The NURBS book
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
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Bounding the distance between 2D parametric Bézier curves and their control polygon
Computing - Geometric modelling dagstuhl 2002
Topologically reliable approximation of composite Bézier curves
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
A simple and efficient approximation of a Bézier piece by its cutdown polygon
Computer Aided Geometric Design
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This paper presents an efficient algorithm for piecewise linear approximation of Bézier curves with improved sharp error bound. Given a Bézier curve of arbitrary degree, an approximation polygon having the same number of vertices as that of the control polygon is obtained through efficient local refinement of the initial control vertices. The approximation produces improved error bound compared with several existing solutions. With the explicit sharp error bound, it is also possible for prior estimation of necessary subdivisions to meet a pre-defined tolerance. The approximation can also be locally and adaptively refined for reducing the number of vertices of the piecewise linear approximation while meeting the required tolerance.