bsplines: B-Splines

In cpr: Control Polygon Reduction

Description

An implementation of Carl de Boor's recursive algorithm for building B-splines.

Usage

bsplines(x, iknots = NULL, df = NULL, bknots = range(x), order = 4L)

Arguments

x	a numeric vector
iknots	internal knots
df	degrees of freedom: sum of the order and internal knots. Ignored if iknots is specified.
bknots	boundary knot locations, defaults to range(x).
order	order of the piecewise polynomials, defaults to 4L.

Details

The difference between this function and splines::bs come in the attributes associated with the output and default options. The cpr::bsplines call is intended to simplify the work needed with respect to the control polygon reduction. Further, the implementation of cpr::bsplines is in C++ and tends to be faster than splines::bs.

See the vignette("cpr-pkg", package = "cpr") for a detailed comparison between the bsplines and bs calls.

Author(s)

Peter DeWitt [e-mail]

References

C. de Boor, "A practical guide to splines. Revised Edition," Springer, 2001.

H. Prautzsch, W. Boehm, M. Paluszny, "Bezier and B-spline Techniques," Springer, 2002.

See Also

plot.cpr_bs for plotting the basis, bsplineD for building the basis matrices for the first and second derivative of a B-spline.

See update_bsplines for info on a tool for updating a cpr_bs object. This is a similar method to the update function from the stats package.

Examples

# build a vector of values to transform
xvec <- seq(-3, 5, length = 100)

# cubic b-spline
bmat <- bsplines(xvec, iknots = c(-2, 0, 0.2))
bmat

# plot the splines
plot(bmat)

# If you want a second x-axis to show the x-values try the following:
second_x_axis <- round(stats::quantile(xvec, probs = seq(0, 1, by = .2)), 2)

plot(bmat) +
ggplot2::annotate(geom = "text", x = second_x_axis, y = -0.02, label = second_x_axis) +
ggplot2::annotate(geom = "linerange", x = second_x_axis, ymin = -0.05, ymax = -0.04) +
ggplot2::coord_cartesian(ylim = c(0, 1))

# quadratic splines
bmat <- bsplines(xvec, iknots = c(-2, 0, 0.2), order = 3L)
bmat
plot(bmat) + ggplot2::ggtitle("Quadratic B-splines")

Example output

Matrix dims: [100 x 7]

          [,1]      [,2]        [,3]         [,4] [,5] [,6] [,7]
[1,] 1.0000000 0.0000000 0.000000000 0.000000e+00    0    0    0
[2,] 0.7766379 0.2170667 0.006240459 5.496587e-05    0    0    0
[3,] 0.5892895 0.3864669 0.023803888 4.397270e-04    0    0    0
[4,] 0.4347887 0.5127739 0.050953366 1.484079e-03    0    0    0
[5,] 0.3099694 0.6005608 0.085951971 3.517816e-03    0    0    0
[6,] 0.2116657 0.6544008 0.127062781 6.870734e-03    0    0    0
Matrix dims: [100 x 6]

          [,1]      [,2]        [,3] [,4] [,5] [,6]
[1,] 1.0000000 0.0000000 0.000000000    0    0    0
[2,] 0.8449138 0.1529096 0.002176649    0    0    0
[3,] 0.7028875 0.2884059 0.008706595    0    0    0
[4,] 0.5739210 0.4064891 0.019589838    0    0    0
[5,] 0.4580145 0.5071591 0.034826378    0    0    0
[6,] 0.3551678 0.5904159 0.054416216    0    0    0

cpr documentation built on May 1, 2019, 10:46 p.m.