BéZIER SPLINE

In the mathematical field of numerical analysis and in computer graphics a 'Bézier spline' is a spline curve where each polynomial of the spline is in Bézier form.

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Definition

See also

Definition

Given a spline ''S'' of degree ''n'' with ''k'' knots ''x''_''i'' we can write the spline as a 'Bézier spline' as:
$$
S(x) := left{
egin{matrix}
S_0(x) := & sum_{
u=0}^{n} eta_{
u,0} b_{
u,n}(x) & x in [x_0, x_1) \
S_1(x) := & sum_{
u=0}^{n} eta_{
u,1} b_{
u,n}(x - x_1) & x in [x_1, x_2) \
dots & dots \
S_{k-2}(x) := & sum_{
u=0}^{n} eta_{
u,k-2} b_{
u,n}(x - x_{k -2}) & x in [x_{k-2}, x_{k-1}] \
end{matrix}
ight.

See also

★ Bézier curve