buckey into "pies"
one time', do you mean that you start with a
Buckyball (i.e. a Buckminsterfullerene) ?

If so, then I think that this is a quite interesting
test, as I am quite fond of those. 

The pentagons and the hexagons of a Buckyballs are
easily dividable into "pies". So such a sphere mesh
would consist of 12*5 + 20*6 = 180 triangles,
wouldn't it ?

Can you please post images that shows the results
of this test ?


Tor Olav


Btw.:

How did the initial grid for the shape to the right
in your attached image look like (before subdivision) ?

24 "quads" ?


Shay wrote:
>...
> > Have you tried to make recursive subdivision
> > algorithms ?
> >
> 
> I'm not 100% sure what you mean, but I'm guessing that you mean an algorithm
> which only adds triangles where they are "necessary." If this is the case, I
> think that splitting each edge as many times as necessary in one pass might
> be simpler and faster than finding the edges and dividing them with multiple
> passes. This was my intention at first, but I decided against it.
> 
> The main reason is that doing so destroys the appearance of the mesh
> approximation. I believe after a *lot* of consideration and experimentation
> that in most cases the number of vertices saved is not worth the sacrifice
> in appearance. An algorithm which splits edges when the angle is over a
> certain threshold attempts to place vertices where they are most needed. It
> fails, however, to take into account viewing angle and the places on the
> shape where a person's eye will generally check for accuracy.
> 
> As an experiment, I created three spheres. One sphere was made up of 24
> quads (48 triangles), a second was made by splitting latitude and longitude
> lines into quads in the middle and a pie on the top and bottom, the third
> was made by dividing a buckey into "pies" one time. All of the spheres had a
> reasonably similar number of triangles (really the buckey had a lot more),
> and the buckey was probably the closest to what a recursive algorithm would
> produce. Without normals, the best looking sphere was the quad sphere. The
> quad and the buckey also had the advantage that the faces could be divided
> over and over again and the triangles would all remain about the same size
> as each other. When I also considered that a buckey was much slower to add
> on to the end of a cylinder or come, quad was the obvious winner, despite
> whatever disadvantages it may have.
> 
> The second reason was that I wanted to make a macro which worked one pass at
> a time. I found that by changing the weights by a multiplier for each pass,
> some useful "special-effects" could be created (see attached pic.)
> 
> Despite all of this, I can see times where using triangles may be necessary.
> In those cases, I will still reduce as far as possible with quads to
> preserve the look of the mesh.
> 
> I am very interested in your or anyone else's opinions about my conclusions.
> If anyone is really interested, I can reproduce the experiment.

Post a reply to this message