Changeset 15278 for stable/HeuristicLab.Problems.BinPacking.Views/3.3/Container3DView.xaml.cs

Timestamp:

07/21/17 11:29:08 (7 years ago)

Author:

abeham

Message:

#2762, #2739: merged revisions 14708, 14709, 14971, 14978, 14979, 15167, 15230, 15233, 15240, 15241, 15276 to stable

Location:

stable

Files:

• . (modified) (1 prop)
• HeuristicLab.Problems.BinPacking.Views (modified) (1 prop)
• HeuristicLab.Problems.BinPacking.Views/3.3/Container3DView.xaml.cs (modified) (6 diffs)

stable/HeuristicLab.Problems.BinPacking.Views/3.3/Container3DView.xaml.cs

@@ -19 +19 @@
 
 using System;
+using System.Collections.Generic;
 using System.Linq;
 using System.Windows;
 using System.Windows.Controls;
 using System.Windows.Input;
+using System.Windows.Media;
 using System.Windows.Media.Media3D;
 using HeuristicLab.Problems.BinPacking3D;
@@ -28 +30 @@
 namespace HeuristicLab.Problems.BinPacking.Views {
   public partial class Container3DView : UserControl {
+    private static readonly Color[] colors = new[] {
+      Color.FromRgb(0x40, 0x6A, 0xB7),
+      Color.FromRgb(0xB1, 0x6D, 0x01),
+      Color.FromRgb(0x4E, 0x8A, 0x06),
+      Color.FromRgb(0x75, 0x50, 0x7B),
+      Color.FromRgb(0x72, 0x9F, 0xCF),
+      Color.FromRgb(0xA4, 0x00, 0x00),
+      Color.FromRgb(0xAD, 0x7F, 0xA8),
+      Color.FromRgb(0x29, 0x50, 0xCF),
+      Color.FromRgb(0x90, 0xB0, 0x60),
+      Color.FromRgb(0xF5, 0x89, 0x30),
+      Color.FromRgb(0x55, 0x57, 0x53),
+      Color.FromRgb(0xEF, 0x59, 0x59),
+      Color.FromRgb(0xED, 0xD4, 0x30),
+      Color.FromRgb(0x63, 0xC2, 0x16),
+    };
+
+    private static readonly Color hiddenColor = Color.FromArgb(0x1A, 0xAA, 0xAA, 0xAA);
+    private static readonly Color containerColor = Color.FromArgb(0x7F, 0xAA, 0xAA, 0xAA);
+
     private Point startPos;
     private bool mouseDown = false;
@@ -45 +67 @@
     }
 
+    private Dictionary<int, DiffuseMaterial> materials;
+
     public Container3DView() {
       InitializeComponent();
       camMain.Position = new Point3D(0.5, 3, 3); // for design time we use a different camera position 
+      materials = new Dictionary<int, DiffuseMaterial>();
       Clear();
     }
@@ -74 +99 @@
       if (packing == null) return; // nothing to display
 
-      // draw all items
-      // order by Z position to reduce artifacts (because of transparent objects) 
-      // TODO: improve code to reduce artifacts 
-      //  - from triangle definitions and lighting
-      //  - from rotation and Z-ordering
-
-      foreach (var item in packing.Items.OrderBy(i => packing.Positions[i.Key].Z)) {
-        var position = packing.Positions[item.Key];
-
-        var w = position.Rotated ? item.Value.Depth : item.Value.Width;
-        var h = item.Value.Height;
-        var d = position.Rotated ? item.Value.Width : item.Value.Depth;
-
-        // ignore the item.Material
-
-        // if nothing is selected then draw all cubes opaque 
-        // otherwise draw only the selected cube opaque and all others transparent
-        if (selectedItemKey < 0 || selectedItemKey == item.Key) {
-          AddCube(meshMain, position.X, position.Y, position.Z, w, h, d);
-        } else {
-          AddCube(meshTransparent, position.X, position.Y, position.Z, w, h, d, addInsideTriangles: true);
+      var modelGroup = (Model3DGroup)MyModel.Content;
+      var hiddenMaterial = new DiffuseMaterial(new SolidColorBrush(hiddenColor));
+
+      if (selectedItemKey >= 0) {
+        var selectedItem = packing.Items.Single(x => selectedItemKey == x.Key);
+        var selectedPos = packing.Positions[selectedItem.Key];
+
+        var colorIdx = selectedItem.Value.Material;
+        while (colorIdx < 0) colorIdx += colors.Length;
+        colorIdx = colorIdx % colors.Length;
+        var color = colors[colorIdx];
+        var material = new DiffuseMaterial { Brush = new SolidColorBrush(color) };
+        materials[selectedItem.Value.Material] = material;
+
+        var selectedModel = new GeometryModel3D { Geometry = new MeshGeometry3D(), Material = material };
+        AddSolidCube((MeshGeometry3D)selectedModel.Geometry, selectedPos.X, selectedPos.Y, selectedPos.Z,
+          selectedPos.Rotated ? selectedItem.Value.Depth : selectedItem.Value.Width,
+          selectedItem.Value.Height,
+          selectedPos.Rotated ? selectedItem.Value.Width : selectedItem.Value.Depth);
+        modelGroup.Children.Add(selectedModel);
+
+        foreach (var item in packing.Items.Where(x => selectedItemKey != x.Key)) {
+          var position = packing.Positions[item.Key];
+
+          var w = position.Rotated ? item.Value.Depth : item.Value.Width;
+          var h = item.Value.Height;
+          var d = position.Rotated ? item.Value.Width : item.Value.Depth;
+
+          var model = new GeometryModel3D { Geometry = new MeshGeometry3D(), Material = hiddenMaterial };
+          AddWireframeCube((MeshGeometry3D)model.Geometry, position.X, position.Y, position.Z, w, h, d, 1);
+          modelGroup.Children.Add(model);
+        }
+      } else {
+        foreach (var item in packing.Items) {
+          var position = packing.Positions[item.Key];
+
+          var w = position.Rotated ? item.Value.Depth : item.Value.Width;
+          var h = item.Value.Height;
+          var d = position.Rotated ? item.Value.Width : item.Value.Depth;
+
+          var model = new GeometryModel3D { Geometry = new MeshGeometry3D() };
+          DiffuseMaterial material;
+          if (!materials.TryGetValue(item.Value.Material, out material)) {
+            var colorIdx = item.Value.Material;
+            while (colorIdx < 0) colorIdx += colors.Length;
+            colorIdx = colorIdx % colors.Length;
+            var color = colors[colorIdx];
+            material = new DiffuseMaterial { Brush = new SolidColorBrush(color) };
+            materials[item.Value.Material] = material;
+          }
+          var selectedModel = new GeometryModel3D { Geometry = new MeshGeometry3D(), Material = material };
+          AddSolidCube((MeshGeometry3D)selectedModel.Geometry, position.X, position.Y, position.Z, w, h, d);
+          modelGroup.Children.Add(selectedModel);
         }
       }
 
       var container = packing.BinShape;
-      // draw a transparent container
-      AddCube(meshTransparent, container.Origin.X, container.Origin.Y, container.Origin.Z, container.Width, container.Height, container.Depth, addInsideTriangles: true);
-
-      // TODO: support cuboids with different side lengths
-      // apply scaling so that the container fits into the unit cube (necessary for the transformations)
-      scale.ScaleX = 1.0 / (container.Width);
-      scale.ScaleY = 1.0 / (container.Height);
-      scale.ScaleZ = 1.0 / (container.Depth);
+      var containerModel = new GeometryModel3D(new MeshGeometry3D(), new DiffuseMaterial(new SolidColorBrush(containerColor)));
+      modelGroup.Children.Add(containerModel);
+      AddWireframeCube((MeshGeometry3D)containerModel.Geometry, container.Origin.X - .5, container.Origin.Y - .5, container.Origin.Z - .5, container.Width + 1, container.Height + 1, container.Depth + 1);
+
+      var ratio = Math.Max(container.Width, Math.Max(container.Height, container.Depth));
+      scale.ScaleX = 1.0 / ratio;
+      scale.ScaleY = 1.0 / ratio;
+      scale.ScaleZ = 1.0 / ratio;
+
+      scaleZoom.CenterX = rotateX.CenterX = rotateY.CenterX = container.Width / (2.0 * ratio);
+      scaleZoom.CenterY = rotateX.CenterY = rotateY.CenterY = container.Height / (2.0 * ratio);
+      scaleZoom.CenterZ = rotateX.CenterZ = rotateY.CenterZ = container.Depth / (2.0 * ratio);
+
+      camMain.Position = new Point3D(
+        scaleZoom.CenterX,
+        3,
+        3);
+      camMain.LookDirection = new Vector3D(
+        0,
+        scaleZoom.CenterY - camMain.Position.Y,
+        scaleZoom.CenterZ - camMain.Position.Z);
     }
 
 
     private void Clear() {
-      meshInsides.Positions.Clear();
-      meshInsides.TriangleIndices.Clear();
-
-      meshMain.Positions.Clear();
-      meshMain.TriangleIndices.Clear();
-
-      meshTransparent.Positions.Clear();
-      meshTransparent.TriangleIndices.Clear();
+      ((Model3DGroup)MyModel.Content).Children.Clear();
+      materials.Clear();
 
       mouseDown = false;
@@ -128 +192 @@
       if (!mouseDown) return;
       var pos = e.GetPosition((IInputElement)this);
-      rotateX.Angle = startAngleX + (pos.X - startPos.X) / 4;
-      rotateY.Angle = startAngleY + (pos.Y - startPos.Y) / 4;
+
+      ((AxisAngleRotation3D)rotateX.Rotation).Angle = startAngleX + (pos.X - startPos.X) / 4;
+      ((AxisAngleRotation3D)rotateY.Rotation).Angle = startAngleY + (pos.Y - startPos.Y) / 4;
     }
 
     private void Container3DView_MouseDown(object sender, MouseButtonEventArgs e) {
-      startAngleX = rotateX.Angle;
-      startAngleY = rotateY.Angle;
+      startAngleX = ((AxisAngleRotation3D)rotateX.Rotation).Angle;
+      startAngleY = ((AxisAngleRotation3D)rotateY.Rotation).Angle;
       this.startPos = e.GetPosition((IInputElement)this);
       this.mouseDown = true;
@@ -155 +220 @@
     }
 
+    private void Container3DView_OnMouseEnter(object sender, MouseEventArgs e) {
+      Focus(); // for mouse wheel events
+    }
 
     #region helper for cubes
-
-    private void AddCube(MeshGeometry3D mesh, int x, int y, int z, int width, int height, int depth, bool addInsideTriangles = false) {
-      AddOutsideTriangles(mesh, AddPoints(mesh, x, y, z, width, height, depth));
-      if (addInsideTriangles) AddInsideTriangles(meshInsides, AddPoints(meshInsides, x, y, z, width, height, depth));
-    }
-
-    private void AddOutsideTriangles(MeshGeometry3D mesh, int[] pointIdx) {
-      // point indices counter-clockwise
-      // back side
-      mesh.TriangleIndices.Add(pointIdx[0]);
-      mesh.TriangleIndices.Add(pointIdx[2]);
-      mesh.TriangleIndices.Add(pointIdx[1]);
-
-      mesh.TriangleIndices.Add(pointIdx[0]);
-      mesh.TriangleIndices.Add(pointIdx[3]);
-      mesh.TriangleIndices.Add(pointIdx[2]);
-
-      // bottom side
-      mesh.TriangleIndices.Add(pointIdx[5]);
-      mesh.TriangleIndices.Add(pointIdx[4]);
-      mesh.TriangleIndices.Add(pointIdx[0]);
-
-      mesh.TriangleIndices.Add(pointIdx[5]);
-      mesh.TriangleIndices.Add(pointIdx[0]);
-      mesh.TriangleIndices.Add(pointIdx[1]);
-
-      // right side
-      mesh.TriangleIndices.Add(pointIdx[2]);
-      mesh.TriangleIndices.Add(pointIdx[6]);
-      mesh.TriangleIndices.Add(pointIdx[5]);
-
-      mesh.TriangleIndices.Add(pointIdx[1]);
-      mesh.TriangleIndices.Add(pointIdx[2]);
-      mesh.TriangleIndices.Add(pointIdx[5]);
-
-      // left side
-      mesh.TriangleIndices.Add(pointIdx[7]);
-      mesh.TriangleIndices.Add(pointIdx[3]);
-      mesh.TriangleIndices.Add(pointIdx[4]);
-
-      mesh.TriangleIndices.Add(pointIdx[4]);
-      mesh.TriangleIndices.Add(pointIdx[3]);
-      mesh.TriangleIndices.Add(pointIdx[0]);
-
-      // top side
-      mesh.TriangleIndices.Add(pointIdx[3]);
-      mesh.TriangleIndices.Add(pointIdx[7]);
-      mesh.TriangleIndices.Add(pointIdx[6]);
-
-      mesh.TriangleIndices.Add(pointIdx[3]);
-      mesh.TriangleIndices.Add(pointIdx[6]);
-      mesh.TriangleIndices.Add(pointIdx[2]);
-
-      // front side
-      mesh.TriangleIndices.Add(pointIdx[6]);
-      mesh.TriangleIndices.Add(pointIdx[7]);
-      mesh.TriangleIndices.Add(pointIdx[4]);
-
-      mesh.TriangleIndices.Add(pointIdx[6]);
-      mesh.TriangleIndices.Add(pointIdx[4]);
-      mesh.TriangleIndices.Add(pointIdx[5]);
-    }
-
-    private void AddInsideTriangles(MeshGeometry3D mesh, int[] pointIdx) {
-      // for each cube we also draw the triangles facing inside because they are visible when a cube is transparent
-      // point indices clockwise
-
-      // back side
-      mesh.TriangleIndices.Add(pointIdx[1]);
-      mesh.TriangleIndices.Add(pointIdx[2]);
-      mesh.TriangleIndices.Add(pointIdx[0]);
-
-      mesh.TriangleIndices.Add(pointIdx[2]);
-      mesh.TriangleIndices.Add(pointIdx[3]);
-      mesh.TriangleIndices.Add(pointIdx[0]);
-
-      // bottom side
-      mesh.TriangleIndices.Add(pointIdx[0]);
-      mesh.TriangleIndices.Add(pointIdx[4]);
-      mesh.TriangleIndices.Add(pointIdx[5]);
-
-      mesh.TriangleIndices.Add(pointIdx[1]);
-      mesh.TriangleIndices.Add(pointIdx[0]);
-      mesh.TriangleIndices.Add(pointIdx[5]);
-
-      // right side
-      mesh.TriangleIndices.Add(pointIdx[5]);
-      mesh.TriangleIndices.Add(pointIdx[6]);
-      mesh.TriangleIndices.Add(pointIdx[2]);
-
-      mesh.TriangleIndices.Add(pointIdx[5]);
-      mesh.TriangleIndices.Add(pointIdx[2]);
-      mesh.TriangleIndices.Add(pointIdx[1]);
-
-      // left side
-      mesh.TriangleIndices.Add(pointIdx[4]);
-      mesh.TriangleIndices.Add(pointIdx[3]);
-      mesh.TriangleIndices.Add(pointIdx[7]);
-
-      mesh.TriangleIndices.Add(pointIdx[0]);
-      mesh.TriangleIndices.Add(pointIdx[3]);
-      mesh.TriangleIndices.Add(pointIdx[4]);
-
-      // top side
-      mesh.TriangleIndices.Add(pointIdx[6]);
-      mesh.TriangleIndices.Add(pointIdx[7]);
-      mesh.TriangleIndices.Add(pointIdx[3]);
-
-      mesh.TriangleIndices.Add(pointIdx[2]);
-      mesh.TriangleIndices.Add(pointIdx[6]);
-      mesh.TriangleIndices.Add(pointIdx[3]);
-
-      // front side
-      mesh.TriangleIndices.Add(pointIdx[4]);
-      mesh.TriangleIndices.Add(pointIdx[7]);
-      mesh.TriangleIndices.Add(pointIdx[6]);
-
-      mesh.TriangleIndices.Add(pointIdx[5]);
-      mesh.TriangleIndices.Add(pointIdx[4]);
-      mesh.TriangleIndices.Add(pointIdx[6]);
-    }
-
-    private int[] AddPoints(MeshGeometry3D mesh, int x, int y, int z, int w, int h, int d) {
+    /// <summary>
+    /// Creates a solid cube by adding the respective points and triangles.
+    /// </summary>
+    /// <param name="mesh">The mesh to which points and triangles are added.</param>
+    /// <param name="x">The leftmost point</param>
+    /// <param name="y">The frontmost point</param>
+    /// <param name="z">The lowest point</param>
+    /// <param name="width">The extension to the right</param>
+    /// <param name="height">The extension to the back</param>
+    /// <param name="depth">The extension to the top</param>
+    private void AddSolidCube(MeshGeometry3D mesh, int x, int y, int z, int width, int height, int depth) {
       // ground
       mesh.Positions.Add(new Point3D(x, y, z));
-      mesh.Positions.Add(new Point3D(x + w, y, z));
-      mesh.Positions.Add(new Point3D(x + w, y + h, z));
-      mesh.Positions.Add(new Point3D(x, y + h, z));
+      mesh.Positions.Add(new Point3D(x + width, y, z));
+      mesh.Positions.Add(new Point3D(x + width, y + height, z));
+      mesh.Positions.Add(new Point3D(x, y + height, z));
       // top
-      mesh.Positions.Add(new Point3D(x, y, z + d));
-      mesh.Positions.Add(new Point3D(x + w, y, z + d));
-      mesh.Positions.Add(new Point3D(x + w, y + h, z + d));
-      mesh.Positions.Add(new Point3D(x, y + h, z + d));
-
-      return Enumerable.Range(mesh.Positions.Count - 8, 8).ToArray();
+      mesh.Positions.Add(new Point3D(x, y, z + depth));
+      mesh.Positions.Add(new Point3D(x + width, y, z + depth));
+      mesh.Positions.Add(new Point3D(x + width, y + height, z + depth));
+      mesh.Positions.Add(new Point3D(x, y + height, z + depth));
+
+      // front
+      AddPlane(mesh, 0, 1, 5, 4);
+      // right side
+      AddPlane(mesh, 1, 2, 6, 5);
+      // back
+      AddPlane(mesh, 3, 7, 6, 2);
+      // left side
+      AddPlane(mesh, 0, 4, 7, 3);
+      // top
+      AddPlane(mesh, 4, 5, 6, 7);
+      // bottom
+      AddPlane(mesh, 0, 3, 2, 1);
+    }
+
+    /// <summary>
+    /// Creates a wireframe cube by adding the respective points and triangles.
+    /// </summary>
+    /// <param name="mesh">The mesh to which points and triangles are added.</param>
+    /// <param name="x">The leftmost point</param>
+    /// <param name="y">The frontmost point</param>
+    /// <param name="z">The lowest point</param>
+    /// <param name="width">The extension to the right</param>
+    /// <param name="height">The extension to the back</param>
+    /// <param name="depth">The extension to the top</param>
+    /// <param name="thickness">The thickness of the frame</param>
+    private void AddWireframeCube(MeshGeometry3D mesh, double x, double y, double z, double width, double height, double depth, double thickness = double.NaN) {
+      // default thickness of the wireframe is 5% of smallest dimension
+      if (double.IsNaN(thickness))
+        thickness = Math.Min(width, Math.Min(height, depth)) * 0.05;
+
+      // The cube contains of 8 corner, each corner has 4 points:
+      // 1. The corner point
+      // 2. A point on the edge to the right of the corner
+      // 3. A point on the edge atop or below the corner
+      // 4. A point on the edge to the left of the corner
+
+      // Point 0, Front Left Bottom
+      mesh.Positions.Add(new Point3D(x, y, z));
+      mesh.Positions.Add(new Point3D(x + thickness, y, z));
+      mesh.Positions.Add(new Point3D(x, y, z + thickness));
+      mesh.Positions.Add(new Point3D(x, y + thickness, z));
+
+      // Point 1, Front Right Bottom
+      mesh.Positions.Add(new Point3D(x + width, y, z));
+      mesh.Positions.Add(new Point3D(x + width, y + thickness, z));
+      mesh.Positions.Add(new Point3D(x + width, y, z + thickness));
+      mesh.Positions.Add(new Point3D(x + width - thickness, y, z));
+
+      // Point 2, Back Right Bottom
+      mesh.Positions.Add(new Point3D(x + width, y + height, z));
+      mesh.Positions.Add(new Point3D(x + width - thickness, y + height, z));
+      mesh.Positions.Add(new Point3D(x + width, y + height, z + thickness));
+      mesh.Positions.Add(new Point3D(x + width, y + height - thickness, z));
+
+      // Point 3, Back Left Bottom
+      mesh.Positions.Add(new Point3D(x, y + height, z));
+      mesh.Positions.Add(new Point3D(x, y + height - thickness, z));
+      mesh.Positions.Add(new Point3D(x, y + height, z + thickness));
+      mesh.Positions.Add(new Point3D(x + thickness, y + height, z));
+
+      // Point 4, Front Left Top
+      mesh.Positions.Add(new Point3D(x, y, z + depth));
+      mesh.Positions.Add(new Point3D(x + thickness, y, z + depth));
+      mesh.Positions.Add(new Point3D(x, y, z + depth - thickness));
+      mesh.Positions.Add(new Point3D(x, y + thickness, z + depth));
+
+      // Point 5, Front Right Top
+      mesh.Positions.Add(new Point3D(x + width, y, z + depth));
+      mesh.Positions.Add(new Point3D(x + width, y + thickness, z + depth));
+      mesh.Positions.Add(new Point3D(x + width, y, z + depth - thickness));
+      mesh.Positions.Add(new Point3D(x + width - thickness, y, z + depth));
+
+      // Point 6, Back Right Top
+      mesh.Positions.Add(new Point3D(x + width, y + height, z + depth));
+      mesh.Positions.Add(new Point3D(x + width - thickness, y + height, z + depth));
+      mesh.Positions.Add(new Point3D(x + width, y + height, z + depth - thickness));
+      mesh.Positions.Add(new Point3D(x + width, y + height - thickness, z + depth));
+
+      // Point 7, Back Left Top
+      mesh.Positions.Add(new Point3D(x, y + height, z + depth));
+      mesh.Positions.Add(new Point3D(x, y + height - thickness, z + depth));
+      mesh.Positions.Add(new Point3D(x, y + height, z + depth - thickness));
+      mesh.Positions.Add(new Point3D(x + thickness, y + height, z + depth));
+
+      // Point 0, non-edge
+      mesh.Positions.Add(new Point3D(x + thickness, y, z + thickness));
+      mesh.Positions.Add(new Point3D(x, y + thickness, z + thickness));
+      mesh.Positions.Add(new Point3D(x + thickness, y + thickness, z));
+
+      // Point 1, non-edge
+      mesh.Positions.Add(new Point3D(x + width, y + thickness, z + thickness));
+      mesh.Positions.Add(new Point3D(x + width - thickness, y, z + thickness));
+      mesh.Positions.Add(new Point3D(x + width - thickness, y + thickness, z));
+
+      // Point 2, non-edge
+      mesh.Positions.Add(new Point3D(x + width - thickness, y + height, z + thickness));
+      mesh.Positions.Add(new Point3D(x + width, y + height - thickness, z + thickness));
+      mesh.Positions.Add(new Point3D(x + width - thickness, y + height - thickness, z));
+
+      // Point 3, non-edge
+      mesh.Positions.Add(new Point3D(x, y + height - thickness, z + thickness));
+      mesh.Positions.Add(new Point3D(x + thickness, y + height, z + thickness));
+      mesh.Positions.Add(new Point3D(x + thickness, y + height - thickness, z));
+
+      // Point 4, non-edge
+      mesh.Positions.Add(new Point3D(x + thickness, y, z + depth - thickness));
+      mesh.Positions.Add(new Point3D(x, y + thickness, z + depth - thickness));
+      mesh.Positions.Add(new Point3D(x + thickness, y + thickness, z + depth));
+
+      // Point 5, non-edge
+      mesh.Positions.Add(new Point3D(x + width, y + thickness, z + depth - thickness));
+      mesh.Positions.Add(new Point3D(x + width - thickness, y, z + depth - thickness));
+      mesh.Positions.Add(new Point3D(x + width - thickness, y + thickness, z + depth));
+
+      // Point 6, non-edge
+      mesh.Positions.Add(new Point3D(x + width - thickness, y + height, z + depth - thickness));
+      mesh.Positions.Add(new Point3D(x + width, y + height - thickness, z + depth - thickness));
+      mesh.Positions.Add(new Point3D(x + width - thickness, y + height - thickness, z + depth));
+
+      // Point 7, non-edge
+      mesh.Positions.Add(new Point3D(x, y + height - thickness, z + depth - thickness));
+      mesh.Positions.Add(new Point3D(x + thickness, y + height, z + depth - thickness));
+      mesh.Positions.Add(new Point3D(x + thickness, y + height - thickness, z + depth));
+
+      // Draw the 24 corner plates
+      AddPlane(mesh, 0, 1, 32, 2);
+      AddPlane(mesh, 0, 2, 33, 3);
+      AddPlane(mesh, 0, 3, 34, 1);
+
+      AddPlane(mesh, 4, 6, 36, 7);
+      AddPlane(mesh, 4, 5, 35, 6);
+      AddPlane(mesh, 4, 7, 37, 5);
+
+      AddPlane(mesh, 8, 10, 39, 11);
+      AddPlane(mesh, 8, 9, 38, 10);
+      AddPlane(mesh, 8, 11, 40, 9);
+
+      AddPlane(mesh, 12, 13, 41, 14);
+      AddPlane(mesh, 12, 14, 42, 15);
+      AddPlane(mesh, 12, 15, 43, 13);
+
+      AddPlane(mesh, 16, 18, 44, 17);
+      AddPlane(mesh, 16, 19, 45, 18);
+      AddPlane(mesh, 16, 17, 46, 19);
+
+      AddPlane(mesh, 20, 23, 48, 22);
+      AddPlane(mesh, 20, 22, 47, 21);
+      AddPlane(mesh, 20, 21, 49, 23);
+
+      AddPlane(mesh, 24, 27, 51, 26);
+      AddPlane(mesh, 24, 26, 50, 25);
+      AddPlane(mesh, 24, 25, 52, 27);
+
+      AddPlane(mesh, 28, 31, 54, 30);
+      AddPlane(mesh, 28, 30, 53, 29);
+      AddPlane(mesh, 28, 29, 55, 31);
+
+      // Draw the connecting plates
+      // on the bottom
+      AddPlane(mesh, 1, 7, 36, 32);
+      AddPlane(mesh, 1, 34, 37, 7);
+
+      AddPlane(mesh, 5, 11, 39, 35);
+      AddPlane(mesh, 5, 37, 40, 11);
+
+      AddPlane(mesh, 9, 15, 42, 38);
+      AddPlane(mesh, 9, 40, 43, 15);
+
+      AddPlane(mesh, 13, 3, 33, 41);
+      AddPlane(mesh, 13, 43, 34, 3);
+
+      // between bottom and top
+      AddPlane(mesh, 2, 32, 44, 18);
+      AddPlane(mesh, 2, 18, 45, 33);
+
+      AddPlane(mesh, 6, 22, 48, 36);
+      AddPlane(mesh, 6, 35, 47, 22);
+
+      AddPlane(mesh, 10, 26, 51, 39);
+      AddPlane(mesh, 10, 38, 50, 26);
+
+      AddPlane(mesh, 14, 30, 54, 42);
+      AddPlane(mesh, 14, 41, 53, 30);
+
+      // on the top
+      AddPlane(mesh, 17, 44, 48, 23);
+      AddPlane(mesh, 17, 23, 49, 46);
+
+      AddPlane(mesh, 21, 47, 51, 27);
+      AddPlane(mesh, 21, 27, 52, 49);
+
+      AddPlane(mesh, 25, 50, 54, 31);
+      AddPlane(mesh, 25, 31, 55, 52);
+
+      AddPlane(mesh, 29, 19, 46, 55);
+      AddPlane(mesh, 29, 53, 45, 19);
+    }
+
+    /// <summary>
+    /// Adds a plane by two triangles. The indices of the points have to be given
+    /// in counter-clockwise sequence.
+    /// </summary>
+    /// <param name="mesh">The mesh to add the triangles to</param>
+    /// <param name="a">The index of the first point</param>
+    /// <param name="b">The index of the second point</param>
+    /// <param name="c">The index of the third point</param>
+    /// <param name="d">The index of the fourth point</param>
+    private void AddPlane(MeshGeometry3D mesh, int a, int b, int c, int d) {
+      // two triangles form a plane
+      mesh.TriangleIndices.Add(a);
+      mesh.TriangleIndices.Add(b);
+      mesh.TriangleIndices.Add(d);
+      mesh.TriangleIndices.Add(c);
+      mesh.TriangleIndices.Add(d);
+      mesh.TriangleIndices.Add(b);
     }
     #endregion
 
-    private void Container3DView_OnMouseEnter(object sender, MouseEventArgs e) {
-      Focus(); // for mouse wheel events
-    }
   }
 }