# [Haskell-cafe] Coplanarity or Colinearity [Was: low-cost matrix rank?]

Carter Schonwald carter.schonwald at gmail.com
Sat Apr 25 15:00:01 UTC 2015

``` Shewchuk has a good number of writings in this topic  including this
random one i found. page 9 appears to be the releavant one?
http://www.cs.berkeley.edu/~jrs/meshpapers/robnotes.pdf

On Sat, Apr 25, 2015 at 10:20 AM, Ertugrul Söylemez <ertesx at gmx.de> wrote:

> >> 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?
> >
> > I have written an experimental [implementation] of a Gauss-Jordan solver
> > and matrix inverter.  You might find some use for it.  It does work and
> > is reasonably fast, though not as fast as hmatrix.  One advantage is
> > that you can feed the points incrementally, and it will tell you
> > immediately when there is no solution.  It will also quickly reject
> > redundant points, even in the presence of rounding errors.
>
> I should note:  The `solve` function isn't yet written, but it also
> doesn't do much.  Once you have fed enough relations, the matrix will
> already have been reduced to the identity, so you can simply extract the
> solutions from the relations.
>
>
> Greets,
> Ertugrul
>
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