The Analysis of PIA Algorithm Efficiency in Converting Rational Bézier Curves into Corresponding Non-rational Curves

This paper presents an efficient method to approximate a rational Bézier curve by the corresponding Non- Rational Bézier curve using Progressive Iterative Approximation (PIA) with the algorithm efficiency analysis. The proposed method samples the input curve into data points and uses a PIA algorithm to calculate new control points for the nonrational curve. The experimental results show that the proposed method has less computational complexity, which yields less computational time, than other methods which approximate the curve using power basis or monomial form conversion. This work also presents the method to find the appropriate degree of the output non-rational curve for each degree-n rational curve input.