Geometric Projection Parameter for Rational Bezier Curves

摘要

This paper introduces the projection parameter and applies it to rational Bezier curves. Firstly, a necessary and sufficient condition for rational Bezier curves parameterized by projection is given. Secondly, some properties of the projection parameter, including symmetry, geometric property, and so on, are discussed. Thirdly, the applications of the projection parameter, such as forming single-value curves, intersection test and adjusting the curve shape are shown. Lastly, the work of reparameterization, including the necessary and sufficient condition and the cases of degree 1 and 2. is studied.