Abstract: This paper presents a quadratic programming method for optimal multi-degree reduction of Bézier curves with G¹-continuity. The L₂ and l₂ measures of distances between the two curves are used as the objective functions. The two additional parameters, available from the coincidence of the oriented tangents, are constrained to be positive so as to satisfy the solvability condition. Finally, degree reduction is changed to solve a quadratic problem of two parameters with linear constraints. Applications of degree reduction of Bézier curves with their parameterizations close to arc-length parameterizations are also discussed.

Key words: Degree reduction, Bézier curves, Optimal approximation, G¹-continuity, Quadratic programming

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