Geometric Projection Parameter for Rational B\'{e}zier Curves
Wanqiang Shen, Guozhao Wang, Cuifang Gao
Geometric Projection Parameter for Rational B\'{e}zier Curves
Wanqiang Shen, Guozhao Wang, Cuifang Gao
Abstract :This paper introduces the projection parameter and applies it to
rational B\'{e}zier curves. Firstly, a necessary and sufficient
condition for rational B\'{e}zier 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.
Key words :
Rational B\'{e}zier Curve
Projection
Projection Parameter
Parametric Curve
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