Sharp, quantitative bounds on the distance between a polynomial piece and its Bézier control polygon
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
Best bounds on the approximation of polynomials and splines by their control structure
Computer Aided Geometric Design
Bounding the distance between 2D parametric Bézier curves and their control polygon
Computing - Geometric modelling dagstuhl 2002
A simple and efficient approximation of a Bézier piece by its cutdown polygon
Computer Aided Geometric Design
Sharp bounds on the approximation of a Bézier polynomial by its quasi-control polygon
Computer Aided Geometric Design
Optimized refinable enclosures of multivariate polynomial pieces
Computer Aided Geometric Design
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This article presents consolidated sharp bounds for Bezier curve approximation using various approximation polygons. The sharp distance bounds between a Bezier 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 Bezier curve approximation using the corner cutting polygon are also obtained. Based on similar methods, various sharp bounds for Bezier curve approximation using control polygons and quasi control polygons are further addressed and extended to parametric Bezier curves in multi-dimensional spaces.