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Freitag, 11. November 2011

A* Star Pathfinding with Jump Point Search. F#, Wpf and Visualisation.

Im letzten Beitrag habe ich meiner Implementierung vom Jump Point Search Algorithmus gezeigt. Hier geht es in erster Linie um F# und Wpf.
Da es in Visual Studio bereits eine Projekt-Vorlage für F# Wpf gibt, habe ich sie auch genommen. Und zwar handelt es sich dabei um eine MVVM-Vorlage. Daher veruschte ich im Rahmen vom MVVM-Pattern zu bleiben.

Typen für das Model und
//JumpSearchModel.fs
//MVVM Model Types.
module JumpMazeModelType =
    open Maze.JumpPointSearchType
    type SelectedCoin =
        | Start of float * float
        | Finish of float * float

    type MazeEnvironment = 
        { maze : JumpPointEnvironment; obstacles : Set<(int * int)>; 
          wallSize : float; coinX : float; coinY : float; targetX : float; targetY : float}
        member this.IsEmpty = Map.isEmpty <| this.maze.grid

    let empty = { maze = empty; obstacles = Set.empty;
                  wallSize = 20.0; coinX = 0.0; coinY = 0.0;targetX = 0.0; targetY = 0.0 }
das ViewModel.
//JumpSearchViewModel.fs
//MVVM ViewModel Class Type
type JumpSearchViewModel() as x =   
    class
        inherit ViewModelBase()
        let mutable env : MazeEnvironment  = JumpMazeModel.empty
        let mutable selectedCoin : SelectedCoin = Start (0.0, 0.0)
        ...
    end
DataContext vom View.
<Window.DataContext>
        <ViewModel:JumpSearchViewModel></ViewModel:JumpSearchViewModel>
</Window.DataContext>
Ich habe nichts besseres gefunden, als das Canvas-Element im CommandParameter-Binding vom Button-Element anzugeben, um es später im ViewModel für den Aufruf von Mouse.GetPosition und für den Zugriff auf die Children-Auflistung des Canvas-Elementes zu verwenden.
...
<Button Command="{Binding CreateMazeCommand}"  CommandParameter="{Binding ElementName=canvas}" >Init Maze</Button>
...
//JumpSearchViewModel.fs
type JumpSearchViewModel() as x=   
    class
        ...
        let mutable canvas : Canvas = null
        
        member x.CreateMazeCommand = 
            new RelayCommand ((fun canExecute ->  x.VerifyX() = null &&  x.VerifyY() = null), (fun element -> x.CreateMaze(element)))

        member x.CreateMaze(element) =
            canvas <- element :?> Canvas
...
Die erste Herausforderung war die Start- und Ziel-Spielmarke mit der Tastatur auf dem Labyrinthbrett zu bewegen. Genauer gesagt wird einen von beiden Chips per Mausklick ausgewählt und dann mit einer Pfeiltaste auf die nächste Zelle bewegt, wenn es da gerade kein Hindernis gibt.
...
<!--coins moving with keys-->
<Window.InputBindings>
        <KeyBinding Command="{Binding CoinMoveCommand}" Key="Down" >
            <KeyBinding.CommandParameter>
                <i:Key>Down</i:Key>
            </KeyBinding.CommandParameter>
        </KeyBinding>
        <KeyBinding Command="{Binding CoinMoveCommand}" Key="Up">
            <KeyBinding.CommandParameter>
                <i:Key>Up</i:Key>
            </KeyBinding.CommandParameter>
        </KeyBinding>
        <KeyBinding Command="{Binding CoinMoveCommand}" Key="Left">
            <KeyBinding.CommandParameter>
                <i:Key>Left</i:Key>
            </KeyBinding.CommandParameter>
        </KeyBinding>
        <KeyBinding Command="{Binding CoinMoveCommand}" Key="Right">
            <KeyBinding.CommandParameter>
                <i:Key>Right</i:Key>
            </KeyBinding.CommandParameter>
        </KeyBinding>
</Window.InputBindings>
...
<!--start and finish coin-->
<Canvas>
    ...
    <Ellipse Name="coin" Fill="Blue"                     
     Canvas.Left="{Binding Path=CoinX }"  
                     Canvas.Top="{Binding Path=CoinY }" />
    <Ellipse Name="target" Canvas.Left="{Binding Path=TargetX}"  
                     Canvas.Top="{Binding Path=TargetY}" />
...
</Canvas>
//JumpSearchViewModel.fs
type JumpSearchViewModel() as x =   
    class
        ...
        member x.CoinX 
            with get () =  
                env.coinX   
            and set value = 
                env <- JumpMazeModel.setCoinX env value coin
                base.RaisePropertyChangedEvent(<@x.CoinX@>) 
    
        member x.CoinY 
            ...
        member x.TargetX 
            with get () =  
                env.targetX   
            and set value = 
                env <- JumpMazeModel.setCoinX env value coin
                base.RaisePropertyChangedEvent(<@x.TargetX@>) 
    
        member x.TargetY 
            ...
        member x.CoinMoveCommand =
            new RelayCommand ((fun _ -> not env.IsEmpty && not timer.IsEnabled && x.Verify "MazeX" = null && x.Verify "MazeY" = null), 
                                (fun key -> x.CoinMove(key)))
        member x.CoinMove(k)= 
            env <- JumpMazeModel.moveCoin {env with obstacles=obstacles} (k :?> Key) selectedCoin 
            match selectedCoin with
            | Start _ ->
                selectedCoin <- Start (env.coinX, env.coinY)
                base.RaisePropertyChangedEvent(<@x.CoinX@>)
                base.RaisePropertyChangedEvent(<@x.CoinY@>)
            | Finish _ ->
                selectedCoin <- Finish (env.targetX, env.targetY)
                base.RaisePropertyChangedEvent(<@x.TargetX@>)
                base.RaisePropertyChangedEvent(<@x.TargetY@>)
...
//JumpSearchModel.fs
...
    let moveCoin (mazeEnv : MazeEnvironment) key selectedCoin =
        let move (coinX, coinY) =
            let cx, cy = (int coinX) / int mazeEnv.wallSize , (int coinY) / int mazeEnv.wallSize
            match key, mazeEnv.IsEmpty with
            | _, true -> coinX, coinY
            | Key.Down, false ->             
                if cy >= mazeEnv.maze.h - 1 || (Set.exists ( fun w -> w = (cx, cy + 1)) mazeEnv.obstacles ) then
                    coinX, coinY
                else
                    coinX, coinY + mazeEnv.wallSize
            | Key.Up, false -> 
                if cy = 0 || (Set.exists ( fun w -> w = (cx, cy - 1)) mazeEnv.obstacles) then
                    coinX, coinY
                else
                    coinX, coinY - mazeEnv.wallSize
            | Key.Right, false -> 
                if cx >= mazeEnv.maze.w - 1 || (Set.exists ( fun w -> w = (cx + 1, cy)) mazeEnv.obstacles) then
                    coinX, coinY
                else
                    coinX + mazeEnv.wallSize, coinY
            | Key.Left, false -> 
                if cx = 0 || (Set.exists ( fun w -> w = (cx - 1, cy)) mazeEnv.obstacles) then
                    coinX, coinY
                else
                    coinX - mazeEnv.wallSize, coinY
            | _, false -> coinX, coinY
        match selectedCoin with
        | Start (dx, dy) -> 
            let moveX, moveY = move (dx, dy)
            {mazeEnv with coinX = moveX; coinY = moveY}
        | Finish (dx, dy) -> 
            let moveX, moveY = move (dx, dy)
            {mazeEnv with targetX = moveX; targetY = moveY}

    let setCoinX (mazeEnv : MazeEnvironment) x selectedCoin = 
        if mazeEnv.IsEmpty |> not && x < float (mazeEnv.maze.w * int mazeEnv.wallSize)  then
               match selectedCoin with
               | Start _ -> {mazeEnv with coinX = x}
               | Finish _ -> {mazeEnv with targetX = x}
        else
            mazeEnv
    
    let setCoinY (mazeEnv : MazeEnvironment) y selectedCoin = 
        ...
Die zweite Herausforderung bestand in der Mausklick-Verarbeitung im Zusammenhang mit der Positionsbestimmung des Mauszeigers. Man sollte per Mausklick entweder ein Chip auswählen können oder ein Hindernis an der entsprechenden Position zu zeichnen oder zu löschen.
...
<Canvas.InputBindings>
                <MouseBinding MouseAction="LeftClick" Command="{Binding LeftClickCommand}" />
                <MouseBinding MouseAction="RightClick"  Command="{Binding RightClickCommand}" />
</Canvas.InputBindings>
...
Wie oben schon erwähnt, wird die Position über den Aufruf von Mouse.GetPosition ermittelt. Die Hindernis-Positionen werden in einer Liste gespeichert und mit der Hilfe von Path-Geometry auf dem Canvas-Element abgebildet.
//JumpSearchViewModel.fs
type JumpSearchViewModel() as x =  
...
        let mutable obstacles = set[]
        let mutable mazeGeometry = Geometry.Parse("")
...
        //maze path geometry.   
        member x.MazeData  
            with get () =  mazeGeometry
            and set value = 
                mazeGeometry <- value
                base.RaisePropertyChangedEvent(<@x.MazeData@>) 

        member x.LeftClickCommand  = 
            // if the mouse position hit the start or the finish coin position,
            // then select a coin. Otherwise add obstacle at mouse position.
            new RelayCommand ((fun canExecute -> not env.IsEmpty && not timer.IsEnabled && x.Verify "MazeX" = null && x.Verify "MazeY" = null), 
                                (fun element -> 
                                    let pos = Mouse.GetPosition(element :?> UIElement)
                                    let cellPos (posx, posy) = (posx / 20.0 |> int), (posy / 20.0 |> int)
                                    //check if the mouse click hit the start or the finish coin position.
                                    match cellPos (pos.X, pos.Y) = cellPos (env.coinX, env.coinY),  cellPos (pos.X, pos.Y) = cellPos (env.targetX, env.targetY) with
                                    | true, _ -> selectedCoin <- Start (env.coinX, env.coinY)
                                    |_, true -> selectedCoin <- Finish (env.targetX, env.targetY)
                                    | _ ->
                                        obstacles <- Set.add (cellPos (pos.X, pos.Y)) obstacles
                                        x.MazeData <- Geometry.Parse(JumpSearchViewModel.CreateMazePath (x.MazeX |> float)  (x.MazeY |> float) x.WallSize obstacles)))
        member x.RightClickCommand  =
            //Remove obstacle at mouse position.
            new RelayCommand ((fun canExecute -> not env.IsEmpty && not timer.IsEnabled && x.Verify "MazeX" = null && x.Verify "MazeY" = null), 
                                (fun element -> 
                                    let pos = Mouse.GetPosition(element :?> UIElement)
                                    let posx, posy = (pos.X/20.0 |> int), (pos.Y / 20.0 |> int)
                                    obstacles <- Set.remove (posx, posy) obstacles
                                    x.MazeData <- Geometry.Parse(JumpSearchViewModel.CreateMazePath (x.MazeX |> float)  (x.MazeY |> float) x.WallSize obstacles)))
...
Das Labyrinth und der Ergebnispfad.
<!--Labirynth and solver result path-->
<Path Name="mazePath" Stroke="Black" Data="{Binding Path=MazeData}" StrokeThickness="4" ></Path>
<Path Name="solverPath" Stroke="Purple"  Data="{Binding Path=SolverData}"  StrokeDashArray="4 2"  StrokeThickness="3" ></Path>
...
<Button Command="{Binding CreateMazeCommand}"  CommandParameter="{Binding ElementName=canvas}"   >Init Maze</Button>
<Button Name="AStar" Command="{Binding CreateAStarCommand}">A* Jump Points Search</Button>
Die komplexe Pfade lassen sich leicht mit der Hilfe von der Markup-Syntax beschreiben.
//JumpSearchViewModel.fs
type JumpSearchViewModel() as x =  
...
        let mutable mazeGeometry = Geometry.Parse("")
        let mutable solverPath = Geometry.Parse("")
...
        static member CreateMazePath w h wallSize points =
        
            let builder = StringBuilder()
        
            let folder (acc : StringBuilder) wall  =
                match wall with
                | (x, y) ->
                    let xf, yf = (float x) * wallSize, (float y) * wallSize
                    acc.Append(sprintf "M%f,%fV%f" xf yf  (yf + wallSize))|>ignore
                    acc.Append(sprintf " H%fV%fH%f" (xf + wallSize) yf xf) 
        
            builder.Append(sprintf "M%f,%f" 0.0 0.0)|>ignore
            builder.Append(sprintf "L%f,%f %f,%f" 0.0   0.0     0.0     (h * wallSize)) |> ignore
            builder.Append(sprintf " %f,%f %f,%f" 0.0   (h * wallSize)  (w * wallSize)  (h * wallSize)) |>ignore
            builder.Append(sprintf " %f,%f %f,%f" (w * wallSize)  (h * wallSize)    (w * wallSize)    0.0) |>ignore
            builder.Append(sprintf " %f,%f %f,%f" (w * wallSize)  0.0   0.0     0.0)|>ignore
            (points |> PSeq.fold folder builder).ToString()
        member x.SolverData  
            with get () =  solverPath
            and set value = 
                solverPath <- value
                base.RaisePropertyChangedEvent(<@x.SolverData@>)

        member x.CreateMazeCommand = 
            new RelayCommand ((fun canExecute -> x.VerifyX = null && x.VerifyY = null), (fun element -> x.CreateMaze(element)))

        member x.CreateMaze(element) =
            ...
            x.MazeData <- Geometry.Parse("")
            x.SolverData <- Geometry.Parse("")
            env <- JumpMazeModel.createMaze x.MazeX x.MazeY x.WallSize
            selectedCoin <- Finish (env.targetX, env.targetY)
            x.TargetX <- env.targetX
            x.TargetY <- env.targetY
            obstacles <- env.obstacles
            x.MazeData <- Geometry.Parse(JumpSearchViewModel.CreateMazePath (x.MazeX |> float)  (x.MazeY |> float) x.WallSize obstacles)

        member x.CreateAStarCommand =
            new RelayCommand (
                                (fun canExecute -> true),
                                 (fun _ -> 
                                     if x.VerifyX = null && x.VerifyY = null then x.CreateAStar()))
        //create solver path.
        member x.CreateAStar() =
            ...
            let jumpPoints = JumpMazeModel.run {env with obstacles = obstacles}
            x.SolverData <- Geometry.Parse(jumpPoints |> JumpMazeModel.resultPath |> JumpMazeModel.solverToPath x.WallSize )
Das Schwierigste war für mich die Visualisierung. Es geht bestimmt irgendwie besser und anders. Meine Lösung ist die Verwendung von der DispatcherTimer-Klasse. Die Positionen von den besuchten Zellen mitsamt Positionen von Vater-Zellen werden in einer Liste - animatePoints - gespeichert. Bei jedem Tick-Ereignis wird ein Listenelement aus der Liste genommen und als ein Ellipse-Element in der Children-Eigenschaft von Canvas gespeichert. Zusätzlich wird der Weg von der Vater-Zelle zu der aktuellen Zelle gezeichnet.
<Canvas Name="canvas">
    ...
    <Path Stroke="BurlyWood" Data="{Binding Path=AnimateData}" StrokeThickness="2"></Path>
    ...
</Canvas>
...
<Button Command="{Binding AnimateCommand}" >Animate</Button>
...
//JumpSearchViewModel.fs
type JumpSearchViewModel() as x=   
    class
...
        let mutable animateData = String.Empty
        let mutable animateResult = String.Empty
        let mutable timer = new DispatcherTimer(DispatcherPriority.Normal)
         //( (int * int) * ((int * int) * Direction) ) list. 
         //( jumpPoint   * (parent      * direction)) list 
        let mutable animatePoints = []
        let mutable undo = []
        let mutable canvas : Canvas = null
        do 
            timer.Interval <- new TimeSpan(0, 0, 0, 0, 400)
            
            timer.Tick.Add(fun _  -> x.AnimateOneStep () )   
...
        member x.AnimateData  
            with get () =  Geometry.Parse(animateData)
            and set value = 
                solverPath <-  Geometry.Parse(value)
                base.RaisePropertyChangedEvent(<@x.AnimateData@>)  
        
        member x.AnimateCommand =
            new RelayCommand ((fun _ -> true), 
                                        (fun _ ->  
                                            match not env.IsEmpty && x.Verify "MazeX" = null && x.Verify "MazeY" = null with
                                            | false -> ()
                                            | true -> 
                                                x.SolverData <- Geometry.Parse("")
                                                x.ResetAnimateData() 
                                                selectedCoin <- Start (env.coinX, env.coinY)
                                                let animateRun =  JumpMazeModel.run {env with obstacles = obstacles}
                                                animateResult <- animateRun |> JumpMazeModel.resultPath |> JumpMazeModel.solverToPath x.WallSize
                                                animatePoints <- animateRun |> JumpMazeModel.animatePoints |> Seq.toList
                                                timer.Start()))

        member x.AnimateOneStep () =
            match animatePoints with
            | [] -> timer.Stop()
            | [((currx, curry),(x',y'), d)] ->
                let x2, y2, x1, y1 = (currx |> float) * env.wallSize + env.wallSize / 2.0, (curry |> float) * env.wallSize + env.wallSize / 2.0, (x' |> float) * env.wallSize + env.wallSize / 2.0, (y' |> float) * env.wallSize + env.wallSize / 2.0
                animateData <- sprintf "%sM%f,%fL%f,%f %f,%f%s" animateData x1 y1 x1 y1 x2 y2 (x.DrawArrow (x2, y2, d))
                x.AnimateData <- animateData
                x.SolverData <-  Geometry.Parse(animateResult)
                timer.Stop()
            | ((currx, curry),(x',y'), d) :: ts->
                let x2, y2, x1, y1 = (currx |> float) * env.wallSize + env.wallSize / 2.0, (curry |> float) * env.wallSize + env.wallSize / 2.0, (x' |> float) * env.wallSize + env.wallSize / 2.0, (y' |> float) * env.wallSize + env.wallSize / 2.0
                // add new Point to Path and draw a line with arrows
                // from the last point to the new point.
                animateData <- sprintf "%sM%f,%fL%f,%f %f,%f%s" animateData x1 y1 x1 y1 x2 y2 (x.DrawArrow (x2, y2, d))
                x.AnimateData <- animateData
                // move the start coin.
                x.CoinX <- x2
                x.CoinY <- y2
                // add new jump point to canvas children collection.
                if canvas <> null then
                    let e = new Ellipse(Width = 6.0, Height= 6.0, Fill = Brushes.Blue)
                    canvas.Children.Add(e)|>ignore
                    Canvas.SetLeft(e, x2 )
                    Canvas.SetTop(e, y2 )
                    //add remove function to undo functon list.
                    undo <- [(fun _ -> canvas.Children.Remove e;)] @ undo

                animatePoints <- ts

        member x.CreateAStar() =
            x.ResetAnimateData()
            ...
        member x.CreateMaze(element) =
            x.ResetAnimateData()
            ...
        member private x.ResetAnimateData() =
            if timer.IsEnabled then
                timer.Stop()
            // Remove all added ellipses.
            List.map (fun f -> f ()) undo|>ignore
            animateData <- String.Empty
            x.AnimateData <- animateData
            ...
Der Code.

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