On the mathematic modeling of non-parametric curves based on cubic Bézier curves

Abstract Bézier splines are widely available in various systems with the curves and surface designs. In general, the Bézier spline can be specified with the Bézier curve segments and a Bézier curve segment can be fitted to any number of control points. The number of control points determines the degree of the Bézier polynomial. This paper presents a method which determines control points for Bézier curves approximating segments of obtained image outline(non-parametric curve) by using the properties of cubic Bézier curves. Proposed method is a technique to determine the control points that has generality and reduces the error of the Bézier curve approximation. Main advantage of proposed method is that it has higher accuracy and compression rate than previous methods. The cubic Bézier spline is obtained from cubic Bézier curve segments. To demonstrate the various performances of the proposed algorithm, experimental results are compared.