Bilinear Interpolation

Bilinear interpolation is a simple extension of linear interpolation. The function performs linear interpolation in each direction. The algorithm is very simple and is typically applied in a variety of fields. See the code in Matlab, R and Python below.

Matlab function [download]

function[fksFinal]=bilinearinterpolation(x1,x2,y1,y2,fun,X,Y)
%Function requires endpoints of x range (x1,x2), endpoints of y range (y1,y2),
%a function (fun) with two variables,
%and point (X,Y) for which you want the function to be approximated.
%Example: bilinearinterpolation(1,10,1,10,@(x,y)(x+y)^2,5,5)

%Evaluate the given expression at endpoints
fQ11=fun(x1,y1);
fQ12=fun(x1,y2);
fQ21=fun(x2,y1);
fQ22=fun(x2,y2);

%First, we do linear interpolation in the x-direction.
fx1= fQ11*((x2-X)/(x2-x1)) + fQ21*((X-x1)/(x2-x1));
fx2= fQ12*((x2-X)/(x2-x1)) + fQ22*((X-x1)/(x2-x1));

%Then, we interpolate in the y-direction.
fksFinal= fx1*((y2-Y)/(y2-y1)) + fx2*((Y-y1)/(y2-y1));

R function [download]

bilinearinterpolation <- function(X1,X2,Y1,Y2,fun,X,Y) {
  #Function requires endpoints of x range (X1,X2), endpoints of y range (Y1,Y2),
  #a function (fun) with two variables x1 and x2 (using lowercase in quotations), as for example "x1+x2",
  #and point (X,Y) for which you want the function to be approximated.
  #Example: bilinearinterpolation(1,10,1,10,"(x1+x2)^2",5,5) 
  
  # Read the given expression (function)
  funct=parse(text=fun)
  
  # Evaluate the given expression at endpoints
  x1 = X1; x2 = Y1; fQ11=eval(funct);
  x1 = X1; x2 = Y2; fQ12=eval(funct);
  x1 = X2; x2 = Y1; fQ21=eval(funct);
  x1 = X2; x2 = Y2; fQ22=eval(funct);
  
  #First, we do linear interpolation in the x-direction.
  fx1= fQ11*((X2-X)/(X2-X1)) + fQ21*((X-X1)/(X2-X1));
  fx2= fQ12*((X2-X)/(X2-X1)) + fQ22*((X-X1)/(X2-X1));
  
  #Then, we interpolate in the y-direction.
  fksFinal= fx1*((Y2-Y)/(Y2-Y1)) + fx2*((Y-Y1)/(Y2-Y1));
  return(fksFinal)
}

Python function [download]

def bilinearinterpolation(X1,X2,Y1,Y2,fun,X,Y):
  #Function requires endpoints of x range (X1,X2), endpoints of y range (Y1,Y2),
  #a function (fun) with two variables x1 and x2 (using lowercase in quotations), as for example "x1+x2",
  #and point (X,Y) for which you want the function to be approximated.
  #Example: bilinearinterpolation(1,10,1,10,"pow(x1+x2,2)",5,5) 
  
  # Evaluate the given expression at endpoints
  x1 = X1; x2 = Y1; fQ11=eval(fun);
  x1 = X1; x2 = Y2; fQ12=eval(fun);
  x1 = X2; x2 = Y1; fQ21=eval(fun);
  x1 = X2; x2 = Y2; fQ22=eval(fun);
  
  #First, we do linear interpolation in the x-direction.
  fx1= fQ11*((X2-X)/(X2-X1)) + fQ21*((X-X1)/(X2-X1));
  fx2= fQ12*((X2-X)/(X2-X1)) + fQ22*((X-X1)/(X2-X1));
  
  #Then, we interpolate in the y-direction.
  fksFinal= fx1*((Y2-Y)/(Y2-Y1)) + fx2*((Y-Y1)/(Y2-Y1));
  return fksFinal