+++ /dev/null
-module KdTree
-
-open System
-
-type I2DCoords =
- abstract X : float32
- abstract Y : float32
-
-// Compare 'e1' and 'e2' by X.
-let cmpX (e1: I2DCoords) (e2: I2DCoords) : int =
- match e1.X.CompareTo(e2.X) with
- | 0 -> match e1.Y.CompareTo(e2.Y) with
- | 0 -> e1.GetHashCode().CompareTo(e2.GetHashCode())
- | v -> v
- | v -> v
-
-// Compare 'e1' and 'e2' by Y.
-let cmpY (e1: I2DCoords) (e2: I2DCoords) : int =
- match e1.Y.CompareTo(e2.Y) with
- | 0 -> match e1.X.CompareTo(e2.X) with
- | 0 -> e1.GetHashCode().CompareTo(e2.GetHashCode())
- | v -> v
- | v -> v
-
-type Region = { minX: float32; maxX: float32; minY: float32; maxY: float32 } with
- member this.Contains px py : bool =
- px >= this.minX && px <= this.maxX &&
- py >= this.minY && py <= this.maxY
-
- member this.IsSub otherRegion : bool =
- this.minX >= otherRegion.minX && this.maxX <= otherRegion.maxX &&
- this.minY >= otherRegion.minY && this.maxY <= otherRegion.maxY
-
- member this.Intersects otherRegion : bool =
- this.minX < otherRegion.maxX && this.maxX >= otherRegion.minX &&
- this.minY < otherRegion.maxY && this.maxY >= otherRegion.minY
-
-type Tree<'a when 'a :> I2DCoords> =
- | Node of float32 * Tree<'a> * Tree<'a>
- | Leaf of 'a
-
- static member BuildTree (l: 'a list) : Tree<'a> =
- let xSorted = List.toArray l
- let ySorted = List.toArray l
- Array.sortInPlaceWith cmpX xSorted
- Array.sortInPlaceWith cmpY ySorted
-
- let rec buildTreeFromSortedArray (pXSorted: 'a[]) (pYSorted: 'a[]) (depth: int) : Tree<'a> =
- if pXSorted.Length = 1
- then
- Leaf pXSorted.[0]
- else
- if depth % 2 = 1 // 'depth' is odd -> vertical splitting else horizontal splitting.
- then
- let leftX, rightX = Array.splitAt ((pXSorted.Length + 1) / 2) pXSorted
- let splitElement = Array.last leftX
- let leftY, rightY = Array.partition (fun (e: 'a) -> cmpX e splitElement <= 0) pYSorted // FIXME: Maybe this operation can be optimized.
- Node (splitElement.X, buildTreeFromSortedArray leftX leftY (depth + 1), buildTreeFromSortedArray rightX rightY (depth + 1))
- else
- let downY, upY = Array.splitAt ((pYSorted.Length + 1) / 2) pYSorted
- let splitElement = Array.last downY
- let downX, upX = Array.partition (fun (e: 'a) -> cmpY e splitElement <= 0) pXSorted // FIXME: Maybe this operation can be optimized.
- Node (splitElement.Y, buildTreeFromSortedArray downX downY (depth + 1), buildTreeFromSortedArray upX upY (depth + 1))
-
- buildTreeFromSortedArray xSorted ySorted 1
-
- member this.Search (searchRegion: Region) : 'a list =
- let rec valuesFrom (tree: Tree<'a>) : 'a list =
- match tree with
- | Leaf v -> [v]
- | Node (_, part1, part2) -> (valuesFrom part1) @ (valuesFrom part2)
-
- let rec searchWithRegion (tree: Tree<'a>) (currentRegion: Region) (depth: int) : 'a list =
- match tree with
- | Leaf v -> if searchRegion.Contains v.X v.Y then [v] else []
- | Node (splitValue, part1, part2) ->
- let valuesInRegion (region: Region) (treeRegion: Tree<'a>) =
- if region.IsSub searchRegion
- then
- valuesFrom treeRegion
- elif region.Intersects searchRegion
- then
- searchWithRegion treeRegion region (depth + 1)
- else
- []
-
- if depth % 2 = 1 // Vertical splitting.
- then
- let leftRegion = { currentRegion with maxX = splitValue }
- let rightRegion = { currentRegion with minX = splitValue }
- (valuesInRegion leftRegion part1) @ (valuesInRegion rightRegion part2)
- else // Horizontal splitting.
- let downRegion = { currentRegion with maxY = splitValue }
- let upRegion = { currentRegion with minY = splitValue }
- (valuesInRegion downRegion part1) @ (valuesInRegion upRegion part2)
-
- searchWithRegion this { minX = Single.MinValue; maxX = Single.MaxValue; minY = Single.MinValue; maxY = Single.MaxValue } 1
-
-///// Tests. TODO: to put in a unit test.
-
-type Point (x: float32, y: float32) =
- interface I2DCoords with
- member this.X = x
- member this.Y = y
-
- override this.ToString () =
- sprintf "(%.1f, %.1f)" x y
-
-// TODO: test with identical X or Y coords
-let test () =
- let pts = [
- Point(1.0f, 1.0f)
- Point(2.0f, 2.0f)
- Point(1.5f, 3.6f)
- Point(3.0f, 3.2f)
- Point(4.0f, 4.0f)
- Point(3.5f, 1.5f)
- Point(2.5f, 0.5f) ]
-
- let tree = Tree.BuildTree pts
- Utils.dprintfn "Tree: %A" tree
-
- let s1 = tree.Search { minX = 0.0f; maxX = 5.0f; minY = 0.0f; maxY = 5.0f } // All points.
- Utils.dprintfn "s1: %A" s1
-
- let s2 = tree.Search { minX = 2.8f; maxX = 4.5f; minY = 3.0f; maxY = 4.5f }
- Utils.dprintfn "s2: %A" s2
-
- let s3 = tree.Search { minX = 2.0f; maxX = 2.0f; minY = 2.0f; maxY = 2.0f }
- Utils.dprintfn "s3: %A" s3
-
-let test2 () =
- let pts = [
- Point(1.0f, 1.0f)
- Point(1.0f, 2.0f)
- Point(1.0f, 3.0f) ]
-
- let tree = Tree.BuildTree pts
- Utils.dprintfn "Tree: %A" tree
-
- let s1 = tree.Search { minX = 1.0f; maxX = 1.0f; minY = 1.0f; maxY = 1.0f }
- Utils.dprintfn "s1: %A" s1
-
- let s2 = tree.Search { minX = 1.0f; maxX = 1.0f; minY = 2.0f; maxY = 2.0f }
- Utils.dprintfn "s2: %A" s2
-
- // This case result is wrong: FIXME
- let s3 = tree.Search { minX = 1.0f; maxX = 1.0f; minY = 3.0f; maxY = 3.0f }
- Utils.dprintfn "s3: %A" s3
-
- let s4 = tree.Search { minX = 0.0f; maxX = 2.0f; minY = 0.0f; maxY = 4.0f }
- Utils.dprintfn "s4: %A" s4
-
projects / master-thesis.git / blobdiff