testing collinearity with algorithm collinear7

Hi,

I was looking for an algorithm to test collinearity and found : http://blogs.mathworks.com/loren/2008/06/06/collinearity/

    function tf = collinear7(p1,p2,p3)
    mat = [p1(1)-p3(1) p1(2)-p3(2); ...
           p2(1)-p3(1) p2(2)-p3(2)];
    tf = det(mat) == 0;

works fine if you test it with eg: p1 = [1 1]; p2 = [3.5 3.5]; p3 = [-7.2 -7.2]; collinear(p1,p2,p3) ans=1

for testing I choose: p1 = [ 123.83 -205.59] p2 = [ 138.38 -990.38] p3=(p1+p2)/2 p3 = 131.11 -597.98

collinear(p1,p2,p3) ans = 0 here I was suprised because two points and the middle point should be collinear no? so I tried it again with p1=[1.5 -5.3] p2=[ 5 -3.8] p3=(p1+p2)/2 collinear(p1,p2,p3) ans = 1 so now it is ok again???

so I tested another approach slightky changed the code from the site

   function tf = collinear1(p1,p2,p3)
     m = slope(p1,p2);
     b = intercept(p1,p2);
     y = (m*p3(1)+b) ;
     tf=abs(y- p3(2))<0.000001;
     end
     function m = slope(p1,p2)
     m = (p2(2)-p1(2))/(p2(1)-p1(1));
     end
     function b = intercept(p1,p2)
    m = slope(p1,p2);
    b = p1(2)-m*p1(1);

   end

with p1 = [ 123.83 -205.59] p2 = [ 138.38 -990.38] p3=(p1+p2)/2

collinear1(p1,p2,p3) is 1=> so collinear?

 I can only think of numerical errors to explain this or am I doing something completely wrong?
regards,J

Answer 1

[Matt J]

Yes, it's a numerical problem. The first version collinear7 uses the criterion

    det(mat) == 0

which demands both perfect collinearity among the points and a perfect determinant calculation, with no tolerance for floating point errors. The other versions apply a tolerance on floating point inaccuracies.