combineBoundaries isn't doing the right thing

[byorgey]

See https://github.com/diagrams/diagrams-lib/blob/master/src/Diagrams/Align.hs#L96 .

If we add an Alignable instance for P2 (which we should probably have anyway):

instance Alignable (Point V2 Double) where defaultBoundary = envelopeBoundary

then we should be able to align lists of points, via the Alignable [b] instance. However, this doesn't seem to do the right thing. If we call envelopeBoundary directly (which goes via the Enveloped instance for lists), it works fine:

>>> envelopeBoundary unitX (triangle 1 :: [P2 Double])
P (V2 0.5000000000000002 0.0)
>>> envelopeBoundary unit_X (triangle 1 :: [P2 Double])
P (V2 (-0.4999999999999999) 0.0)

But if we call defaultBoundary, which goes via the Alignable [b] instance and hence the combineBoundaries function, we get this:

>>> defaultBoundary unitX (triangle 1 :: [P2 Double])
P (V2 0.5000000000000002 0.0)
>>> defaultBoundary unit_X (triangle 1 :: [P2 Double])
P (V2 0.5000000000000002 (-0.0))

Notice we get the same boundary point no matter which direction we query.

[byorgey]

combineBoundaries
  :: (InSpace v n a, Metric v, Ord n, F.Foldable f)
  => (v n -> a -> Point v n) -> v n -> f a -> Point v n
combineBoundaries b v fa
= b v $ F.maximumBy (comparing (quadrance . (.-. origin) . b v)) fa

Comparing the resulting points by their absolute distance from the origin makes no sense. We want the point which is furthest in the direction of v, so we should be comparing them by projecting onto v and comparing the (signed) magnitude of the results.

[byorgey]

I think this is correct but I am not 100% sure.

combineBoundaries b v fa
  = b v $ F.maximumBy (comparing (dot v . (.-.origin) . b v)) fa