Le 04/10/2010 15:05, Graham a écrit :
> Le_Forgeron <lef### [at] freefr> wrote:

>> 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.

The problem is solving the equation of a hyperbolic paraboloid with ABCD.
Notice that the points A, B, C & D are not enough (4 non-coplanar points
do not fix an hyperbolic paraboloid), but you can add that each points
in AB, BC, CD & DA must also be on the surface.

>>
>> 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?
> 

I was not speaking from the POV point of view, but from the mathematical
surface point of view.
The case #3 to #2 is a degeneration of the HP into a plane. no real
discontinuity, as both are conic with 1 fold.
But I believe you have to sacrifice a fold when coming from #1.

Have you look at

http://mathworld.wolfram.com/SkewQuadrilateral.html

?


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