[Haskell-beginners] High precision doubles

[Daniel Fischer]

Am Donnerstag 25 Juni 2009 04:14:19 schrieb Sean Bartell:
> > When adding a new node/hex to the graph/maze, I pick an existing node and
> > get all of its neighbour co-ordinates, filtering out co-ordinates that
> > represent nodes already present in the graph. The problem is that, due to
> > floating point errors, these co-ordinates are not be exact. If hex A has
> > the co-ordinate for hex B in its list of adjacent hexes, hex B would not
> > necessarily have the co-ordinate for hex A in its own list. Things get
> > mismatched quickly.
>
> You won't be able to get it working easily with floating-point numbers.
> Ideally, you would use integers for the code you're describing, then scale
> them to the proper floating-point values later.

Say the hexagons have side length 2, the centre of one is at (0,0) and one of its vertices 
at (2,0). 
Then the centre of any hexagon has coordinates (3*k,m*sqrt 3), for some integers k, m and 
any vertex has coordinates (i,j*sqrt 3) for integers i, j. So in this case, he could work 
with floating point values; using a large tolerance, he could build a gigantic grid before 
having false results.

But of course, it is much better to use (k,m), resp. (i,j), as coordinates and translate 
that to floating point only for drawing.