2008Jisuanji gongcheng yu shejiRequires access

Adaptive algorithm to reduce biquadratic Bézier curve to quadratic Bézier curve

Ouyang Kai-cui

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Abstract

The adaptive algorithm to reduce a biquadratic Bezier curve to piecewise quadratic Bezier curves which based on curve sub-division points is presented.By analyses error calculational method,adopted measure while unsmooth occur on the division points,and according to the nature of Bezier cuver,this adaptive algorithm is improved.This algorithm need not to calculate the left degree reduction nor right degree reduction,it directly improves by the nature of the Bezier curve.Compared with other traditional algorithms which reduces a biquadratic Bezier curve to quadratic Bezier curves,this adaptive algorithm acquires much improvement by the research of de-gree reduction formula of Bezier curve.This algorithm has many advantages such as simply computation,easily understanding and high stability.

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What this paper is about

The adaptive algorithm to reduce a biquadratic Bezier curve to piecewise quadratic Bezier curves which based on curve sub-division points is presented.By analyses error calculational method,adopted measure while unsmooth occur on the division points,and according to the nature of Bezier cuver,this adaptive algorithm is improved.This algorithm need not to calculate the left degree reduction nor right degree reduction,it directly improves by the nature of the Bezier curve.Compared with other traditional algorithms which reduces a biquadratic Bezier curve to quadratic Bezier curves,this adaptive algorithm acquires much improvement by the research of de-gree reduction formula of Bezier curve.This algorithm has many advantages such as simply computation,easily understanding and high stability.

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Available abstract

The adaptive algorithm to reduce a biquadratic Bezier curve to piecewise quadratic Bezier curves which based on curve sub-division points is presented.By analyses error calculational method,adopted measure while unsmooth occur on the division points,and according to the nature of Bezier cuver,this adaptive algorithm is improved.This algorithm need not to calculate the left degree reduction nor right degree reduction,it directly improves by the nature of the Bezier curve.Compared with other traditional algorithms which reduces a biquadratic Bezier curve to quadratic Bezier curves,this adaptive algorithm acquires much improvement by the research of de-gree reduction formula of Bezier curve.This algorithm has many advantages such as simply computation,easily understanding and high stability.

Key concepts: Bézier curve, Piecewise, Reduction (mathematics), Algorithm, Quadratic equation, Degree (music), Curve fitting, Computer science

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