208 lines
6.6 KiB
Haskell
208 lines
6.6 KiB
Haskell
module Algorithms.RangeSearch.Core
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(quadTree,
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quadTreeSquares,
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qtFoldl,
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qtFoldr,
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goQuad,
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findNeighbor,
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lookupByPath',
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getSquareByZipper,
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rootNode,
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testArr,
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Orient(North,East,West,South),
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Quad(NW,NE,SW,SE),
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QuadTree,
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Zipper)
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where
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import Algebra.VectorTypes
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import Algebra.Vector
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import Data.Foldable (foldlM)
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import Data.Maybe (fromJust)
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import Diagrams.TwoD.Types
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-- |The quad tree structure.
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data QuadTree a
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-- |An empty node.
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= TNil
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-- |A leaf containing some value.
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| TLeaf a
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-- |A node with four children.
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| TNode (QuadTree a) (QuadTree a) -- NW NE
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(QuadTree a) (QuadTree a) -- SW SE
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deriving (Show, Eq)
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-- |Represents a Quadrant in the 2D plane.
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data Quad = NW | NE
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| SW | SE
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deriving (Show)
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-- |A Crumb used for the QuadTree Zipper.
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data Crumb a = NWCrumb (QuadTree a) (QuadTree a) (QuadTree a)
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| NECrumb (QuadTree a) (QuadTree a) (QuadTree a)
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| SWCrumb (QuadTree a) (QuadTree a) (QuadTree a)
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| SECrumb (QuadTree a) (QuadTree a) (QuadTree a)
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deriving (Show, Eq)
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-- |A list of Crumbs.
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type Breadbrumbs a = [Crumb a]
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-- |Zipper for the QuadTree.
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type Zipper a = (QuadTree a, Breadbrumbs a)
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-- |Orientation.
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data Orient = North | South | East | West
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deriving (Show)
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-- |Get a sub-square of the current square, e.g. nw, ne, sw or se.
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nwSq, neSq, swSq, seSq :: Square -> Square
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nwSq ((xl, xu), (yl, yu)) = (,) (xl, (xl + xu) / 2) ((yl + yu) / 2, yu)
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neSq ((xl, xu), (yl, yu)) = (,) ((xl + xu) / 2, xu) ((yl + yu) / 2, yu)
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swSq ((xl, xu), (yl, yu)) = (,) (xl, (xl + xu) / 2) (yl, (yl + yu) / 2)
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seSq ((xl, xu), (yl, yu)) = (,) ((xl + xu) / 2, xu) (yl, (yl + yu) / 2)
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-- |Check whether the current Node is an nw, ne, sw or se child of it's
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-- parent.
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isNWchild, isNEchild, isSWchild, isSEchild :: Zipper a -> Bool
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isNWchild (_, NWCrumb {}:_) = True
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isNWchild _ = False
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isNEchild (_, NECrumb {}:_) = True
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isNEchild _ = False
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isSWchild (_, SWCrumb {}:_) = True
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isSWchild _ = False
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isSEchild (_, SECrumb {}:_) = True
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isSEchild _ = False
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-- |Builds a quadtree of a list of points which recursively divides up 2D
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-- space into quadrants, so that every leaf-quadrant stores either zero or one
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-- point.
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quadTree :: [PT] -- ^ the points to divide
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-> Square -- ^ the initial square around the points
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-> QuadTree PT -- ^ the quad tree
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quadTree pts' sq' = go (flip filter pts' . inRange $ sq') sq'
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where
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go [] _ = TNil
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go [pt] _ = TLeaf pt
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go pts sq = TNode (quadTree pts . nwSq $ sq) (quadTree pts . neSq $ sq)
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(quadTree pts . swSq $ sq) (quadTree pts . seSq $ sq)
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-- |Get all squares of a quad tree.
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quadTreeSquares :: Square -- ^ the initial square around the points
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-> QuadTree PT -- ^ the quad tree
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-> [Square] -- ^ all squares of the quad tree
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quadTreeSquares sq (TNil) = [sq]
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quadTreeSquares sq (TLeaf _) = [sq]
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quadTreeSquares sq (TNode nw ne sw se) =
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quadTreeSquares (nwSq sq) nw ++ quadTreeSquares (neSq sq) ne ++
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quadTreeSquares (swSq sq) sw ++ quadTreeSquares (seSq sq) se
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-- |Get the current square of the zipper, relative to the to the given top
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-- square.
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getSquareByZipper :: Square -> Zipper a -> Square
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getSquareByZipper sq z = go sq (reverse . snd $ z)
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where
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go sq' [] = sq'
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go sq' (NWCrumb {}:zs) = go (nwSq sq') zs
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go sq' (NECrumb {}:zs) = go (neSq sq') zs
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go sq' (SWCrumb {}:zs) = go (swSq sq') zs
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go sq' (SECrumb {}:zs) = go (seSq sq') zs
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-- |Left fold over the tree leafs.
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qtFoldl :: (a -> b -> a) -> a -> QuadTree b -> a
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qtFoldl _ sv (TNil) = sv
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qtFoldl f sv (TLeaf a) = f sv a
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qtFoldl f sv (TNode nw ne sw se) = foldl (qtFoldl f) sv [nw, ne, sw, se]
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-- |Right fold over the tree leafs.
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qtFoldr :: (b -> a -> a) -> a -> QuadTree b -> a
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qtFoldr f sv qt = qtFoldl (\g b x -> g (f b x)) id qt sv
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-- |Go to nw, ne, sw or se from the current node, one level deeper.
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goNW, goNE, goSW, goSE :: Zipper a -> Maybe (Zipper a)
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goNW (TNode nw ne sw se, bs) = Just (nw, NWCrumb ne sw se:bs)
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goNW _ = Nothing
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goNE (TNode nw ne sw se, bs) = Just (ne, NECrumb nw sw se:bs)
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goNE _ = Nothing
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goSW (TNode nw ne sw se, bs) = Just (sw, SWCrumb nw ne se:bs)
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goSW _ = Nothing
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goSE (TNode nw ne sw se, bs) = Just (se, SECrumb nw ne sw:bs)
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goSE _ = Nothing
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-- |Go to the given Quad from the current Node, one level deeper.
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goQuad :: Quad -> Zipper a -> Maybe (Zipper a)
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goQuad q = case q of
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NW -> goNW
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NE -> goNE
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SW -> goSW
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SE -> goSE
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-- |Go up to the parent node, if any.
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goUp :: Zipper a -> Maybe (Zipper a)
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goUp (qt, NWCrumb ne sw se:bs) = Just (TNode qt ne sw se, bs)
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goUp (qt, NECrumb nw sw se:bs) = Just (TNode nw qt sw se, bs)
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goUp (qt, SWCrumb nw ne se:bs) = Just (TNode nw ne qt se, bs)
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goUp (qt, SECrumb nw ne sw:bs) = Just (TNode nw ne sw qt, bs)
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goUp _ = Nothing
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-- |Get the root node.
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rootNode :: Zipper a -> Zipper a
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rootNode (qt, []) = (qt, [])
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rootNode z = rootNode . fromJust . goUp $ z
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-- |Look up a node by a given path of Quads.
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lookupByPath' :: [Quad] -> QuadTree a -> Maybe (Zipper a)
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lookupByPath' qs qt = foldlM (flip goQuad) (qt, []) qs
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-- |Find the north, south, east or west neighbor of a given node.
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findNeighbor :: Orient -> Zipper a -> Maybe (Zipper a)
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findNeighbor ot zr = case ot of
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North -> go isSWchild isSEchild isNWchild goNW goNE goSW goSE zr
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South -> go isNWchild isNEchild isSWchild goSW goSE goNW goNE zr
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East -> go isNWchild isSWchild isNEchild goNE goSE goNW goSW zr
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West -> go isNEchild isSEchild isNWchild goNW goSW goNE goSE zr
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where
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go _ _ _ _ _ _ _ (_, []) = Nothing
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go is1 is2 is3 go1 go2 go3 go4 z@(_, _:_)
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| is1 z = goUp z >>= go1
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| is2 z = goUp z >>= go2
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| otherwise = checkParent
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. go is1 is2 is3 go1 go2 go3 go4
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. fromJust
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. goUp
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$ z
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where
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checkParent (Just (z'@(TNode {}, _)))
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| is3 z = go3 z'
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| otherwise = go4 z'
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checkParent (Just z') = Just z'
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checkParent _ = Nothing
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testArr :: [PT]
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testArr = [p2 (200.0, 450.0),
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p2 (400.0, 350.0),
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p2 (100.0, 300.0),
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p2 (25.0 , 350.0),
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p2 (225.0, 225.0),
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p2 (400.0, 150.0),
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p2 (300.0, 100.0),
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p2 (300.0, 300.0),
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p2 (300.0, 350.0),
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p2 (50.0 , 450.0),
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p2 (100.0, 25.0)]
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