Hi Mike,

> Is it just me or does anyone else notice that the edges of that corner surface
> has a minute aberrations, or a 'rumply' appearance?

These kinds of flaws can happen pretty easily with n-sided patch mechanisms. It's pretty tricky to make a really good implementation that forces the surface close enough through the curves but also does not make ripples in the surface in other spots where there are not any fitting points.


> I always thought it would seem like a viable solution to use multiple three or four-sided
> surfaces matched together to provide the solution to such a complex area.

MoI's geometry library does currently use this method - the problem then shifts to there having a tendency to have noticeable ridges and waves in the side-to-side connections, making a kind of star-like pattern that you can see on the generated surfaces.


> Wouldn't forcing the sides and corners of a surface to be stretched like some
> leather skin or screen mesh would yield inaccuracies.

It does - but if it's not accurate enough a good patch fitting mechanism would then add more points to the surface being stretched so that it could be manipulated in finer amounts until it adhered closely enough to the boundary curves.

The good thing about the star method is that it is able to adhere directly to the boundary curves meeting them exactly. But I've done a fair amount of research on the star method trying to refine it and I have not been able to find any way to reduce the star patterns that result. Basically the problem is that at the center vertex point each surface only tries to adapt its shape to be smooth to its immediate left-right neighbors and this tends to produce a ridge (a smooth one but a ridge none the less).

It's actually a good example of how having surface continuity is not a panacea for surface quality...

- Michael