# akima: Univariate Akima Interpolation In pracma: Practical Numerical Math Functions

 akimaInterp R Documentation

## Univariate Akima Interpolation

### Description

Interpolate smooth curve through given points on a plane.

### Usage

``````  akimaInterp(x, y, xi)
``````

### Arguments

 `x, y` x/y-coordinates of (irregular) grid points defining the curve. `xi` x-coordinates of points where to interpolate.

### Details

Implementation of Akima's univariate interpolation method, built from piecewise third order polynomials. There is no need to solve large systems of equations, and the method is therefore computationally very efficient.

### Value

Returns the interpolated values at the points `xi` as a vector.

### Note

There is also a 2-dimensional version in package ‘akima’.

### Author(s)

Matlab code by H. Shamsundar under BSC License; re-implementation in R by Hans W Borchers.

### References

Akima, H. (1970). A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures. Journal of the ACM, Vol. 17(4), pp 589-602.

Hyman, J. (1983). Accurate Monotonicity Preserving Cubic Interpolation. SIAM J. Sci. Stat. Comput., Vol. 4(4), pp. 645-654.

Akima, H. (1996). Algorithm 760: Rectangular-Grid-Data Surface Fitting that Has the Accurancy of a Bicubic Polynomial. ACM TOMS Vol. 22(3), pp. 357-361.

Akima, H. (1996). Algorithm 761: Scattered-Data Surface Fitting that Has the Accuracy of a Cubic Polynomial. ACM TOMS, Vol. 22(3), pp. 362-371.

`kriging`, `akima::aspline`, `akima::interp`

### Examples

``````x <- c( 0,  2,  3,  5,  6,  8,  9,   11, 12, 14, 15)
y <- c(10, 10, 10, 10, 10, 10, 10.5, 15, 50, 60, 85)
xs <- seq(12, 14, 0.5)          # 12.0 12.5     13.0     13.5     14.0
ys <- akimaInterp(x, y, xs)     # 50.0 54.57405 54.84360 55.19135 60.0
xs; ys

## Not run:
plot(x, y, col="blue", main = "Akima Interpolation")
xi <- linspace(0,15,51)
yi <- akimaInterp(x, y, xi)
lines(xi, yi, col = "darkred")
grid()
## End(Not run)
``````

pracma documentation built on Nov. 10, 2023, 1:14 a.m.