Inverse of parametrization

[jonnest]

Hello all,
I am working on a python project, where I want to use the "as-rigid-as-possible" parametrization to transform a 3D mesh to a 2D disk.
I got the "faces" and "vertices" of my 3D triangulated surface.

Then, I use the code from the tutorial to map the 3D geometry onto the 2D disk.

# get boundary id's from faces
bnd = igl.boundary_loop(faces)
# map boundary on circle
bnd_uv = igl.map_vertices_to_circle(vertices, bnd)

# Harmonic parametrization for the internal vertices
uv = igl.harmonic_weights(vertices, faces, bnd, bnd_uv, algorithm_nr)

arap = igl.ARAP(vertices, faces, 2, np.zeros(0))

uva = arap.solve(np.zeros((0, 0)), uv)

v_p = np.hstack([uva, np.zeros((uv.shape[0],1))])

Now, what I am trying to do is, to get the inverse transformation from the "v_p" back to my 3D triangulated mesh.
Basically, I want to use another 'uniform' mesh of the 2D disk and back-transform it in the original 3D space.

Is there any possibility to get this inverse transformation?

[alecjacobson]

There's a reasonably good way to do this but unfortunately we're missing some crucial bindings (#170). There may be a hacky way around it for now that I'll try to post later.

[jonnest]

Thank you @alecjacobson for your response!

I really would be interested in some solution, also in the hacky way.