Bilinear Interpolation in Matlab
(Applied Mathematics)
%3-D interpolation for the use of fuel maps in Engine Control Units (ECUs)
%Develped by Ransalu Senanayake (20-03-2011)
%HELP: fmap(desired_x_value, desired_y value)
function[]=fmap2(realx,realy)
help fmap2
nearx=realx-rem(realx,10);
neary=realy-rem(realy,10);
x=0:10:100;
y=0:10:100;
xval=find(x==nearx);
yval=find(y==neary);
%ploting the fuel map - Assuming desired map is given by z
x=0:10:100;
y=0:10:100;
[X,Y]=meshgrid(x,y);
z=X.*exp(-(X/60).^2-(Y/60).^2);
Z=(z)*100/max(max(z(:)));
surf(X,Y,Z)
view([0 0 180])
xlabel('x-axis')
ylabel('y-axis')
zlabel('z-axis')
title('Fuel Map')
%4 neighbours
x1y1=Z(yval,xval);
x2y1=Z(yval,xval+1);
x1y2=Z(yval+1,xval);
x2y2=Z(yval+1,xval+1);
appears_as=[x1y2 x2y2;x1y1 x2y1]
%finding zy
zy1=((nearx+10-realx)*x1y1+(realx-nearx)*x2y1)/10;
zy2=((nearx+10-realx)*x1y2+(realx-nearx)*x2y2)/10;
zy=((neary+10-realy)*zy1 + (realy-neary)*zy2)/10;
%matlab interpolation
m=0:1:100; n=0:1:100;
[M,N]=meshgrid(m,n);
P=interp2(X,Y,Z,M,N);
%figure, mesh(M,N,P)
Matlab_ans = P(realy+1,realx+1);
%calculating errors
answer_is=zy;
answer_shoud_be=realx*exp(-(realx/60)^2-(realy/60)^2)*100/max(max(z(:)));
my_percentage_error=100*(answer_shoud_be-answer_is)/(max(appears_as(:))-min(appears_as(:)));
Matlab_percentage_error=100*(answer_shoud_be-Matlab_ans)/(max(appears_as(:))-min(appears_as(:)));
%console display
disp(['Answer should be: ',num2str(answer_shoud_be)]);
disp(['My Answer is: ',num2str(zy), ' with error: ',num2str(my_percentage_error),'%'])
disp(['Matlab Answer is: ',num2str(Matlab_ans), ' with error: ',num2str(Matlab_percentage_error),'%'])
