Abstract
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.
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