Triangulate concave mesh

Given a set of nonplanar edges that form a loop, is there a way to triangulate faces within this loop so they don't cross the loop boundary? (The loop is not convex.)

For coplanar BUT noncoplanar
BUT... how about making a collection of the original vertices [array], flattening them [temporarily] to be coplanar by transforming them by vectors to a plane; adding a face to the sides, triangulating that face and them transforming the vertices by vectors back as they were to autofold the face [you have the array of vectors that you used to flatten it initially to rework as their 'reverse']...

Is there a delaunay triangulation that can constrain to a boundary?

I've so far only found someone else asking similar question: http://www.gamedev.net/topic/594535curved3dsurfacetriangulation/

See my idea added to my post... about projecting to a plane and transforming vertices by vectors...
If you temporarily flatten the vertices then the edges will take a face, then you can triangulate that face's mesh, then relocate vertices back as they were  with no risk of malformed triangulations ? 
My initial idea was somewhat similar, project the vertices to a best fit plane and do the triangulation in 2d. However, I didn't even know the algorithm for triangulating 2d within a boundary.
Making a temporary face is one option, but I'd rather avoid that if I can  avoiding the overhead of creating geometry.

Do you want to triangulate the form without faces ?
If not then the tempface mesh triangulated is not a massive imposition.
I fear that there is no bounded delauney method...
I think the mooted way of flattening, facing, triangulating then reinflating is the best option without trying to find some obscure algorithm that might not even exist  or might end up being the equivalent anyway... 
I've got a personal plugin that does this. I shoot rays to test if the line crosses an edge. It works well enough. Though I am not triangulating from each vertex, but from the cursor. I could email you a copy if you want to see it in action.
Chris
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