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Cardinal Quintic B-Spline Interpolator

Source: R/interpolators.R
cardinal_quintic_b_spline.Rd

The cardinal quintic B-spline interpolator is similar to the cubic B-spline but uses basis functions constructed by convolving a box function with itself five times.

Properties:

The basis functions are more smooth (C4) than the cubic B-spline (C2), making this useful for computing second derivatives. The second derivative of the quintic B-spline is a cubic spline.

Usage

cardinal_quintic_b_spline(
  y,
  t0,
  h,
  left_endpoint_derivatives = NULL,
  right_endpoint_derivatives = NULL
)

Arguments

y

Numeric vector of data points to interpolate.

t0

Numeric scalar representing the starting point of the data.

h

Numeric scalar representing the spacing between data points.

left_endpoint_derivatives

Optional two-element numeric vector for the derivative at the left endpoint.

right_endpoint_derivatives

Optional two-element numeric vector for the derivative at the right endpoint.

Value

An object of class cardinal_quintic_b_spline with methods:

  • interpolate(xi): Evaluate the interpolator at point xi.

  • prime(xi): Evaluate the derivative of the interpolator at point xi.

  • double_prime(xi): Evaluate the second derivative of the interpolator at point xi.

See also

Boost Documentation

Examples

y <- seq(0, 1, length.out = 20)
t0 <- 0
h <- 1
interpolator <- cardinal_quintic_b_spline(y, t0, h)
xi <- 0.5
interpolator$interpolate(xi)
#> [1] 0.02631579
interpolator$prime(xi)
#> [1] 0.05263158
interpolator$double_prime(xi)
#> [1] 8.84709e-17