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Reparameterize section #220

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merged 5 commits into from
Oct 27, 2014
Merged

Reparameterize section #220

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ba4ebb8
Work in progress
Oct 11, 2014
50e6227
Merge with master
Oct 17, 2014
627fe26
Fix SegTree section
Oct 19, 2014
62a9344
Remove shadow warning...
Oct 19, 2014
d67f581
Remove unused function.
Oct 19, 2014
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42 changes: 29 additions & 13 deletions src/Diagrams/Trail.hs
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Original file line number Diff line number Diff line change
Expand Up @@ -12,6 +12,7 @@
{-# LANGUAGE ViewPatterns #-}

{-# OPTIONS_GHC -fno-warn-orphans #-}
{-# OPTIONS_GHC -fno-warn-name-shadowing #-}
-- We have an orphan Transformable FingerTree instance here.

-----------------------------------------------------------------------------
Expand Down Expand Up @@ -183,37 +184,52 @@ instance Num n => DomainBounds (SegTree v n)
instance (Metric v, OrderedField n, Real n)
=> EndValues (SegTree v n)

instance (Metric v, OrderedField n, Real n) => Sectionable (SegTree v n) where
splitAtParam (SegTree t) p
type SplitResult v n = ((SegTree v n, n -> n), (SegTree v n, n -> n))

splitAtParam' :: (Metric v, OrderedField n, Real n) => SegTree v n -> n -> SplitResult v n
splitAtParam' tree@(SegTree t) p
| p < 0 = case FT.viewl t of
EmptyL -> emptySplit
seg :< t' ->
case seg `splitAtParam` (p * tSegs) of
(seg1, seg2) -> ( SegTree $ FT.singleton seg1
, SegTree $ seg2 <| t'
(seg1, seg2) -> ( (SegTree $ FT.singleton seg1, \u -> u * p)
, (SegTree $ seg2 <| t', \u -> 1 - (1 - u) * tSegs / (tSegs + 1))
)
| p >= 1 = case FT.viewr t of
EmptyR -> emptySplit
t' :> seg ->
case seg `splitAtParam` (1 - (1 - p)*tSegs) of
(seg1, seg2) -> ( SegTree $ t' |> seg1
, SegTree $ FT.singleton seg2
(seg1, seg2) -> ( (SegTree $ t' |> seg1, \u -> u * tSegs / (tSegs + 1))
, (SegTree $ FT.singleton seg2, \u -> (u - p) / (1 - p))
)
| otherwise = case FT.viewl after of
EmptyL -> emptySplit
EmptyL -> emptySplit
seg :< after' ->
case seg `splitAtParam` mod1 (p * tSegs) of
(seg1, seg2) -> ( SegTree $ before |> seg1
, SegTree $ seg2 <| after'
)
where
let (n, p') = propFrac $ p * tSegs
f p n u | u * tSegs < n = u * tSegs / (n + 1)
| otherwise = (n + (u * tSegs - n) / (p * tSegs - n)) / (n+1)
in case seg `splitAtParam` p' of
(seg1, seg2) -> ( ( SegTree $ before |> seg1 , f p n )
, ( SegTree $ seg2 <| after'
, \v -> 1 - f (1 - p) (tSegs - n - 1) (1 - v)
)
)
where
(before, after) = FT.split ((p * tSegs <) . numSegs) t
tSegs = numSegs t
emptySplit = (SegTree t, SegTree t)
emptySplit = let t' = (tree, id) in (t',t')

propFrac x = let m = signum x * mod1 x in (x - m, m)

instance (Metric v, OrderedField n, Real n) => Sectionable (SegTree v n) where
splitAtParam tree p = let ((a,_),(b,_)) = splitAtParam' tree p in (a,b)

reverseDomain (SegTree t) = SegTree $ FT.reverse t'
where t' = FT.fmap' reverseSegment t

section x t1 t2 = let ((a,fa),_) = splitAtParam' x t2
in snd $ splitAtParam a (fa t1)

-- XXX seems like it should be possible to collapse some of the
-- above cases into one?

Expand Down