Course 3D_WPF: 3D-Computer Graphics with C# + WPF Chapter C4: Sphere Copyright © by V. Miszalok, last update: 2010-01-08
Let me know what you think	Basic sphere   Texture choice with RadioButtons   Rotations   Longitudes-, latitudes- and light-sliders   Cut off slices and floors   Earthquake, Boom, Reset

Basic sphere

Guidance for Visual C# 2010 Express:
1) Main Menu after start of Visual C# 2010 Express: File → New Project... → WPF Application → Name: sphere1 → OK.
2) File → Save All → C:\temp. Check whether the project arrived in C:\temp\sphere1\ !
3) Download and store 5 images to directory C:\temp\sphere1\:
3.1 www.miszalok.de/C_3D_WPF/C4_Sphere/Images/mesh.bmp
3.2 www.miszalok.de/C_3D_WPF/C4_Sphere/Images/randomStripes.bmp
3.3 www.miszalok.de/C_3D_WPF/C4_Sphere/Images/earth.bmp
3.4 www.miszalok.de/C_3D_WPF/C4_Sphere/Images/lena256.bmp
3.5 www.miszalok.de/C_3D_WPF/C4_Sphere/Images/boom.gif
Check whether these 5 images are correctly stored in directory C:\temp\sphere1\ and whether they carry their proper extensions *.bmp or *.gif.
4) Replace the default code of MainWindow.xaml and of MainWindow.xaml.cs by the following codes:

MainWindow.xaml:
<Window x:Class="sphere1.MainWindow" x:Name="window"
 xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
 xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
 Title="sphere1" Width="400" Height="650">
 <Window.Resources>
  <BitmapImage x:Key="meshImage"  UriSource="C:\temp\sphere1\mesh.bmp"/>
  <BitmapImage x:Key="ballImage"  UriSource="C:\temp\sphere1\randomStripes.bmp"/>
  <BitmapImage x:Key="earthImage" UriSource="C:\temp\sphere1\earth.bmp"/>
  <BitmapImage x:Key="faceImage"  UriSource="C:\temp\sphere1\lena256.bmp"/>
  <BitmapImage x:Key="boomImage"  UriSource="C:\temp\sphere1\boom.gif"/>
  <!--alternative (but slower) image sources:
  <BitmapImage x:Key="meshImage"  UriSource="http://www.miszalok.de/C_3D_WPF/C4_Sphere/Images/mesh.bmp"/>
  <BitmapImage x:Key="ballImage"  UriSource="http://www.miszalok.de/C_3D_WPF/C4_Sphere/Images/randomStripes.bmp"/>
  <BitmapImage x:Key="earthImage" UriSource="http://www.miszalok.de/C_3D_WPF/C4_Sphere/Images/earth.bmp"/>
  <BitmapImage x:Key="faceImage"  UriSource="http://www.miszalok.de/C_3D_WPF/C4_Sphere/Images/lena256.bmp"/>
  <BitmapImage x:Key="boomImage"  UriSource="http://www.miszalok.de/C_3D_WPF/C4_Sphere/Images/boom.gif"/>
  -->
  <ImageBrush  x:Key="meshBrush"  ImageSource="{ StaticResource meshImage  }"/>
  <ImageBrush  x:Key="ballBrush"  ImageSource="{ StaticResource ballImage  }"/>
  <ImageBrush  x:Key="earthBrush" ImageSource="{ StaticResource earthImage }"/>
  <ImageBrush  x:Key="faceBrush"  ImageSource="{ StaticResource faceImage  }"/>
  <SolidColorBrush x:Key="solidColorBrush" Color="Red"/>
  <DiffuseMaterial x:Key="backMaterial" Brush="{ StaticResource solidColorBrush }"/>
 </Window.Resources>
 <StackPanel Orientation="Vertical" Margin="0 0 0 0">
  <!--Viewport3D is a drawing canvas which resizes its Content automatically-->
  <Viewport3D x:Name="viewport">
   <Viewport3D.Camera>
    <PerspectiveCamera x:Name="perspectiveCamera"
                       Position=" 0 0 3" LookDirection=" 0 0 -1" UpDirection=" 0 1 0"/>
    </Viewport3D.Camera>
    <!--Any 3D-content must be packed in a ModelVisual3D-object-->
    <ModelVisual3D>
     <ModelVisual3D.Content>
      <!--Only one Content is allowed. Thus we use a Model3DGroup as envelope for our 
       two lights and all further GeometryModel3Ds.-->
      <Model3DGroup x:Name="model3DGroup">
       <AmbientLight Color="#444444"/>
       <DirectionalLight x:Name="directionalLight" Color="#ffffff" Direction="-1 -1 -1" />
       <!--A lot of GeometryModel3Ds will be inserted here.-->
      </Model3DGroup>
    </ModelVisual3D.Content>
   </ModelVisual3D>
  </Viewport3D>
 </StackPanel><!--end of the uppermost StackPanel which contains everything-->
</Window>


MainWindow.xaml.cs
using System;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Media.Media3D;

namespace sphere1
{ public partial class MainWindow : Window
  { private const int maxLongitudes = 100; //maximum
    private const int maxLatitudes  = 100; //maximum
    private Point3D[,] position = new Point3D[maxLongitudes+1,maxLatitudes];
    private Point  [,] texture  = new Point  [maxLongitudes+1,maxLatitudes];
    private DiffuseMaterial[] frontMaterial = new DiffuseMaterial[maxLatitudes-1];
    private int longitudes; //actual <= maximum
    private int latitudes;  //actual <= maximum
    private int emptySlices = 0; //cuts slices out of the apple
    private int IndexOfFirstGeometryModel3DInModel3DGroup; //= no of lights = 2
    private Matrix3D matrix = Matrix3D.Identity;
    private MatrixTransform3D matrixTransform3D;
    private Quaternion qX = new Quaternion( new Vector3D(1,0,0), 1 ); //rotations around X-axis
    private Quaternion qY = new Quaternion( new Vector3D(0,1,0), 1 ); //rotations around Y-axis
    private Quaternion qZ = new Quaternion( new Vector3D(0,0,1), 1 ); //rotations around Z-axis
    private System.Windows.Threading.DispatcherTimer timer = new System.Windows.Threading.DispatcherTimer();

    public MainWindow() //constructor
    { InitializeComponent();
      IndexOfFirstGeometryModel3DInModel3DGroup = model3DGroup.Children.Count;
      longitudes = 50;
      latitudes  = 50;
      GenerateImageMaterials();
      GenerateSphere( longitudes, latitudes );
      GenerateAllCylinders();
    }

    protected override void OnRenderSizeChanged( SizeChangedInfo sizeInfo ) 
    { try { viewport.Width = viewport.Height = window.ActualWidth; } catch {}
    }
    
    private void GenerateImageMaterials()
    { ImageBrush imageBrush;
      double minus = (double)(longitudes-emptySlices);
      imageBrush          = (ImageBrush)Resources["meshBrush"];
      imageBrush.Viewport = new Rect( 0, 0, 1.0/minus, 1 );
      imageBrush.TileMode = TileMode.Tile;
      for ( int lat=0; lat < latitudes-1; lat++ )
        frontMaterial[lat] = new DiffuseMaterial( imageBrush );
    }

    private void GenerateSphere( int longitudes, int latitudes )
    { double latitudeArcusIncrement    =     Math.PI / (latitudes-1);
      double longitudeArcusIncrement   = 2.0*Math.PI / longitudes;
      for ( int lat=0; lat < latitudes; lat++ )
      { double latitudeArcus = lat * latitudeArcusIncrement;
        double radius = Math.Sin( latitudeArcus );
        //if ( lat == latitudes/2 ) radius *= 1.3;
        double y      = Math.Cos( latitudeArcus );
        double textureY = (double)lat / (latitudes-1);
        for ( int lon=0; lon <= longitudes; lon++ )
        { double longitudeArcus = lon * longitudeArcusIncrement;
          position[lon,lat].X =  radius * Math.Cos( longitudeArcus );
          position[lon,lat].Y =  y;
          position[lon,lat].Z = -radius * Math.Sin( longitudeArcus );
          texture [lon,lat].X = (double)lon / longitudes;
          texture [lon,lat].Y = textureY;
        }
      }
    }

    private void GenerateAllCylinders()
    { //At first delete all existing flats beginning with the last one
      for ( int i=model3DGroup.Children.Count-1; i >= IndexOfFirstGeometryModel3DInModel3DGroup; i-- ) 
        model3DGroup.Children.Remove( (GeometryModel3D)model3DGroup.Children[i] );
      for ( int lat=0; lat < latitudes-1; lat++ )
      { GeometryModel3D geometryModel3D = new GeometryModel3D();
        geometryModel3D.Geometry = GenerateCylinder( lat );
        geometryModel3D.Material = frontMaterial[lat];
        geometryModel3D.BackMaterial = (DiffuseMaterial)Resources["backMaterial"];
        model3DGroup.Children.Add( geometryModel3D );
      }
    }

    private MeshGeometry3D GenerateCylinder( int lat )
    { MeshGeometry3D meshGeometry3D = new MeshGeometry3D();
      for ( int lon = 0; lon <= longitudes - emptySlices; lon++ )    //create a zigzag point collection
      { Point3D  p0 = position[lon,lat  ];                           //on the ceiling
        Point3D  p1 = position[lon,lat+1];                           //on the floor
        meshGeometry3D.Positions.Add( p0 );                          //on the ceiling
        meshGeometry3D.Positions.Add( p1 );                          //on the floor
        meshGeometry3D.Normals.Add( (Vector3D)p0 );                  //ceiling normal
        meshGeometry3D.Normals.Add( (Vector3D)p1 );                  //floor normal
        meshGeometry3D.TextureCoordinates.Add( texture[lon,lat  ] ); //on the ceiling
        meshGeometry3D.TextureCoordinates.Add( texture[lon,lat+1] ); //on the floor
      }
      for (int lon = 1; lon < meshGeometry3D.Positions.Count - 2; lon+=2)
      { //first triangle = left upper part of a rectangle
        meshGeometry3D.TriangleIndices.Add( lon-1 ); //left  upper point
        meshGeometry3D.TriangleIndices.Add( lon   ); //left  lower point
        meshGeometry3D.TriangleIndices.Add( lon+1 ); //right upper point
        //second triangle = right lower part of the rectangle
        meshGeometry3D.TriangleIndices.Add( lon+1 ); //right upper point
        meshGeometry3D.TriangleIndices.Add( lon   ); //left  lower point
        meshGeometry3D.TriangleIndices.Add( lon+2 ); //right lower point
      }
      return meshGeometry3D;
    }
  }
}

Have a look at the images:

Experiments in MainWindow.xaml.cs: (Restore the original values after any experiment.)

Texture choice with RadioButtons

Changes in MainWindow.xaml:
Insert two Styles into the <Windows.Resources>-tag below the line:
  <DiffuseMaterial x:Key="backMaterial" Brush="{ StaticResource solidColorBrush }"/>

  <Style TargetType="{x:Type StackPanel}">
   <Setter Property="Orientation"         Value="Horizontal"/>
   <Setter Property="HorizontalAlignment" Value="Center"/>
   <Setter Property="Margin"              Value="5 5 5 5"/>
  </Style>
  <Style TargetType="{x:Type RadioButton}">
   <Setter Property="Width"    Value="70"/>
   <Setter Property="FontSize" Value="9"/>
   <EventSetter Event="Click" Handler="on_radioButton_clicked"/>
  </Style>

Insert a horizontal StackPanel with 4 RadioButtons below the line:
  <StackPanel Orientation="Vertical" Margin="0 0 0 0">

  <StackPanel>
   <RadioButton x:Name="mesh"  Content="Mesh" IsChecked="True"/>
   <RadioButton x:Name="ball"  Content="BeachBall"/>
   <RadioButton x:Name="earth" Content="Earth"/>
   <RadioButton x:Name="face"  Content="Face"/>
  </StackPanel>

Changes in MainWindow.xaml.cs:
Replace the function GenerateImageMaterials() by:

    private void GenerateImageMaterials()
    { ImageBrush imageBrush;
      double flatThickness = 1.0/(latitudes-1);
      double minus = (double)(longitudes-emptySlices);
      if ( (bool)mesh.IsChecked )
      { imageBrush          = (ImageBrush)Resources["meshBrush"];
        imageBrush.Viewport = new Rect( 0, 0, 1.0/minus, 1 );
        imageBrush.TileMode = TileMode.Tile;
        for ( int lat=0; lat < latitudes-1; lat++ )
          frontMaterial[lat] = new DiffuseMaterial( imageBrush );
      }
      else if ( (bool)ball.IsChecked )
      { imageBrush          = (ImageBrush)Resources["ballBrush"];
        imageBrush.Viewbox  = new Rect( 0, 0, minus/maxLongitudes, flatThickness );
        for ( int lat=0; lat < latitudes-1; lat++ )
          frontMaterial[lat] = new DiffuseMaterial( imageBrush );
      }
      else if ( (bool)earth.IsChecked )
        for ( int lat=0; lat < latitudes-1; lat++ ) 
        { imageBrush         = new ImageBrush( (BitmapImage)Resources["earthImage"] );
          imageBrush.Viewbox = new Rect( 0, lat*flatThickness, minus/longitudes, flatThickness );
          frontMaterial[lat] = new DiffuseMaterial( imageBrush );
        }
      else if ( (bool)face.IsChecked )
        for ( int lat=0; lat < latitudes-1; lat++ ) 
        { imageBrush         = new ImageBrush( (BitmapImage)Resources["faceImage"] );
          imageBrush.Viewbox = new Rect( 0, lat*flatThickness, minus/longitudes, flatThickness );
          frontMaterial[lat] = new DiffuseMaterial( imageBrush );
        }
    }

Add a new event handler on_radioButton_clicked below the GenerateCylinder( int lat )-function but above the 2 last closing braces } of MainWindow.xaml.cs:

    private void on_radioButton_clicked(object sender, EventArgs e)
    { GenerateImageMaterials();
      for ( int i=IndexOfFirstGeometryModel3DInModel3DGroup, j=0; i < model3DGroup.Children.Count; i++, j++ )
        ((GeometryModel3D)model3DGroup.Children[i]).Material = frontMaterial[j];
    }

Rotations

Changes in MainWindow.xaml:
Insert an additional Style-definition in <Window.Resources> below the existing Styles:

  <Style TargetType="{x:Type CheckBox}">
   <Setter Property="Width"    Value="70"/>
   <Setter Property="FontSize" Value="9"/>
   <EventSetter Event="Click" Handler="on_checkbox_clicked"/>
  </Style>

Insert a horizontal StackPanel with 3 CheckBoxes below the StackPanel with the RadioButtons:

  <StackPanel Margin="5,5,5,1">
   <CheckBox x:Name="X_Rotate" Content="X-Rotate"/>
   <CheckBox x:Name="Y_Rotate" Content="Y-Rotate"/>
   <CheckBox x:Name="Z_Rotate" Content="Z-Rotate"/>
  </StackPanel>

Changes in MainWindow.xaml.cs:
Add two additional lines to the constructor MainWindow():

      timer.Interval = TimeSpan.FromMilliseconds( 1 );
      timer.Tick += TimerOnTick;

Add two new event handlers below the on_radioButton_clicked event handler but above the 2 last closing braces } of MainWindow.xaml.cs:

    private void on_checkbox_clicked(object sender, EventArgs e)
    { timer.Stop();
      matrix = Matrix3D.Identity;
           if ( (bool)X_Rotate.IsChecked ) timer.Start();
      else if ( (bool)Y_Rotate.IsChecked ) timer.Start();
      else if ( (bool)Z_Rotate.IsChecked ) timer.Start();
    }

    private void TimerOnTick( Object sender, EventArgs args )
    { if ( (bool)X_Rotate.IsChecked ) matrix.Rotate( qX );
      if ( (bool)Y_Rotate.IsChecked ) matrix.Rotate( qY );
      if ( (bool)Z_Rotate.IsChecked ) matrix.Rotate( qZ );
      matrixTransform3D = new MatrixTransform3D( matrix );
      for ( int i=IndexOfFirstGeometryModel3DInModel3DGroup; i < model3DGroup.Children.Count; i++ )
        ((GeometryModel3D)model3DGroup.Children[i]).Transform = matrixTransform3D;
    }

Longitudes-, latitudes- and light-sliders

Changes in MainWindow.xaml:
Add four new Style-definitions in <Window.Resources>:

  <Style TargetType="{x:Type DockPanel}">
   <Setter Property="Background"          Value="LightGray"/>
   <Setter Property="LastChildFill"       Value="True"/>
   <Setter Property="Margin"              Value="5 1 5 1"/>
  </Style>
  <Style TargetType="{x:Type Label}">
   <Setter Property="FontSize" Value="10"/>
   <Setter Property="Width" Value="90"/>
   <Setter Property="DockPanel.Dock" Value="Left"/>
  </Style>
  <Style TargetType="{x:Type Slider}">
   <Setter Property="HorizontalAlignment" Value="Center"/>
   <Setter Property="Width" Value="200"/>
   <EventSetter Event="ValueChanged" Handler="on_slider_value_changed"/>
  </Style>
  <Style TargetType="{x:Type TextBox}">
   <Setter Property="DockPanel.Dock" Value="Right"/>
   <Setter Property="Width" Value="35"/>
  </Style>

Insert an empty StackPanel and 4 DockPanel-controls below the existing </StackPanel>s.
Each DockPanel contains a Label docked by default at the left side, a TextBox docked at the right side and a Slider which occupies the remaining space in the middle.

  <StackPanel/>
  <DockPanel>
   <Label Content="No. Latitudes"/>
   <TextBox x:Name="latitudes_slider_textBox" DockPanel.Dock="Right"/>
   <Slider  x:Name="latitudes_slider" Minimum="3" Maximum="100" Value="30"/>
  </DockPanel>
  <DockPanel>
   <Label Content="No. Longitudes"/>
   <TextBox x:Name="longitudes_slider_textBox" DockPanel.Dock="Right"/>
   <Slider  x:Name="longitudes_slider" Minimum="3" Maximum="100" Value="30"/>
  </DockPanel>
  <DockPanel>
   <Label Content="Light Direction"/> 
   <TextBox x:Name="light_move_slider_textBox" DockPanel.Dock="Right"/>
   <Slider  x:Name="light_move_slider" Minimum="-180" Maximum="180" Value="45"/>
  </DockPanel>
  <DockPanel>
   <Label Content="Quake Magnitude"/>
   <TextBox x:Name="quake_magnitude_slider_textBox" DockPanel.Dock="Right"/>
   <Slider  x:Name="quake_magnitude_slider" Minimum="1" Maximum="10" Value="5"/>
  </DockPanel>

Changes in MainWindow.xaml.cs:
Inside the constructor MainWindow() replace the lines:
longitudes = 50;
latitutes  = 50; by:

      longitudes = Convert.ToInt32( longitudes_slider.Value );
      latitudes  = Convert.ToInt32( latitudes_slider.Value  );
      longitudes_slider_textBox     .Text = Convert.ToInt32( longitudes ).ToString();
      latitudes_slider_textBox      .Text = Convert.ToInt32( latitudes  ).ToString();
      quake_magnitude_slider_textBox.Text = Convert.ToInt32( quake_magnitude_slider.Value ).ToString();
      light_move_slider_textBox     .Text = Convert.ToInt32( light_move_slider.Value      ).ToString();

Above the last two braces insert the common event handler for all 4 Sliders:

    private void on_slider_value_changed(object sender, EventArgs e)
    { switch( ((Slider)sender).Name )
      { case "latitudes_slider":
             latitudes = Convert.ToInt32( latitudes_slider.Value );
             latitudes_slider_textBox.Text = Convert.ToInt32( latitudes_slider.Value ).ToString();
             GenerateImageMaterials();
             GenerateSphere( longitudes, latitudes );
             GenerateAllCylinders();
             break;
        case "longitudes_slider":
             longitudes = Convert.ToInt32( longitudes_slider.Value );
             longitudes_slider_textBox.Text = Convert.ToInt32( longitudes_slider.Value ).ToString();
             if ( longitudes < emptySlices ) emptySlices = 0;
             if ( (bool)mesh.IsChecked | (bool)ball.IsChecked) GenerateImageMaterials();
             GenerateSphere( longitudes, latitudes );
             GenerateAllCylinders();
             break;
        case "light_move_slider":
             double arcus = 2.0*Math.PI*light_move_slider.Value / 360;
             Vector3D v = new Vector3D();
             v.X = -3.0 * Math.Sin( arcus );
             v.Y = 0;
             v.Z = -3.0 * Math.Cos( arcus );
             directionalLight.Direction = v;
             light_move_slider_textBox.Text = Convert.ToInt32( light_move_slider.Value ).ToString();
             break;
        case "quake_magnitude_slider":
             quake_magnitude_slider_textBox.Text = Convert.ToInt32( quake_magnitude_slider.Value ).ToString();
             break;
      }
    }

Cut off slices and floors

Changes in MainWindow.xaml:
Add a new Style-definition in <Window.Resources>:

  <Style TargetType="{x:Type Button}">
   <Setter Property="Width"    Value="60"/>
   <Setter Property="FontSize" Value="8"/>
   <EventSetter Event="Click" Handler="on_button_clicked"/>
  </Style>

Insert a StackPanel with 5 Button-controls together with 4 empty Label distance holders between them below the last </DockPanel><.

  <StackPanel>
   <Button x:Name="slices"  Content="Cut off Slices"  /><Label Width="10"/>
   <Button x:Name="north"   Content="Cut from North"  /><Label Width="10"/>
   <Button x:Name="south"   Content="Cut from South"  /><Label Width="10"/>
   <Button x:Name="equator" Content="Cut from Equator"/><Label Width="10"/>
   <Button x:Name="stacks"  Content="Cut off Stacks"  />
  </StackPanel>

Changes in MainWindow.xaml.cs:
Above the last two braces insert the common event handler for all 5 Buttons:

    private void on_button_clicked( object sender, EventArgs e )
    { switch( ((Button)sender).Name )
      { case "slices":
            emptySlices++;
            if ( emptySlices > longitudes ) emptySlices = 0;
            GenerateImageMaterials();
            GenerateAllCylinders();
            perspectiveCamera.Position      = new Point3D (  3,0,  1 );
            perspectiveCamera.LookDirection = new Vector3D( -3,0, -1 );
            break;
       case "north":
            if ( model3DGroup.Children.Count > IndexOfFirstGeometryModel3DInModel3DGroup )
              model3DGroup.Children.RemoveAt( IndexOfFirstGeometryModel3DInModel3DGroup );
            break;
       case "south":
            if ( model3DGroup.Children.Count > IndexOfFirstGeometryModel3DInModel3DGroup )
              model3DGroup.Children.RemoveAt( model3DGroup.Children.Count-1 );
            break;
       case "equator":
            if ( model3DGroup.Children.Count > IndexOfFirstGeometryModel3DInModel3DGroup )
            {  int mid = (model3DGroup.Children.Count - IndexOfFirstGeometryModel3DInModel3DGroup)/2;
               mid += IndexOfFirstGeometryModel3DInModel3DGroup;
               model3DGroup.Children.RemoveAt( mid );
            }
            break;
       case "stacks":
            for ( int i=model3DGroup.Children.Count-1; i >= IndexOfFirstGeometryModel3DInModel3DGroup; i-=2 )
              model3DGroup.Children.RemoveAt( i );
            break;
      } //end of switch
    } // end of on_button_clicked(...)

Earthquake, Boom, Reset

Changes in MainWindow.xaml:
Insert another StackPanel with 3 Button-controls together with 2 empty Label distance holders between them below the last </StackPanel>.

  <StackPanel>
   <Button x:Name="earthquake" Content="Earthquake" FontSize="10"/>
   <Label Width="10"/>
   <Button x:Name="boom" Height="40"><Image Source="{StaticResource boomImage}"/></Button>
   <Label Width="10"/>
   <Button x:Name="reset" Content="Reset" FontSize="10"/>
  </StackPanel>

Changes in MainWindow.xaml.cs:
Add three additional cases into the common event handler on_button_clicked( ... ):

       case "boom":
            Point3D cp = perspectiveCamera.Position;
            if ( cp.Z > 3 ) break; //already boomed
            double amplitude = 3;  //earthquake magnitude: 30
            cp.Z += 4;             //step back from explosion
            perspectiveCamera.Position = cp;
            goto earthquake;
       case "earthquake":
            amplitude = quake_magnitude_slider.Value * 0.01;
earthquake: Point3D p = new Point3D();
            double ah = amplitude / 2.0;
            Random  r = new Random();
            for ( int i=IndexOfFirstGeometryModel3DInModel3DGroup+2; i < model3DGroup.Children.Count-2; i++ )
            { GeometryModel3D geometryModel3D = (GeometryModel3D)model3DGroup.Children[i];
              MeshGeometry3D meshGeometry3D = (MeshGeometry3D)geometryModel3D.Geometry;
              for ( int j=0; j < meshGeometry3D.Positions.Count; j++ )
              { p = meshGeometry3D.Positions[j];
                p.Z += - ah + amplitude*r.NextDouble();
                p.Y += - ah + amplitude*r.NextDouble();
                p.X += - ah + amplitude*r.NextDouble();
                meshGeometry3D.Positions.RemoveAt( j );
                meshGeometry3D.Positions.Insert( j, p );
              }
            }
            break;
       case "reset":
            perspectiveCamera.Position      = new Point3D ( 0,0, 3 );
            perspectiveCamera.LookDirection = new Vector3D( 0,0,-1 );
            emptySlices = 0;
            GenerateImageMaterials();
            GenerateAllCylinders();
            break;

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