The Normal Form of a Planar Curve And Its Application to Curve Design

Erich Hartmann

(in Mathematical Methods for Curves and Surfaces II, M. Daehlen, T. Lyche, L. Schumaker eds., Vanderbild Univ. Press, Nashville, 237-244)

Abstract:
Analogously to the Hessian normal form of a line, the normal form tex2html_wrap_inline24 of a planar curve is defined. Thus any planar curve for which the normal form exists can be considered as an implicit curve and all such curves can be treated in a uniform way. Hence the simple implicit blending methods are applicable. Offsets are just level curves of the oriented distance function h. Bisectors of two curves have simple implicit representations.

 figure18
Figure 1: tex2html_wrap_inline44-blending of two Bézier curves



Erich Hartmann
Wed Feb 3 10:53:12 MET 1999