Abstract:
For the sake of simplification and convenience, the derivative bound estimation problem was usually turned into another estimation problem of parameter
λ such that||
R'(
t)|| ≤
λ \mathop \max \limits_i ||
Pi-
Pi+1||, where
Pi is the
i-th control point of a rational Bèzier curve
R(
t). This paper focuses on the estimation of the derivative bounds of a rational quadratic Bèzier curve, and provides the optimal low bound of the parameter
λ. Firstly, it divides all of the cases of the three weights of
R(
t) into eight cases; secondly, it explicitly expresses the optimal bound of
λ in the three weights for each case; finally, it leads to a general conclusion for all of the cases. Numerical examples are also given to illustrate that the bounds of the new method are better than those of prevailing methods.