stinepack (version 1.5)

stinterp: A consistently well behaved method of interpolation

Description

Returns the values of an interpolating function that runs through a set of points in the xy-plane according to the algorithm of Stineman (1980).

Usage

stinterp(x,y,xout,yp,method=c("scaledstineman","stineman","parabola"))

Value

stinterp returns a list with components 'x' and 'y' with the coordinates of the interpolant at the points specified by xout.

Arguments

x,y

coordinates of points defining the interpolating function. NAs are not allowed, but see na.stinterp for gap-filling based on stinterp.

xout

the x-coordinate where the interpolant is to be found.

yp

slopes of the interpolating function at x. Optional: only given if they are known, else the argument is not used.

method

method for computing the slope at the given points if the slope is not known. With method="stineman", Stineman's original method based on an interpolating circle is used. Use method="scaledstineman" if scaling of x and y is to be carried out before Stineman's method is applied, and use method="parabola" to calculate the slopes from a parabola through every three points. Partial argument matching is supported (for example m="pa" instead of method="parabola").

Author

Tomas Johannesson, Halldor Bjornsson

References

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

See Also

na.stinterp, stinemanSlopes and parabolaSlopes.

Examples

## Interpolation with rational functions
#This example shows how the rational interpolating functions used in
#`stinterp' have a monotonic slope over an interval with widely varying
#slopes specified at the end points, consistent with Stineman's
#requirements above. A third degree interpolating function (commonly
#used in spline interpolation), on the other hand, leads to
#spurious oscillations, which are a well known problem in
#interpolation with a single polynomial function and also
#in piecewise polynomial interpolation.
if (FALSE) {
xo <- seq(0,1,by=1/50)
plot(c(0,1),c(0,1),xlim=c(0,1),ylim=c(-1,1),xlab="",ylab="")
for (s in 2:10) {
lines(stinterp(c(0,1),c(0,1),xo,yp=c(0,s)))
lines(xo,xo^2*((s-2)*xo-s+3),col=2) }
}
#Note that the two interpolation functions almost coincide for the
#lowest value (s=2) of the slope at the right end point.
#The user may verify that the rational interpolating functions continue
#to provide "reasonable" results for much higher values of the slope at the
#right end point (for example s=15, s=25 or s=100), for which the third degree
#polynomial leads to absurd results (for most practical purposes).

## Interpolate a smooth curve
#This example illustrates that the interpolation procedure
#reproduces a smooth function with known slopes at the specified
#points very well. If the slopes are not known, both methods for
#estimating the slopes at the specified points (the default method
#and method="parabola") lead to good interpolating functions, but
#the "parabola" method is slightly more accurate. The traditional 
#spline interpolation method leads to a similar result as Stineman's 
#method with slopes computed with method="parabola".
x <- seq(0,2*pi,by=pi/6)
y <- sin(x)
yp <- cos(x)
xo <- seq(0,2*pi,by=pi/150)
y1 <- stinterp(x,y,xo,yp)$y
y2 <- stinterp(x,y,xo)$y
y3 <- stinterp(x,y,xo,m="pa")$y
if (FALSE) {
plot(x,y)
lines(xo,sin(xo))
points(stinterp(x,y,xo,yp),cex=1/5,col=2)
points(stinterp(x,y,xo),cex=1/5,col=3)
points(stinterp(x,y,xo,method="parabola"),cex=1/5,col=4)
points(spline(x,y,n=length(xo)),cex=1/5,col=5)
}

## Interpolate through a sharp oscillation
#This example shows that Stineman's interpolation, with the default
#method for estimating slopes at the given points, results in no oscillations
#in the neighbourhood of a spike. If the slopes at the given points are
#computed with method="parabola", some overshooting can be seen and
#spline interpolation leads to repeated oscillations near the spike.
if (FALSE) {
yy <- y
yy[3] <- -1.5
plot(x,yy,ylim=c(-1.5,1.5))
points(stinterp(x,yy,xo),cex=1/5,col=3)
points(stinterp(x,yy,xo,method="parabola"),cex=1/5,col=4)
points(spline(x,yy,n=length(xo)),cex=1/5,col=5)
}