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.
stinemanSlopes(x,y,scale=FALSE)
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. |
Returns an estimate of the slope of the interpolant at (x,y).
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.
Tomas Johannesson
Stineman, R. W. A Consistently Well Behaved Method of Interpolation. Creative Computing (1980), volume 6, number 7, p. 54-57.
stinterp and parabolaSlopes.
## 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)
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