Does anyone know if using relaxations to compute interior coordinates is still the state of the art? Once you've done this, do you end up computing a dense MxN

Does anyone know if using relaxations to compute interior coordinates is still the state of the art? Once you've done this, do you end up computing a dense MxN matrix-vector product for each component of an internal mesh point displacement, where M is the number of internal mesh vertices, and N is the number of cage vertices? It seems like you could do much better by exploiting the fact that nearby interior point displacements are similar, using a fast multipole method: http://math.nyu.edu/faculty/greengar/shortcourse_fmm.pdf http://math.nyu.edu/faculty/greengar/shortcourse_fmm.pdf If anyone here is an expert, has this idea been tried and discarded for some reason?