"JimT" <nomail@nomail> wrote:

> I think what you are looking for, given a topologically rectangular array of
> points, with coordinates that are in some way geometrically rectangular,
> cylindrical or toroidal, is to generate a mesh2 of smooth triangles,
> interpolating the points of the grid, with a high apparent level of continuity.
> I doubt that an intermediate stage involving Bezier quadrilaterals is the way to
> go.

Perhaps not - I hadn't gotten far enough along with the 3x3 Bezier patch project
to know its exact set of pros and cons.
But the thought was that there would be definite points that the patch passed
through, and those could be used as part of the subdivision.


> I would think about using Hermite cubics to form the gridlines and Coons patches
> with Hermite, rather than linear, interpolation for the surface, though for the
> cylindrical and toroidal geometry, I think you would need to specify a curvature
> at the joins.

Yes, that sounds right.
https://en.wikipedia.org/wiki/Coons_patch

> Most of the big commercial modellers seem to use NURBS for complex
> surfaces so I'm not sure how widely such an idea has been implemented. You need
> to solve a tridiagonal set of equations to generate the Hermite cubics,  but
> that can be done with for loops.

Yes, I had worked out doing de Casteljau's algorithm in SDL, and it seemed to
work.

> This should produce e.g a generalised approximate torus using as few as 16
> co-ordinates, plus another 8 numbers specifying curvature at the joins.
>
> If you think the idea is interesting, I would do some work on it.
>
> JimT

It is - and perhaps you could offer me some insight as to what I got mucked up
in the Bezier patch project, since they seem so similar.

Thanks for your observations and advice   :)

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