Yes, solving it directly is probably a better tact. I believe There's
quite a bit of research literature on this out there in the computational
geometry literature.
Have you looked at the CGal c++ lib to check if they have any specialized
code for low dimensional geoemtry? CGal or something like it is very likely
to have what you want.
Perhaps more importantly: what are your precision needs? Cause some of
these questions have very real precision trade offs depending on your goals
On Saturday, April 25, 2015, Mike Meyer
Well, none of the suggested solutions for computing the rank of a matrix really suited my needs, as dragging in something like BLAS introduce more cost than just integrating the bed-and-breakfast library into my own library. So let me try a different track.
My real problem is that I've got a list of points in R3 and want to decide if they determine a plane, meaning they are coplanar but not colinear. Similarly, given a list of points in R2, I want to verify that they aren't colinear. Both of these can be done by converting the list of points to a matrix and finding the rank of the matrix, but I only use the rank function in the definitions of colinear and coplanar.
Maybe there's an easier way to tackle the underlying problems. Anyone got a suggestion for such?