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
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
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
Sharp bounds on the approximation of a Bézier polynomial by its quasi-control polygon
Computer Aided Geometric Design
Efficient piecewise linear approximation of bézier curves with improved sharp error bound
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Optimized refinable enclosures of multivariate polynomial pieces
Computer Aided Geometric Design
A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Aided Geometric Design
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A new concept named the cutdown polygon is introduced for a Bezier piece approximation. The cutdown polygon is constructed by directly connecting some selected control points of the Bezier piece. Based on the proposed approximation, we obtained two explicit quantitative bounds. Apart from the degree of the polynomial, the two bounds depend only on the maximal absolute second differences or the sum of absolute second differences of the sequence of control points, respectively. Compared with control polygon approximation, the key advantage of using the cutdown polygon is that the edge number can be dramatically reduced to about one half of that using control polygon approximation or less while maintaining the same estimate bound.