| Title: | Some Interpolation Methods |
| Version: | 1.0.1 |
| Description: | Some interpolation methods taken from 'Boost': barycentric rational interpolation, modified Akima interpolation, PCHIP (piecewise cubic Hermite interpolating polynomial) interpolation, and Catmull-Rom splines. |
| License: | GPL-3 |
| URL: | https://github.com/stla/interpolators |
| BugReports: | https://github.com/stla/interpolators/issues |
| Imports: | Rcpp |
| LinkingTo: | BH, Rcpp |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | yes |
| Packaged: | 2023-11-10 15:37:44 UTC; SDL96354 |
| Author: | Stéphane Laurent [aut, cre] |
| Maintainer: | Stéphane Laurent <laurent_step@outlook.fr> |
| Repository: | CRAN |
| Date/Publication: | 2023-11-10 19:33:19 UTC |
Interpolator evaluation
Description
Evaluation of an interpolator at some given values.
Usage
evalInterpolator(ipr, x, derivative = 0)
Arguments
ipr |
an interpolator |
x |
numeric vector giving the values to be interpolated; missing values are not allowed; for Catmull-Rom splines, the values must be between 0 and 1 |
derivative |
order of differentiation, 0 or 1 |
Value
Numeric vector of interpolated values, or numeric matrix of interpolated points for the Catmull-Rom interpolator.
Barycentric rational interpolator
Description
Barycentric rational interpolator.
Usage
iprBarycentricRational(x, y, ao = 3)
Arguments
x, y |
numeric vectors giving the coordinates of the known points, without missing value |
ao |
approximation order, an integer greater than or equal to 3 |
Details
See Barycentric rational interpolation.
Value
An interpolator, for usage in evalInterpolator.
Examples
library(interpolators)
x <- c(1, 2, 4, 5)
y <- x^2
ipr <- iprBarycentricRational(x, y)
evalInterpolator(ipr, c(2, 3))
evalInterpolator(ipr, c(2, 3), derivative = 1)
Catmull-Rom interpolator
Description
Catmull-Rom interpolator for 2-dimensional or 3-dimensional points.
Usage
iprCatmullRom(points, closed = FALSE, alpha = 0.5)
Arguments
points |
numeric matrix of 2D or 3D points, one point per row |
closed |
Boolean, whether the curve is closed |
alpha |
parameter between 0 and 1; the default value 0.5 is recommended |
Details
See Catmull-Rom splines.
Value
An interpolator, for usage in evalInterpolator.
Examples
library(interpolators)
points <- rbind(
c(0, 2.5),
c(2, 4),
c(3, 2),
c(4, 1.5),
c(5, 6),
c(6, 5),
c(7, 3),
c(9, 1),
c(10, 2.5),
c(11, 7),
c(9, 5),
c(8, 6),
c(7, 5.5)
)
ipr <- iprCatmullRom(points)
s <- seq(0, 1, length.out = 400)
Curve <- evalInterpolator(ipr, s)
head(Curve)
plot(Curve, type = "l", lwd = 2)
points(points, pch = 19)
# a closed example (pentagram) ####
rho <- sqrt((5 - sqrt(5))/10)
R <- sqrt((25 - 11*sqrt(5))/10)
points <- matrix(NA_real_, nrow = 10L, ncol = 2L)
points[c(1, 3, 5, 7, 9), ] <- t(vapply(0:4, function(i){
c(rho*cospi(2*i/5), rho*sinpi(2*i/5))
}, numeric(2L)))
points[c(2, 4, 6, 8, 10), ] <- t(vapply(0:4, function(i){
c(R*cospi(2*i/5 + 1/5), R*sinpi(2*i/5 + 1/5))
}, numeric(2L)))
ipr <- iprCatmullRom(points, closed = TRUE)
s <- seq(0, 1, length.out = 400L)
Curve <- evalInterpolator(ipr, s)
plot(Curve, type = "l", lwd = 2, asp = 1)
points(points, pch = 19)
Modified Akima interpolator
Description
Modified Akima interpolator.
Usage
iprMakima(x, y)
Arguments
x, y |
numeric vectors giving the coordinates of the known points, without missing value |
Details
See Modified Akima interpolation.
Value
An interpolator, for usage in evalInterpolator.
Examples
library(interpolators)
x <- seq(0, 4*pi, length.out = 9L)
y <- x - sin(x)
ipr <- iprMakima(x, y)
curve(x - sin(x), from = 0, to = 4*pi, lwd = 2)
curve(
evalInterpolator(ipr, x),
add = TRUE, col = "blue", lwd = 3, lty = "dashed"
)
points(x, y, pch = 19)
PCHIP interpolator
Description
PCHIP interpolator. It is monotonic.
Usage
iprPCHIP(x, y)
Arguments
x, y |
numeric vectors giving the coordinates of the known points, without missing value |
Details
See PCHIP interpolation.
Value
An interpolator, for usage in evalInterpolator.
Examples
library(interpolators)
x <- seq(0, 4*pi, length.out = 9L)
y <- x - sin(x)
ipr <- iprPCHIP(x, y)
curve(x - sin(x), from = 0, to = 4*pi, lwd = 2)
curve(
evalInterpolator(ipr, x),
add = TRUE, col = "blue", lwd = 3, lty = "dashed"
)
points(x, y, pch = 19)