module Data.Octree.Internal(Vector3(..), dist,
Octree(..), lookup, nearest, withinRange, fromList, toList, insert,
ODir,
octreeStep, octantDistance, splitBy', joinStep, splitStep, allOctants, octantDistance',
cmp,
pickClosest
) where
import Data.Vector.V3
import Data.Vector.Class
import Prelude hiding(lookup)
import Data.List(sort, sortBy)
import Data.Maybe(maybeToList, listToMaybe)
import Data.Bits((.&.))
import Test.QuickCheck.All(quickCheckAll)
import Test.QuickCheck.Arbitrary
norm :: Vector v => v -> Scalar
norm a = a `vdot` a
dist :: Vector v => v -> v -> Scalar
dist u v = norm (u v)
data Octree a = Node { split :: Vector3,
nwu, nwd, neu, ned, swu, swd, seu, sed :: Octree a } |
Leaf { unLeaf :: [(Vector3, a)] } deriving (Show)
instance Functor Octree where
fmap f (Leaf l) = Leaf . fmap (\(c, a) -> (c, f a)) $ l
fmap f (Node { split = sp,
nwu = anwu,
nwd = anwd,
neu = aneu,
ned = aned,
swu = aswu,
swd = aswd,
seu = aseu,
sed = ased }) = Node { split = sp,
nwu = fmap f anwu,
nwd = fmap f anwd,
neu = fmap f aneu,
ned = fmap f aned,
swu = fmap f aswu,
swd = fmap f aswd,
seu = fmap f aseu,
sed = fmap f ased }
data ODir = SWD | SED | NWD | NED | SWU | SEU | NWU | NEU deriving (Eq, Ord, Enum, Show, Bounded)
cmp :: Vector3 -> Vector3 -> ODir
cmp ca cb = joinStep (cx, cy, cz)
where cx = v3x ca >= v3x cb
cy = v3y ca >= v3y cb
cz = v3z ca >= v3z cb
joinStep :: (Enum a1, Enum a3, Enum a2, Enum a) => (a1, a2, a3) -> a
joinStep (cx, cy, cz) = toEnum (fromEnum cx + 2 * fromEnum cy + 4 * fromEnum cz)
octreeStep :: Octree a -> ODir -> Octree a
octreeStep ot NWU = nwu ot
octreeStep ot NWD = nwd ot
octreeStep ot NEU = neu ot
octreeStep ot NED = ned ot
octreeStep ot SWU = swu ot
octreeStep ot SWD = swd ot
octreeStep ot SEU = seu ot
octreeStep ot SED = sed ot
splitStep :: ODir -> (Bool, Bool, Bool)
splitStep step = ((val .&. 1) == 1, (val .&. 2) == 2, (val .&. 4) == 4)
where val = fromEnum step
octantDistance' :: Vector3 -> ODir -> Scalar
octantDistance' dp NEU = 0.0
octantDistance' dp NWU = v3x dp
octantDistance' dp SEU = v3y dp
octantDistance' dp NED = v3z dp
octantDistance' dp SWU = sqrt ( v3x dp * v3x dp + v3y dp * v3y dp)
octantDistance' dp SED = sqrt ( v3y dp * v3y dp + v3z dp * v3z dp)
octantDistance' dp NWD = sqrt ( v3x dp * v3x dp + v3z dp * v3z dp)
octantDistance' dp SWD = norm dp
allOctants :: [ODir]
allOctants = [minBound..maxBound]
xor :: Bool -> Bool -> Bool
xor = (/=)
octantDistance :: Vector3 -> ODir -> Double
octantDistance dp odir = octantDistance' (abs dp) (toggle dp odir)
toggle :: Vector3 -> ODir -> ODir
toggle dp odir =
joinStep ((v3x dp >= 0) `xor` not u,
(v3y dp >= 0) `xor` not v,
(v3z dp >= 0) `xor` not w)
where (u, v, w) = splitStep odir
octantDistances :: Vector3 -> [(ODir, Double)]
octantDistances dp = [(o, octantDistance dp o) | o <- allOctants]
splitBy :: Vector3 -> [(Vector3, a)] -> ([(Vector3, a)],
[(Vector3, a)],
[(Vector3, a)],
[(Vector3, a)],
[(Vector3, a)],
[(Vector3, a)],
[(Vector3, a)],
[(Vector3, a)])
splitBy _splitPoint [] = ([], [], [], [], [], [], [], [])
splitBy splitPoint ((pt@(coord, a)):aList) =
case i of
SWD -> (pt:swd, sed, nwd, ned, swu, seu, nwu, neu)
SED -> ( swd, pt:sed, nwd, ned, swu, seu, nwu, neu)
NWD -> ( swd, sed, pt:nwd, ned, swu, seu, nwu, neu)
NED -> ( swd, sed, nwd, pt:ned, swu, seu, nwu, neu)
SWU -> ( swd, sed, nwd, ned, pt:swu, seu, nwu, neu)
SEU -> ( swd, sed, nwd, ned, swu, pt:seu, nwu, neu)
NWU -> ( swd, sed, nwd, ned, swu, seu, pt:nwu, neu)
NEU -> ( swd, sed, nwd, ned, swu, seu, nwu, pt:neu)
where i = cmp coord splitPoint
(swd, sed, nwd, ned, swu, seu, nwu, neu) = splitBy splitPoint aList
massCenter :: Fractional a => [(a, b)] -> a
massCenter aList = sum (map fst aList) / count
where
count = fromInteger . toInteger . length $ aList
tmap :: (t -> t1)-> (t, t, t, t, t, t, t, t)-> (t1, t1, t1, t1, t1, t1, t1, t1)
tmap t (a, b, c, d, e, f, g, h) = (t a, t b, t c, t d, t e, t f, t g, t h)
leafLimit :: Int
leafLimit = 16
fromList :: [(Vector3, a)] -> Octree a
fromList aList = if length aList <= leafLimit
then Leaf aList
else let splitPoint :: Vector3 = massCenter aList
in splitBy' fromList splitPoint aList
splitBy' :: ([(Vector3, a)] -> Octree a1)-> Vector3-> [(Vector3, a)]-> Octree a1
splitBy' f splitPoint aList = Node { split = splitPoint,
nwu = tnwu,
nwd = tnwd,
neu = tneu,
ned = tned,
swu = tswu,
swd = tswd,
seu = tseu,
sed = tsed }
where
(tswd, tsed, tnwd, tned, tswu, tseu, tnwu, tneu) = tmap f $ splitBy splitPoint aList
toList' :: Octree t -> [(Vector3, t)] -> [(Vector3, t)]
toList' (Leaf l ) tmp = l ++ tmp
toList' (Node { nwu = a,
nwd = b,
neu = c,
ned = d,
swu = e,
swd = f,
seu = g,
sed = h }) tmp = foldr toList' tmp [a, b, c, d, e, f, g, h]
toList :: Octree t -> [(Vector3, t)]
toList t = toList' t []
pathTo :: Vector3 -> Octree a -> [ODir]
pathTo pt (Leaf _) = []
pathTo pt node = aStep : pathTo pt (octreeStep node aStep)
where aStep = cmp pt (split node)
applyByPath :: (Octree a -> Octree a) -> [ODir] -> Octree a -> Octree a
applyByPath f [] ot = f ot
applyByPath f (step:path) node = case step of
NWU -> node{ nwu = applyByPath f path (nwu node) }
NWD -> node{ nwd = applyByPath f path (nwd node) }
NEU -> node{ neu = applyByPath f path (neu node) }
NED -> node{ ned = applyByPath f path (ned node) }
SWU -> node{ swu = applyByPath f path (swu node) }
SWD -> node{ swd = applyByPath f path (swd node) }
SEU -> node{ seu = applyByPath f path (seu node) }
SED -> node{ sed = applyByPath f path (sed node) }
insert :: (Vector3, a) -> Octree a -> Octree a
insert (pt, dat) ot = applyByPath insert' path ot
where path = pathTo pt ot
insert' (Leaf l) = fromList ((pt, dat) : l)
insert' _ = error "Impossible in insert'"
candidates' :: Vector3 -> Octree a -> [(ODir, Double, [(Vector3, a)])]
candidates' pt (Leaf l) = []
candidates' pt node = map findCandidates . sortBy compareDistance . octantDistances $ pt split node
where
findCandidates (octant, d) = (octant, d, maybeToList . pickClosest pt . toList . octreeStep node $ octant)
compareDistance a b = compare (snd a) (snd b)
lookup :: Octree a -> Vector3 -> Maybe (Vector3, a)
lookup (Leaf l) pt = listToMaybe . filter ((==pt) . fst) $ l
lookup node pt = flip lookup pt . octreeStep node . cmp pt . split $ node
nearest :: Octree a -> Vector3 -> Maybe (Vector3, a)
nearest (Leaf l) pt = pickClosest pt l
nearest node pt = selectFrom candidates
where candidates = map findCandidate . sortBy compareDistance . octantDistances $ pt split node
compareDistance a b = compare (snd a) (snd b)
findCandidate (octant, d) = (maybeToList . nearest' $ octreeStep node $ octant, d)
selectFrom (([], _d) : cs) = selectFrom cs
selectFrom (([best], _d) : cs) = selectFrom' best cs
selectFrom [] = Nothing
nearest' n = nearest n pt
selectFrom' best (([], d) : cs) = selectFrom' best cs
selectFrom' best ((c, d) : cs) | d > dist pt (fst best) = Just best
selectFrom' best (([next], d) : cs) = selectFrom' nextBest cs
where nextBest = if dist pt (fst best) <= dist pt (fst next)
then best
else next
selectFrom' best [] = Just best
pickClosest :: Vector v => v -> [(v, t)] -> Maybe (v, t)
pickClosest pt [] = Nothing
pickClosest pt (a:as) = Just $ foldr (pickCloser pt) a as
pickCloser pt va@(a, _a) vb@(b, _b) = if dist pt a <= dist pt b
then va
else vb
withinRange :: Scalar -> Vector3 -> Octree a -> [(Vector3, a)]
withinRange r pt (Leaf l) = filter (\(lpt, _) -> dist pt lpt <= r) l
withinRange r pt node = (concat .
map recurseOctant .
filter ((<=r) . snd) .
octantDistances $ pt split node)
where
recurseOctant (octant, _d) = withinRange r pt . octreeStep node $ octant