Normals of subdivision surfaces and their control polyhedra

Authors:
I. Ginkel;J. Peters;G. Umlauf
Affiliations:
University of Kaiserslautern, Germany;University of Florida, Gainesville, FL, USA;University of Kaiserslautern, Germany
Venue:
Computer Aided Geometric Design
Year:
2007

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Abstract

For planar spline curves and bivariate box-spline functions, the cone of normals of a polynomial spline piece is enclosed by the cone of normals of its spline control polyhedron. This note collects some concrete examples to show that this is not true for subdivision surfaces, both at extraordinary points and in the regular, box-spline setting. A larger set, the cross products of families of control net edges, has to be considered.