Normals of subdivision surfaces and their control polyhedra

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. Key words: normals, splines, subdivision, control polyhedron

• Type: Journal
• Year: 2007
• Where: CAGD
• Authors: Ingo Ginkel, Jörg Peters, Georg Umlauf
• Keywords: CAGD 2007, Control Polyhedron, Polynomial Spline Piece, Spline Control Polyhedron