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2015•College MathematicsRequires access

Research on Smooth Connection between CE-Bézier Curves and Quadratic B-spline Curves

Hong Lin

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Abstract

Based on the theory of curvessmooth connection,the paper researched the connection problem between Bezier curves with multiple shape parameters(CE-Bezier)and uniform B-spline curves,through converting B-spline curves to Bezier representation.The necessary and sufficient conditions of G0,G1,G2 splicing between CE-Bezier curves and uniform B-spline curves were proposed.After meeting the splicing conditions,by changing the shape parameters of CE-Bezier curve,the shape of the stitching curve can be adjusted flexibly.

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What this paper is about

Based on the theory of curvessmooth connection,the paper researched the connection problem between Bezier curves with multiple shape parameters(CE-Bezier)and uniform B-spline curves,through converting B-spline curves to Bezier representation.The necessary and sufficient conditions of G0,G1,G2 splicing between CE-Bezier curves and uniform B-spline curves were proposed.After meeting the splicing conditions,by changing the shape parameters of CE-Bezier curve,the shape of the stitching curve can be adjusted flexibly.

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Available abstract

Based on the theory of curvessmooth connection,the paper researched the connection problem between Bezier curves with multiple shape parameters(CE-Bezier)and uniform B-spline curves,through converting B-spline curves to Bezier representation.The necessary and sufficient conditions of G0,G1,G2 splicing between CE-Bezier curves and uniform B-spline curves were proposed.After meeting the splicing conditions,by changing the shape parameters of CE-Bezier curve,the shape of the stitching curve can be adjusted flexibly.

Key concepts: Mathematics, Bézier curve, Family of curves, Connection (principal bundle), Image stitching, Quadratic equation, B-spline, Differential geometry of curves

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