These functions implement bivariate interpolation onto a grid for irregularly spaced input data. Bilinear or bicubic spline interpolation is applied using different versions of algorithms from Akima.
interp(x, y=NULL, z, xo=seq(min(x), max(x), length = nx),
yo=seq(min(y), max(y), length = ny),
linear = TRUE, extrap=FALSE, duplicate = "error", dupfun = NULL,
nx = 40, ny = 40,
jitter = 10^-12, jitter.iter = 6, jitter.random = FALSE,
remove = !linear)list with 3 components:
vectors of x- and y- coordinates of output grid, the same as the input
argument xo, or yo, if present. Otherwise, their
default, a vector 40 points evenly spaced over the range of the
input x.
matrix of fitted z-values. The value z[i,j] is computed
at the x,y point xo[i], yo[j]. z has
dimensions length(xo) times length(yo).
If input is a SpatialPointsDataFrame a
SpatialPixelssDataFrame is returned.
vector of x-coordinates of data points or a
SpatialPointsDataFrame object.
Missing values are not accepted.
vector of y-coordinates of data points. Missing values are not accepted.
If left as NULL indicates that x should be a
SpatialPointsDataFrame and z names the variable of
interest in this dataframe.
vector of z-coordinates of data points or a character variable
naming the variable of interest in the
SpatialPointsDataFrame x.
Missing values are not accepted.
x, y, and z must be the same length
(execpt if x is a SpatialPointsDataFrame) and may
contain no fewer than four points. The points of x and
y should not be collinear, i.e, they should not fall on the same line
(two vectors x and y such that y = ax + b for
some a, b will not produce menaningful results). Some
heuristics is built in to avoid this case by adding small jitter to
x and y when the number of NA values in the
result exceeds 10%.
interp is
meant for cases in which you have x, y values
scattered over a plane and a z value for each. If, instead,
you are trying to evaluate a mathematical function, or get a
graphical interpretation of relationships that can be described by a
polynomial, try outer().
vector of x-coordinates of output grid. The default is 40 points
evenly spaced over the range of x. If extrapolation is not being
used (extrap=FALSE, the default), xo should have a
range that is close to or inside of the range of x for the
results to be meaningful.
vector of y-coordinates of output grid; analogous to
xo, see above.
logical -- indicating wether linear or spline interpolation should be used.
logical flag: should extrapolation be used outside of the convex hull determined by the data points?
character string indicating how to handle duplicate data points. Possible values are
"error"produces an error message,
"strip"remove duplicate z values,
"mean","median","user"calculate
mean , median or user defined function (dupfun) of duplicate
z values.
a function, applied to duplicate points if
duplicate= "user".
dimension of output grid in x direction
dimension of output grid in y direction
Jitter of amount of diff(range(XX))*jitter (XX=x
or y) will be added to coordinates if collinear points are
detected. Afterwards interpolation will be tried once again.
Note that the jitter is not generated randomly unless
jitter.random is set to TRUE. This ensures
reproducable result. tri.mesh of package
tripack uses the same jitter mechanism. That means you can
plot the triangulation on top of the interpolation and see the
same triangulation as used for interpolation, see examples below.
number of iterations to retry with jitter, amount
will be multiplied in each iteration by iter^1.5
logical, see jitter, defaults to
FALSE
logical, indicates whether Akimas removal of thin triangles along
the border of the convex hull should be performed, experimental setting!
defaults to !linear, so it will be left out for linear interpolation
by default. For some point configurations it is the only
available option to skip this removal step.
If linear is TRUE (default), linear
interpolation is used in the triangles bounded by data points.
Cubic interpolation is done if linear is set to FALSE.
If extrap is FALSE, z-values for points outside the
convex hull are returned as NA.
No extrapolation can be performed for the linear case.
The interp function handles duplicate (x,y) points
in different ways. As default it will stop with an error message. But
it can give duplicate points an unique z value according to the
parameter duplicate (mean,median or any other
user defined function).
The triangulation scheme used by interp works well if x
and y have similar scales but will appear stretched if they have
very different scales. The spreads of x and y must be
within four orders of magnitude of each other for interp to work.
Akima, H. (1978). A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points. ACM Transactions on Mathematical Software 4, 148-164.
Akima, H. (1996). Algorithm 761: scattered-data surface fitting that has the accuracy of a cubic polynomial. ACM Transactions on Mathematical Software 22, 362--371.
R. J. Renka (1996). Algorithm 751: TRIPACK: a constrained two-dimensional Delaunay triangulation package. ACM Transactions on Mathematical Software. 22, 1-8.
R. J. Renka and Ron Brown (1998). Remark on algorithm 761. ACM Transactions on Mathematical Software. 24, 383-385.