Modeling of Bézier Curves Using a Combination of Linear and Circular Arc Approximations

This paper presents the new approach of the Bézier curve rendering using linear and circular arc approximations, instead of a recursive method that calculates all points on the curve pixel by pixel. The new developed algorithm also works better than a pure-linear approximation which generates rough output, and a pure-circular-arc approximation which involves with too many parameters. The purposed algorithm subdivides the curve into a series of lines and arcs satisfying the user-defined tolerance. This new method can reduce the number of points involved with the calculation and also decrease the computational time since the software built-in line and arc functions calculate faster than the recursive method. This algorithm is based on the monomial form approach which can provides more efficiency and flexibility, compare with traditional methods that are mostly based on a polynomial basis or the de Casteljau's algorithm.