# stinemanSlopes

##### Estimate the slope of an interpolating function using an arc

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

`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.

##### References

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

##### See Also

`stinterp`

and `parabolaSlopes`

.

##### Examples

```
# NOT RUN {
## 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)
# }
```

*Documentation reproduced from package stinepack, version 1.3, License: GPL-2*