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|
module Spear.Math.QuadTree
(
QuadTree
, makeQuadTree
, clone
, Spear.Math.QuadTree.insert
, Spear.Math.QuadTree.map
, gmap
)
where
import Spear.Collision
import Spear.Math.AABB
import Spear.Math.Vector
import Control.Applicative ((<*>))
import Data.List
import Data.Functor
import Data.Monoid
import qualified Data.Foldable as F
-- | Represents an QuadTree.
data QuadTree e
= QuadTree
{ root :: !AABB
, ents :: ![e]
, c1 :: !(QuadTree e)
, c2 :: !(QuadTree e)
, c3 :: !(QuadTree e)
, c4 :: !(QuadTree e)
, c5 :: !(QuadTree e)
, c6 :: !(QuadTree e)
, c7 :: !(QuadTree e)
, c8 :: !(QuadTree e)
}
|
Leaf
{ root :: !AABB
, ents :: ![e]
}
-- | Builds an QuadTree using the specified AABB as the root and having the specified depth.
makeQuadTree :: Int -> AABB -> QuadTree e
makeQuadTree d root@(AABB min max)
| d == 0 = Leaf root []
| otherwise = QuadTree root [] c1 c2 c3 c4 c5 c6 c7 c8
where
boxes = subdivide root
c1 = makeQuadTree (d-1) $ boxes !! 0
c2 = makeQuadTree (d-1) $ boxes !! 1
c3 = makeQuadTree (d-1) $ boxes !! 2
c4 = makeQuadTree (d-1) $ boxes !! 3
c5 = makeQuadTree (d-1) $ boxes !! 4
c6 = makeQuadTree (d-1) $ boxes !! 5
c7 = makeQuadTree (d-1) $ boxes !! 6
c8 = makeQuadTree (d-1) $ boxes !! 7
subdivide :: AABB -> [AABB]
subdivide (AABB min max) = [a1, a2, a3, a4, a5, a6, a7, a8]
where
v = (max-min) / 2
c = vec2 (x min + x v) (y min + y v)
a1 = AABB min c
a2 = AABB ( vec2 (x min) (y min)) ( vec2 (x c) (y c) )
a3 = AABB ( vec2 (x min) (y c) ) ( vec2 (x c) (y max))
a4 = AABB ( vec2 (x min) (y c) ) ( vec2 (x c) (y max))
a5 = AABB ( vec2 (x c) (y min)) ( vec2 (x max) (y c) )
a6 = AABB ( vec2 (x c) (y min)) ( vec2 (x max) (y c) )
a7 = AABB ( vec2 (x c) (y c) ) ( vec2 (x max) (y max))
a8 = AABB c max
-- | Clones the structure of an octree. The new octree has no entities.
clone :: QuadTree e -> QuadTree e
clone (Leaf root ents) = Leaf root []
clone (QuadTree root ents c1 c2 c3 c4 c5 c6 c7 c8) = QuadTree root [] c1' c2' c3' c4' c5' c6' c7' c8'
where
c1' = clone c1
c2' = clone c2
c3' = clone c3
c4' = clone c4
c5' = clone c5
c6' = clone c6
c7' = clone c7
c8' = clone c8
keep :: (e -> AABB -> CollisionType) -> AABB -> e -> Bool
keep testAABB aabb e = test == FullyContainedBy
where test = e `testAABB` aabb
-- | Inserts a list of entities into the given octree.
insert :: (e -> AABB -> CollisionType) -> QuadTree e -> [e] -> QuadTree e
insert testAABB octree es = octree' where (octree', _) = insert' testAABB es octree
insert' :: (e -> AABB -> CollisionType) -> [e] -> QuadTree e -> (QuadTree e, [e])
insert' testAABB es (Leaf root ents) = (Leaf root ents', outliers)
where
ents' = ents ++ ents_kept
ents_kept = filter (keep testAABB root) es
outliers = filter (not . keep testAABB root) es
insert' testAABB es (QuadTree root ents c1 c2 c3 c4 c5 c6 c7 c8) =
(QuadTree root ents' c1' c2' c3' c4' c5' c6' c7' c8', outliers)
where
ents' = ents ++ ents_kept
new_ents = es ++ ents1 ++ ents2 ++ ents3 ++ ents4 ++ ents5 ++ ents6 ++ ents7 ++ ents8
ents_kept = filter (keep testAABB root) new_ents
outliers = filter (not . keep testAABB root) new_ents
(c1', ents1) = insert' testAABB es c1
(c2', ents2) = insert' testAABB es c2
(c3', ents3) = insert' testAABB es c3
(c4', ents4) = insert' testAABB es c4
(c5', ents5) = insert' testAABB es c5
(c6', ents6) = insert' testAABB es c6
(c7', ents7) = insert' testAABB es c7
(c8', ents8) = insert' testAABB es c8
-- | Extracts all entities from an octree. The resulting octree has no entities.
extract :: QuadTree e -> (QuadTree e, [e])
extract (Leaf root ents) = (Leaf root [], ents)
extract (QuadTree root ents c1 c2 c3 c4 c5 c6 c7 c8) = (QuadTree root [] c1' c2' c3' c4' c5' c6' c7' c8', ents')
where
(c1', ents1) = extract c1
(c2', ents2) = extract c2
(c3', ents3) = extract c3
(c4', ents4) = extract c4
(c5', ents5) = extract c5
(c6', ents6) = extract c6
(c7', ents7) = extract c7
(c8', ents8) = extract c8
ents' = ents ++ ents1 ++ ents2 ++ ents3 ++ ents4 ++ ents5 ++ ents6 ++ ents7 ++ ents8
-- | Applies the given function to the entities in the octree.
-- Entities that break out of their cell are reallocated appropriately.
map :: (e -> AABB -> CollisionType) -> (e -> e) -> QuadTree e -> QuadTree e
map testAABB f o =
let (o', outliers) = map' testAABB f o
in Spear.Math.QuadTree.insert testAABB o' outliers
map' :: (e -> AABB -> CollisionType) -> (e -> e) -> QuadTree e -> (QuadTree e, [e])
map' testAABB f (Leaf root ents) = (Leaf root ents_kept, outliers)
where
ents' = fmap f ents
ents_kept = filter (keep testAABB root) ents'
outliers = filter (not . keep testAABB root) ents'
map' testAABB f (QuadTree root ents c1 c2 c3 c4 c5 c6 c7 c8) =
(QuadTree root ents_kept c1' c2' c3' c4' c5' c6' c7' c8', outliers)
where
ents' = (fmap f ents) ++ out1 ++ out2 ++ out3 ++ out4 ++ out5 ++ out6 ++ out7 ++ out8
ents_kept = filter (keep testAABB root) ents'
outliers = filter (not . keep testAABB root) ents'
(c1', out1) = map' testAABB f c1
(c2', out2) = map' testAABB f c2
(c3', out3) = map' testAABB f c3
(c4', out4) = map' testAABB f c4
(c5', out5) = map' testAABB f c5
(c6', out6) = map' testAABB f c6
(c7', out7) = map' testAABB f c7
(c8', out8) = map' testAABB f c8
-- | Applies a function to the entity groups in the octree.
-- Entities that break out of their cell are reallocated appropriately.
gmap :: (e -> AABB -> CollisionType) -> (e -> e -> e) -> QuadTree e -> QuadTree e
gmap testAABB f o =
let (o', outliers) = gmap' testAABB f o
in Spear.Math.QuadTree.insert testAABB o' outliers
gmap' :: (e -> AABB -> CollisionType) -> (e -> e -> e) -> QuadTree e -> (QuadTree e, [e])
gmap' testAABB f (Leaf root ents) = (Leaf root ents_kept, outliers)
where
ents' = f <$> ents <*> ents
ents_kept = filter (keep testAABB root) ents'
outliers = filter (not . keep testAABB root) ents'
gmap' testAABB f (QuadTree root ents c1 c2 c3 c4 c5 c6 c7 c8) =
(QuadTree root ents_kept c1' c2' c3' c4' c5' c6' c7' c8', outliers)
where
ents' = (f <$> ents <*> ents) ++ out1 ++ out2 ++ out3 ++ out4 ++ out5 ++ out6 ++ out7 ++ out8
ents_kept = filter (keep testAABB root) ents'
outliers = filter (not . keep testAABB root) ents'
(c1', out1) = gmap' testAABB f c1
(c2', out2) = gmap' testAABB f c2
(c3', out3) = gmap' testAABB f c3
(c4', out4) = gmap' testAABB f c4
(c5', out5) = gmap' testAABB f c5
(c6', out6) = gmap' testAABB f c6
(c7', out7) = gmap' testAABB f c7
(c8', out8) = gmap' testAABB f c8
population :: QuadTree e -> Int
population = F.foldr (\_ acc -> acc+1) 0
instance Functor QuadTree where
fmap f (Leaf root ents) = Leaf root $ fmap f ents
fmap f (QuadTree root ents c1 c2 c3 c4 c5 c6 c7 c8) =
QuadTree root (fmap f ents) c1' c2' c3' c4' c5' c6' c7' c8'
where
c1' = fmap f c1
c2' = fmap f c2
c3' = fmap f c3
c4' = fmap f c4
c5' = fmap f c5
c6' = fmap f c6
c7' = fmap f c7
c8' = fmap f c8
instance F.Foldable QuadTree where
foldMap f (Leaf root ents) = mconcat . fmap f $ ents
foldMap f (QuadTree root ents c1 c2 c3 c4 c5 c6 c7 c8) =
mconcat (fmap f ents) `mappend`
c1' `mappend` c2' `mappend` c3' `mappend` c4' `mappend`
c5' `mappend` c6' `mappend` c7' `mappend` c8'
where
c1' = F.foldMap f c1
c2' = F.foldMap f c2
c3' = F.foldMap f c3
c4' = F.foldMap f c4
c5' = F.foldMap f c5
c6' = F.foldMap f c6
c7' = F.foldMap f c7
c8' = F.foldMap f c8
|
