While hexahedral mesh elements are preferred by a variety of simulation techniques, constructing quality all-hex meshes of general shapes remains a challenge. An attractive hex-meshing approach, often referred to as submapping, uses a low distortion mapping between the input model and a PolyCube (a solid formed from a union of cubes), to transfer a regular hex grid from the PolyCube to the input model. Unfortunately, the construction of suitable PolyCubes and corresponding volumetric maps for arbitrary shapes remains an open problem. Our work introduces a new method for computing low-distortion volumetric PolyCube deformations of general shapes and for subsequent all-hex remeshing. For a given input model, our method simultaneously generates an appropriate PolyCube structure and mapping between the input model and the PolyCube. From these we automatically generate good quality all-hex meshes of complex natural and man-made shapes.

Recent algorithmic improvements are discussed here.


  author  = {J. Gregson and A. Sheffer and E. Zhang},
  title   = {All-Hex Mesh Generation via Volumetric PolyCube Deformation},
  journal = {Computer Graphics Forum (Special Issue of Symposium on Geometry Processing 2011)},
  year    = {2011},
  volume  = {30},
  number  = {5},
  pages   = {to appear}


Slides from our presentation at SGP 2011.



Some selected parameterization domains and all-hex meshesh automatically generated by our method are pictured below. Sample data for a selected set of models for comparison purposes is also available in .mesh format as a zip archive. The .mesh format is readable by Graphite.