  In this work, we present a technique to map any genus zero solid object onto
a hexahedral decomposition of a solid cube. This problem appears in many
applications ranging from finite element methods to visual tracking. From this,
one can then hopefully utilize the proposed technique for shape analysis,
registration, as well as other related computer graphics tasks. More
importantly, given that we seek to establish a one-to-one correspondence of an
input volume to that of a solid cube, our algorithm can naturally generate a
quality hexahedral mesh as an output. In addition, we constrain the mapping
itself to be volume preserving allowing for the possibility of further mesh
simplification. We demonstrate our method both qualitatively and quantitatively
on various 3D solid models
