interp.surface: Fast bilinear interpolator from a grid.

Description

Uses bilinear weights to interpolate values on a rectangular grid to arbitrary locations or to another grid.

Usage

interp.surface(obj, loc)
interp.surface.grid(obj, grid.list)
interp.surface.FFT(obj, M)
fillGrid( gridList, M)

Value

interp.surface An vector of interpolated values. NA are returned for regions of the z matrix that are NA and also for locations outside of the range of the parent grid.

interp.surface.grid Interpolated values using bilinear interpolation in the list/image format with comonents: x, y, z.

interp.surface.FFT Interpolated values using the FFT method in an image format with the grid refined by the factor M.

Arguments

obj: A list with components x,y, and z in the same style as used by contour, persp, image etc. x and y are the X and Y grid values and z is a matrix with the corresponding values of the surface. For the FFT method there must be an odd number of grid points.
loc: A matrix of (irregular) locations to interpolate. First column of loc isthe X coordinates and second is the Y's.
grid.list: A list with components x and y describing the grid to interpolate. The grids do not need to be equally spaced.
gridList: Just a newer name for a grid list object.
M: A muliple of the source grid to interpolate to create the target grid. E.g. if M=5 then a 10X20 source grid in obj will give an interpolated grid of (10*5)X(20*5). See the fillGrid function that creates the larger grid.

Details

interp.surface Here is a brief explanation of the interpolation: Suppose that the location, (locx, locy) lies in between the first two grid points in both x an y. That is locx is between x1 and x2 and locy is between y1 and y2. Let ex= (l1-x1)/(x2-x1) ey= (l2-y1)/(y2-y1). The interpolant is

( 1-ex)(1-ey)*z11 + (1- ex)(ey)*z12 + ( ex)(1-ey)*z21 + ( ex)(ey)*z22

Where the z's are the corresponding elements of the Z matrix.

Note that bilinear interpolation can produce some artifacts related to the grid and not reproduce higher behavior in the surface. For, example the extrema of the interpolated surface will always be at the parent grid locations. There is nothing special about about interpolating to another grid, this function just includes a for loop over one dimension and a call to the function for irregular locations. It was included in fields for convenience. since the grid format is so common.

See also the akima package for fast interpolation from irrgeular locations. Many thanks to Jean-Olivier Irisson for making this code more efficient and concise.

interp.surface.FFT This version does the interpolation via the usual sin /cosine basis and the FFT. This method only makes sense for interpolating to a target grid that is a refinement of the source grid. E.g. if M=5 then a 10X20 source grid in obj will give an interpolated grid of (10*5)X(20*5) = 50X200. endpoints of this grid match the endpoints of the source.

Note the FFT interpolation is "C infinity " accurate which means in practice that this method will do well for smooth fields. Sharp changes will induce the usual Gibbs oscillations around large the changes. The interpolation is also peridic in both dimensions ( a torus) and so might give strange results for non-periodic fields. Pad the edges to mitigate this artifact.

The algorithm in brief is 1) FFT of the source image/matrix. 2) Stuff this into corners of a larger matrix of zeroes and of the size of the refined grid. 3) Inverse FFT of stuffed matrix.

Examples

Run this code

#
# evaluate an image object  at a finer grid
# 

data( lennon)
# create an example in the right list format like image or contour or persp.
obj<- list( x= 1:21, y=1:21, z= lennon[ 201:221, 201:221])

set.seed( 123)
# lots of random points
N<- 500
loc<- cbind( runif(N)*20, runif(N)*20)
z.new<- interp.surface( obj, loc)
# compare the image with bilinear interpolation at scattered points
set.panel(2,2)
image.plot( obj)
quilt.plot( loc, z.new) 

# sample at 100X100 equally spaced points on a grid

grid.list<- list( x= seq( 1,20,,100), y=  seq( 1,20,,100))

interp.surface.grid( obj, grid.list)-> look

# this will give an error in the FFT version because 
# there are an even number of grid points for x.
# objTest<- list( x= 1:20, y=1:21, z= lennon[ 201:220, 201:221])
# look2<- interp.surface.FFT( objTest, M=10)

look2<- interp.surface.FFT( obj, M=20)-> look2
# take a look
set.panel(2,2)
image.plot( obj)
image.plot( look)
image.plot( look2)