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Cardinal Quadratic B-Spline Interpolator

Source: R/interpolators.R
cardinal_quadratic_b_spline.Rd

The cardinal quadratic B-spline interpolator is very nearly the same as the cubic B-spline interpolator, but uses quadratic basis functions.

Use Cases:

Basis functions are constructed by convolving a box function with itself twice. Since the basis functions are less smooth than the cubic B-spline, this is primarily useful for approximating functions of reduced smoothness. It is appropriate for functions which are two or three times continuously differentiable.

Usage

cardinal_quadratic_b_spline(
  y,
  t0,
  h,
  left_endpoint_derivative = NULL,
  right_endpoint_derivative = 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_derivative

Optional numeric scalar for the derivative at the left endpoint.

right_endpoint_derivative

Optional numeric scalar for the derivative at the right endpoint.

Value

An object of class cardinal_quadratic_b_spline with methods:

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

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

See also

Boost Documentation

Examples

y <- c(0, 1, 0, 1)
t0 <- 0
h <- 1
interpolator <- cardinal_quadratic_b_spline(y, t0, h)
xi <- 0.5
interpolator$interpolate(xi)
#> [1] 0.7857143
interpolator$prime(xi)
#> [1] 1.142857