Consolidated sharp bounds for Bézier curve approximation with cutdown polygon and corner cutting polygon

This article presents consolidated sharp bounds for Bézier curve approximation using various approximation polygons. The sharp distance bounds between a Bézier curve and its cutdown polygon, which is introduced recently, are first obtained. The result is a further extension and consolidation over recent results. A polygon named corner cutting polygon is further constructed by using the well-known de Casteljau central corner cutting algorithm. The sharp bounds for Bézier curve approximation using the corner cutting polygon are also obtained. Based on similar methods, various sharp bounds for Bézier curve approximation using control polygons and quasi control polygons are further addressed and extended to parametric Bézier curves in multi-dimensional spaces.