Conversion of Rational Bezier Curves into Non-rational Bezier Curves Using Progressive Iterative Approximation

Abstract

This paper presents a method to convert rational Bézier curves into non-rational Bézier curve. Using the proposed method, a series of points are first sampled from the input rational Bézier curve. Then a Progressive Iterative Approximation algorithm is used to calculate for a non-rational Bézier curve that fits the sampling points. Demonstration of using the proposed algorithm to approximate input rational Bézier curves is illustrated. Experimental results show that using more sampling points provides better approximation. However, rendering a Bézier curve with too many control points is time-consuming. The optimal result should provide good approximation using as less sampling points as possible. Quality of the approximation also depend on positions of sampling points.