Package 'interpolators'

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.

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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)

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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)

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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)

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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)

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