function [pltx,plty]=finddecisionboundary(class1,class2,var1,var2,ninc)

% get means and covariance matrices of training data for finding decision bound
% (this section assumes that we used a linear discriminant as a classifier)
cls1=[class1(:,var1) class1(:,var2)];
cls2=[class2(:,var1) class2(:,var2)];
m1=mean(cls1)
m2=mean(cls2)
cov1=cov(cls1)
cov2=cov(cls2)
invcov1=inv(cov1);
invcov2=inv(cov2);
logdetcov1 = log(det(cov1));
logdetcov2 = log(det(cov2));
% test each point in a 200 x 200 grid to see if it is on the decision
% boundary
pltx=[]; plty=[];
mini=min(min(cls1(:,1)),min(cls2(:,1)))
maxi=max(max(cls1(:,1)),max(cls2(:,1)))
minj=min(min(cls1(:,2)),min(cls2(:,2)))
maxj=max(max(cls1(:,2)),max(cls2(:,2)))
for i=mini:((maxi-mini)/ninc):maxi
  for j=minj:((maxj-minj)/ninc):maxj
    x = [i j];
    d1 = -0.5 * (x-m1)*invcov1*(x-m1)' - 0.5*logdetcov1 ;
    d2 = -0.5 * (x-m2)*invcov2*(x-m2)' - 0.5*logdetcov2 ;
% if the distance for a point to each of the classes is approximately the
% same, remember it
    if (abs(d1-d2)<0.05)
     pltx=[pltx; i];
     plty=[plty; j];
    end;
  end;
end;