Handling CSDN self https://blog.csdn.net/u013213111/article/details/94067849
Reference:
Bezier curve literacy
appreciated Bezier curve
Bezier curve plotted multipoint connection
a Bezier Curves and Surfaces
a Bezier Drawing Algorithms the Curve
Construction of Bézier Curves
First, let's look at the Bezier curve intuitively what.
This is a quadratic Bezier curve, after \ (P_0 \) and \ (P_2 \) the two points, and by the \ (P_1 \) tow point:
expression profile is also very beautiful:
\ [C (T) = (. 1-T) ^ 2 + T P_0 (. 1-T) + T ^ 2P_2 P_1, T \ in [0,1] \]
(Curve C means)
In fact, such a look should also be able to understand the thoughts of a Bezier curve, that is, the data points given different "weights" an curve to calculate these points and determine the weight of a certain trend curve.
A somewhat stricter definition given point it:
in a given space in the n + 1 point \ (P_0 \) , \ (P_1 \) , \ (P_2 \) , ..., and \ (of P_n \) , these Bezier curve defined by points is
\ [C (u) = \
sum_ {i = 0} ^ n B_ {n, i} (u) P_i \] wherein, \ (B_n, _i (U) = \ FRAC {n-! {I}! (Ni)! ^ U} I (. 1-U)} ^ {Ni \) , also referred to as Bernstein polynomials.
Bezier curve is calculated by the Bernstein polynomials be apparent method, but this method is not a stable value (numerical errors will be introduced), so in practice, generally employed is de Casteljau algorithm.