Convex hull

Hello, I have two vectors, x, and y:

 x = [0.3333 0.5000 0.6667 0.7000]

x =

    0.3333    0.5000    0.6667    0.7000

>> y = [0.6667 0.5000 0.3333 0.7000]

y =

    0.6667    0.5000    0.3333    0.7000

>> convhull(x,y)

ans =

     1
     3
     4
     1

>> I know that (0.5 0.5) should theoretically be in the hull. If I try this, it works: x = single(x)

x =

    0.3333    0.5000    0.6667    0.7000

>> y = single(y)

y =

    0.6667    0.5000    0.3333    0.7000

>> x = double(x)

x =

    0.3333    0.5000    0.6667    0.7000

>> y = double(y)

y =

    0.6667    0.5000    0.3333    0.7000

>> convhull(x,y)

ans =

     1
     2
     3
     4
     1

Now notice point 2 appears. So two questions: 1) Why does switching to single and coming back to double work? 2) Why does (0.5,0.5) not appear initially as part of the hull? Thank you, Raghu

Answer 1

[Jan]

The point (0.5, 0.5) is almost an element of the edge. Rounding to SINGLE and increasing the precision back to DOUBLE can move all points a little bit. Remember that 0.6667 is not 2*0.3333 and that floating point numbers in decimal notation do not have necessarily an exactly equal representation in binary notation, which are used for computations.

See also:

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F