Efficient Algorithms for Non-Rational and Rational Bézier Curves

In this paper, a new basis with linear computational complexity has been introduced and used to form non-rational and rational curves. Two algorithms for computing points on non-rational and rational proposed curves are expressed with their linear complexity. Moreover, the relationships between these proposed curves and the Bezier curves, for both non-rational and rational forms, are given by using polar form and homogeneous coordinate approaches. Consequently, two efficient algorithms with linear complexity have been introduced to be used in drawing non-rational and rational Bezier curves.