Erich Hartmann
(Comp. Aided Geom. Des. 16, 355-376)
Abstract:
The normalform h=0 of a curve (surface) is a generalization of
the Hesse normalform of a line in (plane in ).
It was introduced and applied to curve and surface design in recent
papers.
For determining the curvature of a curve (surface) defined via
normalforms it is necessary to have formulas for the second
derivatives of the normalform function h depending on the
unit normal and the normal curvatures of three tangential
directions of the surface . These are derived and
applied to visualization of the curvature of bisectors and blending
curves, isophotes, curvature lines, feature lines and intersection
curves of surfaces.
The idea of the normalform is an appropriate tool for
proving theoretical statements, too. As an example a simple proof
of the Linkage Curve Theorem is given.
Keywords: normalform, Hessian matrix, curvature, normal curvature, bisector, -blending, -continuity, umbilic points, isophote, curvature line, feature line, ridge, ravine, intersection curve, foot point,
Figure 1: Isophotes of a -blending of two tensor product Bézier surfaces