Bounds on the Moving Control Points of Hybrid Curves

Hybrid curves provide an attractive method for approximating rational Bézier curves by polynomial Bézier curves. In this paper, several methods are provided to estimate the error bounds for the approximation to the moving control point of the hybrid curves. When the given rational Bézier curves satisfies the convergent conditions for moving control point of the hybrid curve, by these methods we can choose a hybrid curve with a certain degree such that the distance between the moving control point and a special point is less than a given error bound ϵ. So the polynomial Bézier curves to approximate the rational Bézier curve can be obtained by replacing the moving control point with the special point.