Subdivision Surfaces


An example of a subdivision surface
with control mesh shown.

characteristic map

An approximation to a characteristic map;
such maps are used to analyze smoothness
properties of subdivision.

Difference operation applied to
two subdivision surfaces.

Subdivision is an algorithmic technique to generate smooth surfaces as a sequence of successively refined polyhedral meshes. Subdivision algorithms are exceptionally simple, work for arbitrary control meshes and produce globally smooth surfaces. Special choices of subdivision rules allow for the introduction of features into a surface in a simple way. Subdivision-based representations of complex geometry can be manipulated and rendered very efficiently, which makes subdivision a highly suitable tool for interactive animation and modeling systems. Over the last few years, subdivision surfaces were integrated into a number of commerical modeling and rendering systems, including Pixar's Renderman, Alias|Wavefront's Maya 3.0, Newtek's Lightwave 3D, Nichimen's Mirai, Intel Architechture Lab's 3D Software Technologies. Subdivision surfaces were used to create characters in Pixar and Disney/Pixar productions Geri's Game, Bug's Life, Toy Story 2.

Subdivision and related multiresolution are active areas of research in our lab; Our curent research directions include




Subdivide our implementation of piecwise smooth subdivision surfaces.


Nonmanifold Subdivision
Lexing Ying, Denis Zorin
Proceedings of IEEE Visualization 2001.
4–8 Subdivision
Luiz Velho, Denis Zorin
CAGD, volume 18, Issue 5, Pages 397-427.
A Unified Framework for Primal/Dual Quadrilateral Subdivision Schemes
Denis Zorin, Peter Schröder
CAGD, volume 18, Issue 5, Pages 429-454.
Piecewise Smooth Subdivision Surfaces with Normal Control
Henning Biermann, Adi Levin, Denis Zorin
Computer Graphics (SIGGRAPH 2000 Proceedings), pp. 113-120
Subdivision for Modeling and Animation
D. Zorin, P. Schröder, A. DeRose, L. Kobbelt, A. Levin, W. Sweldens
SIGGRAPH 2000 Course Notes.
Smoothness of subdivision on irregular meshes
Denis Zorin
Constructive Approximation, vol. 16, no. 3, 2000, pp. 359-397.
A method for analysis of C1-continuity of subdivision surfaces
Denis Zorin
SIAM Journal of Numerical Analysis, vol. 37, no. 5, 2000, pp. 1677-1708.
Interpolating subdivision for meshes of arbitrary topology
D. Zorin, W. Sweldens, P. Schröder.
SIGGRAPH 96 Conference Proceedings, pp. 189-192.