Parasitemia/ParasitemiaCore/KdTree.fs

   1 module ParasitemiaCore.KdTree
   2
   3 open System
   4
   5 type I2DCoords =
   6     abstract X : float32
   7     abstract Y : float32
   8
   9 // Compare 'e1' and 'e2' by X.
  10 let cmpX (e1 : I2DCoords) (e2 : I2DCoords) : int =
  11     match e1.X.CompareTo(e2.X) with
  12     | 0 -> match e1.Y.CompareTo(e2.Y) with
  13            | 0 -> e1.GetHashCode().CompareTo(e2.GetHashCode())
  14            | v -> v
  15     | v -> v
  16
  17 // Compare 'e1' and 'e2' by Y.
  18 let cmpY (e1 : I2DCoords) (e2 : I2DCoords) : int =
  19     match e1.Y.CompareTo(e2.Y) with
  20     | 0 -> match e1.X.CompareTo(e2.X) with
  21            | 0 -> e1.GetHashCode().CompareTo(e2.GetHashCode())
  22            | v -> v
  23     | v -> v
  24
  25 type Region = { minX : float32; maxX : float32; minY : float32; maxY : float32 } with
  26     member this.Contains px py : bool =
  27         px >= this.minX && px <= this.maxX &&
  28         py >= this.minY && py <= this.maxY
  29
  30     member this.IsSub otherRegion : bool =
  31         this.minX >= otherRegion.minX && this.maxX <= otherRegion.maxX &&
  32         this.minY >= otherRegion.minY && this.maxY <= otherRegion.maxY
  33
  34     member this.Intersects otherRegion : bool =
  35         this.minX < otherRegion.maxX && this.maxX >= otherRegion.minX &&
  36         this.minY < otherRegion.maxY && this.maxY >= otherRegion.minY
  37
  38 type Tree<'a when 'a :> I2DCoords> =
  39     | Node of float32 * Tree<'a> * Tree<'a>
  40     | Leaf of 'a
  41
  42     static member BuildTree (l : 'a list) : Tree<'a> =
  43         let xSorted = List.toArray l
  44         let ySorted = List.toArray l
  45         Array.sortInPlaceWith cmpX xSorted
  46         Array.sortInPlaceWith cmpY ySorted
  47
  48         let rec buildTreeFromSortedArray (pXSorted : 'a[]) (pYSorted : 'a[]) (depth : int) : Tree<'a> =
  49             if pXSorted.Length = 1 then
  50                 Leaf pXSorted.[0]
  51             else
  52                 if depth % 2 = 1 then // 'depth' is odd -> vertical splitting else horizontal splitting.
  53                     let leftX, rightX = Array.splitAt ((pXSorted.Length + 1) / 2) pXSorted
  54                     let splitElement = Array.last leftX
  55                     let leftY, rightY = Array.partition (fun (e : 'a) -> cmpX e splitElement <= 0) pYSorted // FIXME: Maybe this operation can be optimized.
  56                     Node (splitElement.X, buildTreeFromSortedArray leftX leftY (depth + 1), buildTreeFromSortedArray rightX rightY (depth + 1))
  57                 else
  58                     let downY, upY = Array.splitAt ((pYSorted.Length + 1) / 2) pYSorted
  59                     let splitElement = Array.last downY
  60                     let downX, upX = Array.partition (fun (e : 'a) -> cmpY e splitElement <= 0) pXSorted // FIXME: Maybe this operation can be optimized.
  61                     Node (splitElement.Y, buildTreeFromSortedArray downX downY (depth + 1), buildTreeFromSortedArray upX upY (depth + 1))
  62
  63         buildTreeFromSortedArray xSorted ySorted 1
  64
  65     member this.Search (searchRegion : Region) : 'a list =
  66         let rec valuesFrom (tree : Tree<'a>) (acc : 'a list) : 'a list =
  67             match tree with
  68             | Node (_, left, right) -> (valuesFrom right (valuesFrom left acc))
  69             | Leaf v -> v :: acc
  70
  71         let rec searchWithRegion (tree : Tree<'a>) (currentRegion : Region) (depth : int) : 'a list =
  72             match tree with
  73             | Leaf v -> if searchRegion.Contains v.X v.Y then [v] else []
  74             | Node (splitValue, part1, part2) ->
  75                 let valuesInRegion (region : Region) (treeRegion : Tree<'a>) =
  76                     if region.IsSub searchRegion then
  77                         valuesFrom treeRegion []
  78                     elif region.Intersects searchRegion then
  79                         searchWithRegion treeRegion region (depth + 1)
  80                     else
  81                         []
  82
  83                 if depth % 2 = 1 then // Vertical splitting.
  84                     let leftRegion = { currentRegion with maxX = splitValue }
  85                     let rightRegion = { currentRegion with minX = splitValue }
  86                     (valuesInRegion leftRegion part1) @ (valuesInRegion rightRegion part2)
  87                 else // Horizontal splitting.
  88                     let downRegion = { currentRegion with maxY = splitValue }
  89                     let upRegion = { currentRegion with minY = splitValue }
  90                     (valuesInRegion downRegion part1) @ (valuesInRegion upRegion part2)
  91
  92         searchWithRegion this { minX = Single.MinValue; maxX = Single.MaxValue; minY = Single.MinValue; maxY = Single.MaxValue } 1
  93
  94 ///// Tests. TODO: to put in a unit test.
  95
  96 type Point (x : float32, y : float32) =
  97     interface I2DCoords with
  98         member this.X = x
  99         member this.Y = y
 100
 101     override this.ToString () =
 102         sprintf "(%.1f, %.1f)" x y
 103
 104 // TODO: test with identical X or Y coords
 105 let test () =
 106     let pts =
 107         [
 108             Point(1.0f, 1.0f)
 109             Point(2.0f, 2.0f)
 110             Point(1.5f, 3.6f)
 111             Point(3.0f, 3.2f)
 112             Point(4.0f, 4.0f)
 113             Point(3.5f, 1.5f)
 114             Point(2.5f, 0.5f)
 115         ]
 116
 117     let tree = Tree.BuildTree pts
 118     Utils.dprintfn "Tree: %A" tree
 119
 120     let s1 = tree.Search { minX = 0.0f; maxX = 5.0f; minY = 0.0f; maxY = 5.0f } // All points.
 121     Utils.dprintfn "s1: %A" s1
 122
 123     let s2 = tree.Search { minX = 2.8f; maxX = 4.5f; minY = 3.0f; maxY = 4.5f }
 124     Utils.dprintfn "s2: %A" s2
 125
 126     let s3 = tree.Search { minX = 2.0f; maxX = 2.0f; minY = 2.0f; maxY = 2.0f }
 127     Utils.dprintfn "s3: %A" s3
 128
 129 let test2 () =
 130     let pts =
 131         [
 132             Point(1.0f, 1.0f)
 133             Point(1.0f, 2.0f)
 134             Point(1.0f, 3.0f)
 135         ]
 136
 137     let tree = Tree.BuildTree pts
 138     Utils.dprintfn "Tree: %A" tree
 139
 140     let s1 = tree.Search { minX = 1.0f; maxX = 1.0f; minY = 1.0f; maxY = 1.0f }
 141     Utils.dprintfn "s1: %A" s1
 142
 143     let s2 = tree.Search { minX = 1.0f; maxX = 1.0f; minY = 2.0f; maxY = 2.0f }
 144     Utils.dprintfn "s2: %A" s2
 145
 146     // This case result is wrong: FIXME
 147     let s3 = tree.Search { minX = 1.0f; maxX = 1.0f; minY = 3.0f; maxY = 3.0f }
 148     Utils.dprintfn "s3: %A" s3
 149
 150     let s4 = tree.Search { minX = 0.0f; maxX = 2.0f; minY = 0.0f; maxY = 4.0f }
 151     Utils.dprintfn "s4: %A" s4
 152