I wanted to make a patch type object that passed through all control points.
After doing some web research, I found that the schemes for which I could
actually find an algorithm were not optimal for this purpose. These
algorithms had all been designed for animation and concentrated on speed of
calculation.

None that I found would put points directly in the centers of all uv squares
even when the control points were laid out in a flat grid. This is because
the algorithms handle corners and sides by increasing the weight of points
near the edges to make up for calculation points which are not present. My
algorithm uses the available points to guess where "missing" control points
might be and assures a proper weight for all points.

The best algorithm I could find that went through all of the control points
worked with triangles only. I prefer to work with squares when possible,
because the selective division of squares suggested to me by Hugo allows for
a better looking surface with far fewer control points. Since this patch
passes through all control points, using squares instead of triangles also
decreases the degree to which the object's shape is forced.

I really wrote this to see if I could do it. I don't think that I will
pursue this much further, because I prefer to build meshes myself with EVERY
point used as a "control point."

What do y'all think of this?

 -Shay

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