A subdivision scheme for hexahedral meshes Academic Article uri icon


  • In a landmark paper, Catmull and Clark described a simple generalization of the subdivision rules for bi-cubic B-splines to arbitrary quadrilateral surface meshes. This subdivision scheme has become a mainstay of surface modeling systems. Joy and MacCracken described a generalization of this surface scheme to volume meshes. Unfortunately, little is known about the smoothness and regularity of this scheme due to the complexity of the subdivision rules. This paper presents an alternative subdivision scheme for hexahedral volume meshes that consist of a simple split and average algorithm. Along extraordinary edges of the volume mesh, the scheme provably converges to a smooth limit volume. At extraordinary vertices, the authors supply strong experimental evidence that the scheme also converges to a smooth limit volume. The scheme automatically produces reasonable rules for non-manifold topology and can easily be extended to incorporate boundaries and embedded creases expressed as Catmull-Clark surfaces and B-spline curves.

published proceedings

  • The Visual Computer

author list (cited authors)

  • Bajaj, C., Schaefer, S., Warren, J., & Xu, G.

citation count

  • 47

complete list of authors

  • Bajaj, Chandrajit||Schaefer, Scott||Warren, Joe||Xu, Guoliang

publication date

  • August 2002