Quadratic approximation to plane parametric curves and its application in approximate implicitization

Abstract

Expressing complex curves with simple parametric curve segments is widely used in computer graphics, CAD and so on. This paper applies rational quadratic B-spline curves to give a global C1 continuous approximation to a large class of plane parametric curves including rational parametric curves. Its application in approximate implicitization is also explored. The approximated parametric curve is first divided into intrinsic triangle convex segments which can be efficiently approximated with rational quadratic Bezier curves. With this approximation, we keep the convexity and the cusp (sharp) points of the approximated curve with simple computations. High accuracy approximation is achieved with a small number of quadratic segments. Experimental results are given to demonstrate the operation and efficiency of the algorithm.