Le_Forgeron <lef### [at] freefr> wrote:
> > Given 4 unique and non-coplanar points (A, B, C, & D) in space (3D) what is
> > the simplest way of defining the surface that would result from a film
> > being stretched over a frame composed of four sides (AB, BC, CD, & DA), or
> > that frame being immersed and removed from a suitable liquid for bubble
> > making?
> >
> > I think a hyperbolic paraboloid would be about the right shape, but that
> > hasn't yielded a reasonable result thus far.
> >
> >
> Looks for minimal surface tension.
Looks like the phrase that was eluding me.
>
> 3 points defining a plane, it's only a matter of positioning the fourth
> one in regard to the open triangle.
>
> case #1: ABCD is a tetraedron. The film is likely to be two-fold, each
> fold as two faces.
True. Given the two edges of the tetrahedron that aren't a part of our
frame are effectively the hinge of a pair of triangles each, it would make
some sense that the angles of the faces meeting at the hinges would both
contribute to the final equation, and they can be determined easily enough
from the normals to the faces determined by their two used vector sides.
>
> case #2: ABCD is flat, the film is flat too.
The case I had originally filtered out (because it didn't matter
much which pair of triangles I used to make the quadrilateral - as one
angle approaches pi so does the other. This is interesting if not relevant
given that our four points set the angles in stone.) I had also filtered
out (most of) the degenerate faces by capturing (separately) consecutive
and non-consecutive co-located points.
>
> case #3: you can hope for a HyperbolicParaboloid
I'm confident, but I'd really be hoping for an existing include file with
a macro that takes the four points as input variables and returns the
section of surface in position (but that might be asking too much). Failing
that, pointers in the right direction. I'm happy writing macros - I'd
written my own "Conic Frustrum Tangentially Connecting Two Spheres" macro
before running across the included one.
>
> Hint: transition from #2 to #3 seems easy. But How do you evolve from #1
> to #3 ?
I'm guessing the best answer would involve Mesh2(to preserve CSG, and given
what I'm already thinking about the surface it would be relatively simple to
generate a number of points), but is there a better non-Mesh solution?

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