Error bounds for Loop subdivision surfaces

Abstract

In this paper, we obtain the error bounds on the distance between a Loop subdivision surface and its control mesh. Both local and global bounds are derived by means of computing and analysing the control meshes with two rounds of refinement directly. The bounds can be expressed with the maximum edge length of all triangles in the initial control mesh. Our results can be used as posterior estimates and also can be used to predict the subdivision depth for any given tolerance.

Keywords:

• error bound
• Loop subdivision surfaces
• control mesh
• distance
• the rate of convergence

2010 AMS Subject Classifications:

• 65D17
• 65D18
• 41A25

Acknowledgements

The authors thank the associate editor and the referee for their important comments which improved the quality of the paper. This work was supported by the National Natural Science Foundation of China under Grant No. 61170324 and Grant No. 61100105.