What do you mean by 1 bit image? Black & White?
What you show looks like a Voronoi tesselation. There are libraries to do this kind of effect.

With 1 bit I mean, an image where is quite easy to determine the shape. Black & White (0xFFFFFF and 0x000000) for instance.

This is something similar to what I need:  http://www.mathworks.com/matlabcentral/fileexchange/25555-mesh2d-automatic-mesh-generation

Looks like this library can be handy (and you had already look into it ;))

I would love to hear if you've managed to get anything working. I've been thinking of doing something similar but gotten rather stumped along the way.

Indeed, I missed the triangle requirement...
And I think it isn't easy to do on a bitmap image. In general, indeed, the starting point is a set of vectorial points, here you need to do a kind of shape identification / vectorization to know what is inside the shape and what is outside, to find points on the curve that are approximatively even-spaced, to trace lines not going outside on concave curvatures, etc.
Are you sure this is done from a bitmap image? That not manual point entry has been done? Etc.
It can be done, of course, but it won't be easy (out of my league, unless perhaps I have LOTS of free time, which I don't have).