Approximating odd degree Bézier pieces by degree-elevation cutdown polygons

Abstract

Cutdown polygon, constructed by directly connecting some selected control points of the Bézier piece, is proposed for Bézier piece approximation by Zhang and Ma. However, for Bézier piece with odd degree, there are multiple solutions for selecting control points of cutdown polygon. In this note we propose to approximate odd degree Bézier piece by a unique cutdown polygon of its degree-elevation Bézier piece, i.e. its degree-elevation cutdown polygon. The degree-elevation cutdown polygon has the same edge number as original cutdown polygon, but has sharper error bound.