GEOMETRIC CONSTRUCTION FOR SETBACK VERTEX BLENDING

Setback vertex blends merge edge blends by broadening them at certain distances from the vertex. In this way an overall smooth transition is provided. The necessity of this type of vertex blend is illustrated b y examples. We suggest a scheme where vertex blends are represented by 2n-sided patches, though special cases may also arise with an odd num ber of sides. Standard polynomial patches are combined according to th e so-called setback split, which provides a natural structure to defin e vertex blends and offers free parameters to adjust the interior shap e. The steps to create setback vertex blends and the basic mathematica l constraints to be satisfied are illustrated by the control frame con struction, which follows a repeated chamfering strategy. The control f rame approximates the vertex blend and indirectly determines most of t he surface qualities. A few special vertex blends are analysed in the last part of the paper. (C) 1997 Elsevier Science Ltd.