  Polycube layouts for 3D models effectively support a wide variety of
applications such as hexahedral mesh construction, seamless texture mapping,
spline fitting, and multi-block grid generation. However, the automated
construction of valid polycube layouts suffers from robustness issues: the
state-of-the-art deformation-based methods are not guaranteed to find a valid
solution. In this paper we present a novel approach which is guaranteed to
return a valid polycube layout for 3D models of genus 0. Our algorithm is based
on a dual representation of polycubes; we construct polycube layouts by
iteratively adding or removing dual loops. The iterative nature of our
algorithm facilitates a seamless trade-off between quality and complexity of
the solution. Our method is efficient and can be implemented using
comparatively simple algorithmic building blocks. We experimentally compare the
results of our algorithm against state-of-the-art methods. Our fully automated
method always produces provably valid polycube layouts whose quality - assessed
via the quality of derived hexahedral meshes - is on par with state-of-the-art
deformation methods.
