Spline¶
standard mode | Standard category
Inputs¶
x
(real) - the input coordinate (x-axis)
Outputs¶
y
(real) - the value of the spline at x
Parameters¶
beta1
(real ∈ [0, ∞], default = 1) :the skew or bias parameter (only available for type beta)
beta2
(real ∈ [0, ∞), default = 0) :the tension parameter
type
(string ∈ {b, beta, quadratic}, default = b) :the type of spline to be computed
xPoints
(vector_real, default = [0, 1]) :the x-coordinates where data is specified (the points must be arranged in ascending order and cannot contain duplicates)
yPoints
(vector_real, default = [0, 1]) :the y-coordinates to be interpolated (i.e. the known data)
Description¶
Evaluates a piecewise spline of type b, beta or quadratic. The input value, i.e. the point at which the spline is to be evaluated typically should be between xPoins[0] and xPoinst[size-1]. If the value lies outside this range, extrapolation is used. Regarding spline types:
B: evaluates a cubic B spline approximant.
Beta: evaluates a cubic beta spline approximant. For beta splines parameters ‘beta1’ and ‘beta2’ can be supplied. For no bias set beta1 to 1 and for no tension set beta2 to 0. Note that if beta1=1 and beta2=0, the cubic beta becomes a cubic B spline. On the other hand if beta1=1 and beta2 is large the beta spline turns into a linear spline.
Quadratic: evaluates a piecewise quadratic spline at a point. Note that size of input must be odd.
- References:
[1] Spline interpolation - Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Spline_interpolation
Source code¶
See also¶
Spline (streaming)