Le_Forgeron <jgr### [at] freefr> wrote:

> Ok, then I have a simpler solution, but not without my extension:

Yes, it's definitely tricky to try to take a sheet (OP's "bent plane") and
orient it properly with the points lying in the plane.   Especially if the
points aren't somehow axis-aligned --- without a lot of analytical geometry and
jumping through hoops.

Looking at the Bezier patches again, the 4 corners are coincident with the
surface, so maybe generate a spline that could be "extruded" into a curved
"plane" and just use a series of edge-to-edge Bezier patches that follow the
spline.

I may have something workable as well which would give a very large background
area (I'm just assuming that's what he wants) and maybe for what he needs it
will be "close enough".  I think I need to sort the 3 points used to find the
centroid based on distance from where the 4th point gets projected onto that
plane, but maybe that can just be done by hand as a one-off solution.
Basically an inverse prism - a hollow rounded-square tube in solid space.
(*)

I'm wondering though if there's a polynomial shape or something that would take
the coordinates of the 4 (ordered) points as arguments.  That would be elegant.

Also, I recall clipka repeatedly stating how "trivial" it would be to make a
fillet between two surfaces if they were meshes.  Maybe that's a way to go.

And now that I've gotten this far (only 1/2 a cup of coffee in, folks!) maybe we
can just blob together two isosurface planes.

*And now, just writing that about the tube - one should be able to take a box,
and align a face of it with 3 of the points, and then just slide it over so that
another face is coincident with the 4th.  Then you could use an inverse rounded
box.

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