# stinemanSlopes: Estimate the slope of an interpolating function using an arc In stinepack: Stineman, a Consistently Well Behaved Method of Interpolation

## Description

Returns estimates of the slope of an interpolating function that runs through a set of points in the xy-plane. The slopes are calculated using to the algorithm of Stineman (1980), i.e. from the tangent of circles passing through every three consecutive points.

## Usage

 `1` ``` stinemanSlopes(x,y,scale=FALSE) ```

## Arguments

 `x,y` coordinates of points defining the interpolating function. `scale` if true (default) then the x and y values are normalized prior to the slope calculation.

## Value

Returns an estimate of the slope of the interpolant at (x,y).

## Note

This function is used as part of the Stineman interpolation function `stinterp`. It is rarely called directly by the user, and checking of x and y must be performed by the calling function.

Stineman's method provides a more robust interpolating function near abrupt steps or spikes in the point sequence than the alternative method based on a second degree interpolating polynomial, which is provided by the function `parabolaSlopes` (see the documentation of the function `stinterp` for further information), but it results in slightly less accuracy for smooth functions.

## Author(s)

Tomas Johannesson

## References

Stineman, R. W. A Consistently Well Behaved Method of Interpolation. Creative Computing (1980), volume 6, number 7, p. 54-57.

`stinterp` and `parabolaSlopes`.

## Examples

 ```1 2 3 4 5``` ```## Interpolate a smooth curve x <- seq(0,2*pi,by=pi/6) y <- sin(x) stinemanSlopes(x,y,scale=TRUE) stinemanSlopes(x,y,scale=FALSE) ```

### Example output

``` [1]  1.116638e+00  7.932212e-01  3.535473e-01  0.000000e+00 -3.535473e-01
[6] -7.932212e-01 -9.549297e-01 -7.932212e-01 -3.535473e-01  5.434010e-17
[11]  3.535473e-01  7.932212e-01  1.116638e+00
[1]  1.098788e+00  8.110713e-01  4.407481e-01  2.268417e-17 -4.407481e-01
[6] -8.110713e-01 -9.549297e-01 -8.110713e-01 -4.407481e-01 -1.587892e-16
[11]  4.407481e-01  8.110713e-01  1.098788e+00
```

stinepack documentation built on May 1, 2019, 10:10 p.m.