A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Cubic recursive division with bounded curvature
Curves and surfaces
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
Computer Aided Geometric Design
Piecewise Rational Manifold Surfaces with Sharp Features
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Subdivision surfaces integrated in a CAD system
Computer-Aided Design
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It has long been known how to achieve bounded curvature at extraordinary points of a subdivision scheme by using eigenanalysis and then adjusting the mask of each extraordinary point. This paper provides an alternative insight, based on the use of second divided differences, and applies it to three familiar schemes. A single concept is shown to work in three different contexts. In each case a bounded curvature variant results, with a very simple and elegant implementation.