Cardinal Quintic B-Spline Interpolator

Constructs a cardinal quintic B-spline interpolator given control points.

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.

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