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// function let point x // function let point3D
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to initialize a point y = new Point(x, y) to initialize a "d point x y = new Point3D(x, y, 0.0)
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// create all the points necessary for a square in the plane let createSquare f (xStep : float) (yStep : float) (list : List<_>) (x : int) (y : int) = let x' = Float.of_int x * xStep let y' = Float.of_int y * yStep list.Add(f x' y') list.Add(f (x' + xStep) y') list.Add(f (x' + xStep) (y' + yStep)) list.Add(f (x' + xStep) (y' + yStep)) list.Add(f x' (y' + yStep)) list.Add(f x' y') // create all items in a plane let createPlanePoints f xRes yRes = let xStep = 1.0 / Float.of_int xRes let yStep = 1.0 / Float.of_int yRes createPlaneItemList (createSquare f xStep yStep) xRes yRes // create the 3D positions for a plane, i.e., the thing that says where // the plane will be in 3D space let createPlanePositions xRes yRes = let list = createPlanePoints point3D xRes yRes new Point3DCollection(list) // create the texture mappings for a plane, i.e., the thing that // maps the 2D image to the 3D plane let createPlaneTextures xRes yRes = let list = createPlanePoints point xRes yRes new PointCollection(list) // create indices list for all our triangles let createIndicesPlane width height = let list = new System.Collections.Generic.List<int>() for index = 0 to width * height * 6 do list.Add(index) new Int32Collection(list) // center the plane in the field of view let mapPositionsCenter (positions : Point3DCollection) = let newPositions = positions |> Seq.map
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(fun position -> new Point3D( (position.X - 0.5 ) * -1.0 , (position.Y - 0.5 ) * -1.0, position.Z)) new Point3DCollection(newPositions) // create a plane and add it to the given mesh let addPlaneToMesh (mesh : MeshGeometry3D) xRes yRes = mesh.Positions <- mapPositionsCenter (createPlanePositions xRes yRes) mesh.TextureCoordinates <- createPlaneTextures xRes yRes mesh.TriangleIndices <- createIndicesPlane xRes yRes let movingWaves (t : float) x y = (Math.Cos((x + t) * Math.PI * 4.0) / 3.0) * (Math.Cos(y * Math.PI * 2.0) / 3.0) // create our window let window = createWindow "Window2.xaml" let mesh = // grab the 3D view port let viewport = window.FindName("ViewPort") : > Viewport3D // find all the meshes and get the first one let meshes = findMeshes viewport let mesh = Seq.hd meshes // add plane to the mesh addPlaneToMesh mesh 20 20 mesh let changePositions () = let dispatcherTimer = new DispatcherTimer() dispatcherTimer.Tick.Add (fun e -> let t = (float_of_int DateTime.Now.Millisecond) / 2000.0 let newPositions = mesh.Positions |> Seq.map (fun position -> let z = movingWaves t position.X position.Y new Point3D(position.X, position.Y, z)) mesh.Positions <- new Point3DCollection(newPositions)) dispatcherTimer.Interval <- new TimeSpan(0,0,0,0,100) dispatcherTimer.Start()
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let main() = let app = new Application() changePositions() // show the window app.Run(window) |> ignore [<STAThread>] do main() Figure 8-12 shows the resulting window. It doesn t show off the animated results, so I encourage you to try the application yourself.
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Figure 8-12. A 3D scene created using XAML and F# One other thing I encourage you to do is play with this sample in fsi. You can subtly alter the sample to run inside fsi, and then the function applied to the plane can be altered dynamically. The original script must be altered in several small ways. First, you must set the reference to the .dll files in an fsi style: #I #r #r #r @"C:\Program Files\Reference Assemblies\Microsoft\Framework\v3.0" ;; @"PresentationCore.dll" ;; @"PresentationFramework.dll" ;; @"WindowsBase.dll" ;;
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Then, you must alter the changePositions function to use a mutable function: // mutable function that is used within changePositions function let mutable f = (fun (t : float) (x : float) (y : float) -> 0.0) // function for changing the plane over time let changePositions () = let dispatcherTimer = new DispatcherTimer() dispatcherTimer.Tick.Add (fun e -> let t = (float_of_int DateTime.Now.Millisecond) / 2000.0 let newPositions = mesh.Positions |> Seq.map (fun position -> let z = f t position.X position.Y new Point3D(position.X, position.Y, z)) mesh.Positions <- new Point3DCollection(newPositions)) dispatcherTimer.Interval <- new TimeSpan(0,0,0,0,100) dispatcherTimer.Start() Then, finally, you show the window using its .Show() method rather than the Application class s Run method, not forgetting to set its Topmost property to true so that it is easy to interact with the window and see the results: // show the window, set it the top, and activate the function that will // set it moving window.Show() window.Topmost <- true changePositions () Finally, you need to define some other functions to map across the plane. This can be any function that takes three floating-point numbers (the first representing the time and the next two representing the X and Y coordinates, respectively) and returns a third floating-point representing the Z coordinate. I m practically fond of using sine and cosine functions because these generate interesting wave patterns. Here are some examples of what you could use, but please feel free to invent your own: let cosXY _ x y = Math.Cos(x * Math.PI) * Math.Cos(y * Math.PI) let movingCosXY (t : float) x y = Math.Cos((x + t) * Math.PI) * Math.Cos((y - t) * Math.PI) You can then easily apply these functions to the plane by updating the mutable function: f <- movingCosXY Using this technique produces the image in Figure 8-13.
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