Weighted G1-Multi-Degree Reduction of Bézier Curves

Abstract—In this paper, weighted G1-multi-degree reduction of Bézier curves is considered. The degree reduction of a given Bézier curve of degree n is used to write it as a Bézier curve of degree m,m < n. Exact degree reduction is not possible, and, therefore, approximation methods are used. The weight function w(t) = 2t(1 − t), t ∈ [0, 1] is used with the L2-norm in multi-degree reduction with G1-continuity at the end points of the curve. Since we consider boundary conditions this weight function improves approximation in the middle of the curve. Numerical results and comparisons show that the proposed method produces fewer errors and outperform all existing methods. Keywords—Bézier curves; multiple degree reduction; G1-continuity; geometric continuity I