# interp.surface: Fast bilinear interpolator from a grid. In fields: Tools for Spatial Data

## Description

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

## Usage

 ```1 2``` ```interp.surface(obj, loc) interp.surface.grid(obj, grid.list) ```

## 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 `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.

## Details

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.

## Value

An vector of interpolated values. NA are returned for regions of the obj\\$z that are NA and also for locations outside of the range of the parent grid.

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ```# # evaluate an image at a finer grid # data( lennon) # create an example in the right list format like image or contour obj<- list( x= 1:20, y=1:20, z= lennon[ 201:220, 201:220]) 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 # take a look set.panel(2,2) image.plot( obj) image.plot( look) ```