Surface algorithms using bounds on derivatives
Computer Aided Geometric Design
The termination criterion for subdivision of the rational Be´zier curves
CVGIP: Graphical Models and Image Processing
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
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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By connecting the points which are the kind of linear combinations of Bézier control points, a broken line polygon called quasi-control polygon is produced. Using it to approximate Bézier segment, this paper obtains two sharp, quantitative bounds, besides depending on the degree of the polynomial, the bounds depend only on the maximal absolute second differences or the sum of absolute second differences of the control point sequence respectively. The advantage of this method is hardly increasing calculation, the effect of using quasi-control polygon to approximate is better than that of using control polygon to approximate.