Computing curvature bounds for bounded curvature subdivision Original Research Article

For a stationary, affine invariant, symmetric, linear and local subdivision scheme that is C2 apart from the extraordinary point the curvature is bounded if the square of the subdominant eigenvalue equals the subsubdominant eigenvalue. This paper gives a technique for quickly establishing an interval to which the curvature is confined at the extraordinary point. The approach factors the work into precomputed intervals that depend only on the scheme and a mesh-specific component. When the intervals are tight enough they can be used as a test of shape-faithfulness of the given subdivision scheme; i.e., if the limit surface in the neighborhood of the extraordinary point of the subdivision scheme is consistent with the geometry implied by the input mesh.