Public Shared Function Densify( _
   ByVal geom As Geometry, _
   ByVal maxSegmentLength As Double _
) As Geometry

public static Geometry Densify( 
   Geometry geom,
   double maxSegmentLength
)

<Grid x:Name="LayoutRoot">
  
  <!-- Add a Map control. -->
  <esri:Map Background="White" HorizontalAlignment="Left" Margin="12,107,0,0" Name="Map1" 
          VerticalAlignment="Top" Height="318" Width="483"  WrapAround="True"
            Extent="-119.35,-27.77,50.44,84.02">
  
    <!--  Add a backdrop ArcGISTiledMapServiceLayer. The SpatialReference = 4326 (Geographic Coordinate System).-->
    <esri:ArcGISTiledMapServiceLayer ID="PhysicalTiledLayer" 
           Url="http://services.arcgisonline.com/ArcGIS/rest/services/ESRI_StreetMap_World_2D/MapServer"/>
    
  </esri:Map>
  
  <!-- 
  Add two RadioButtons that use the same Click Event handlers to draw a Polyline or Polygon
  Graphics on the Map control in the code-behind. Each RadioButton has a 'Tag' attribute set that 
  will be used to decide which Geometry type to draw. 
  -->
  <RadioButton Content="Polyline" Height="16" HorizontalAlignment="Left" Margin="12,85,0,0" Name="rbPolyline" 
             VerticalAlignment="Top" Tag="Polyline" Click="rb_Click"/>
  <RadioButton Content="Polygon" Height="16" HorizontalAlignment="Left" Margin="108,85,0,0" Name="rbPolygon" 
             VerticalAlignment="Top" Tag="Polygon" Click="rb_Click"/>
  
  <!-- 
  Add a button to perform a Geodesic.Densify on an existing Polyline or Polygon in the Map to create
  a 'densified' version of the same type and add it to the Map.
  -->
  <Button Content="Geometry.Geodesic.Densify" Height="23" HorizontalAlignment="Left" Margin="230,78,0,0" 
          Name="Button_Geometry_GeoDesicDensify" VerticalAlignment="Top" Width="265" 
          Click="Button_Geometry_GeoDesicDensify_Click" Visibility="Collapsed"/>
  
  <!-- Provide the instructions on how to use the sample code. -->
  <TextBlock Height="79" HorizontalAlignment="Left" Name="TextBlock1" VerticalAlignment="Top" Width="757" TextWrapping="Wrap" 
             Text="Click on a RadioButton (Polyline or Polygon) to draw a simple Graphic generated in code-behind on the Map 
             Control (Note: the verticies that make up that Polyline or Polygon will also be added). Then click the Button 
             add a new Graphic based upon the Geometry.Geodesic.Densify Method from the input Polyline or Polygon. Notice
             how the shape of the new Graphic is based upon the 'great circle' geodesic algorithm (Note: the verticies that 
             make up the new Geodesic Polyline or Polygon will also be added)." />
  
</Grid>

private void rb_Click(object sender, System.Windows.RoutedEventArgs e)
{
  // Cast the sender object to a RadioButton.
  System.Windows.Controls.RadioButton theRadioButton = (System.Windows.Controls.RadioButton)sender;
  
  // Get the Tag Property (a String) of the RadioButton that was set in XAML. Possible options for the Tag
  // Property are: "Polyline" and "Polygon".
  string theGraphicType = theRadioButton.Tag.ToString();
  
  // Remove any existing GraphicsLayer objects that are in the Map. This allows the user to choose the
  // different RadioButtons over and over.
  if (Map1.Layers.Count > 1)
  {
    Map1.Layers.RemoveAt(1);
  }
  
  // Create a new instance of the GraphicsLayer object.
  ESRI.ArcGIS.Client.GraphicsLayer theGraphicsLayer = new ESRI.ArcGIS.Client.GraphicsLayer();
  theGraphicsLayer.ID = "MyGraphicsLayer";
  
  // Call the function that generates a single Graphic based upon the RadioButton Tag and add it to the GraphicsLayer.
  ESRI.ArcGIS.Client.Graphic theGraphic = GetAGraphicFromStaticSource(theGraphicType);
  theGraphicsLayer.Graphics.Add(theGraphic);
  
  // Add the GraphicsLayer to the Layers collection of the Map. 
  Map1.Layers.Add(theGraphicsLayer);
  
  // Make the Button to perform the Geodesic.Densify work visible.
  Button_Geometry_GeoDesicDensify.Visibility = Windows.Visibility.Visible;
  
  // Add the verticies that make up the Graphic to the Map for easy visualization.
  AddVisualVertices(theGraphic, 
                    theGraphicsLayer, 
                    ESRI.ArcGIS.Client.Symbols.SimpleMarkerSymbol.SimpleMarkerStyle.Square, 
                    Colors.Yellow, 
                    12);
}
  
private void Button_Geometry_GeoDesicDensify_Click(object sender, System.Windows.RoutedEventArgs e)
{
  // Get the GraphicsLayer.
  ESRI.ArcGIS.Client.GraphicsLayer theGraphicsLayer = (ESRI.ArcGIS.Client.GraphicsLayer)(Map1.Layers["MyGraphicsLayer"]);
  
  // Create a new instance of one Graphic.
  ESRI.ArcGIS.Client.Graphic aGraphic = new ESRI.ArcGIS.Client.Graphic();
  
  // Loop through all of the Graphics in the GraphicsLayer.
  foreach (ESRI.ArcGIS.Client.Graphic theGraphic in theGraphicsLayer)
  {
    // Get the Geometry from the Graphic.
    ESRI.ArcGIS.Client.Geometry.Geometry theGeometry = theGraphic.Geometry;
    
    // Create a placeholder for the new Geometry that will be created from the Shared/static Geometry.Geodesic.Densify Method.
    ESRI.ArcGIS.Client.Geometry.Geometry theGeometry2 = null;
    
    if ((theGeometry) is ESRI.ArcGIS.Client.Geometry.Polyline)
    {
      // For Polyline Geometries do the following:
      
      // Do the densification.
      theGeometry2 = ESRI.ArcGIS.Client.Geometry.Geodesic.Densify(theGeometry, 1000000); // Examples: 10, 100, 1000, 10000, 100000
      
      // Create a new instance of a SimpleLineSymbol and set its Color, Style, and Width Properties.
      ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol theSimpleLineSymbol = CreateSimpleLineSymbol(Colors.Red, 
                                                                                               ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol.LineStyle.Solid, 
                                                                                               2);
      
      // Apply the Graphic's Geometry and Symbol Properties.
      aGraphic.Geometry = theGeometry2;
      aGraphic.Symbol = (ESRI.ArcGIS.Client.Symbols.Symbol)theSimpleLineSymbol;
    }
    else if ((theGeometry) is ESRI.ArcGIS.Client.Geometry.Polygon)
    {
      // For Polygon Geometries do the following:
      
      // Do the densification.
      theGeometry2 = ESRI.ArcGIS.Client.Geometry.Geodesic.Densify(theGeometry, 1000000); // Examples: 10, 100, 1000, 10000, 100000
      
      // Create a new instance of a SimpleFillSymbol and set its Color, BorderBrush, BorderThickness, and Opacity Properties.
      ESRI.ArcGIS.Client.Symbols.SimpleFillSymbol theSimpleFillSymbol = CreateSimpleFillSymbol(Colors.Blue, Colors.Red, 2, 0.5);
      
      // Apply the Graphic's Geometry and Symbol Properties.
      aGraphic.Geometry = theGeometry2;
      aGraphic.Symbol = (ESRI.ArcGIS.Client.Symbols.Symbol)theSimpleFillSymbol;
    }
  }
  
  // Add the 'densified' Graphics into the GraphicsLayer.
  theGraphicsLayer.Graphics.Add(aGraphic);
  
  // Add the verticies that make up the Graphic to the Map for easy visualization.
  AddVisualVertices(aGraphic, 
                    theGraphicsLayer, 
                    ESRI.ArcGIS.Client.Symbols.SimpleMarkerSymbol.SimpleMarkerStyle.Circle, 
                    Colors.Red, 
                    6);
}
  
public void AddVisualVertices(ESRI.ArcGIS.Client.Graphic aGraphic, 
                              ESRI.ArcGIS.Client.GraphicsLayer theGraphicsLayer, 
                              ESRI.ArcGIS.Client.Symbols.SimpleMarkerSymbol.SimpleMarkerStyle theSimpleMarkerSytle, 
                              System.Windows.Media.Color theColor, double theSize)
{
  // This function displays the verticies of the Densifiy Geometry.
  
  // Create an ObservableCollection<PointCollection>
  Collections.ObjectModel.ObservableCollection<ESRI.ArcGIS.Client.Geometry.PointCollection> theCollectonOfPointCollections = null;
  
  if (aGraphic.Geometry is ESRI.ArcGIS.Client.Geometry.Polyline)
  {
    // For Polyline Geometries do the following:
    
    // Cast the generic Geometry into a Polyline.
    ESRI.ArcGIS.Client.Geometry.Polyline theDensifiedPolyline = (ESRI.ArcGIS.Client.Geometry.Polyline)aGraphic.Geometry;
    
    // Set the ObservableCollecton<PointCollection> to the Polyline.Paths 
    theCollectonOfPointCollections = theDensifiedPolyline.Paths;
  }
  else if (aGraphic.Geometry is ESRI.ArcGIS.Client.Geometry.Polygon)
  {
    // For Polygon Geometries do the following:
    
    // Cast the generic Geometry into a Polygon.
    ESRI.ArcGIS.Client.Geometry.Polygon theDensifiedPolygon = (ESRI.ArcGIS.Client.Geometry.Polygon)aGraphic.Geometry;
    
    // Set the ObservableCollecton<PointCollection>) to the Polygon.Rings 
    theCollectonOfPointCollections = theDensifiedPolygon.Rings;
  }
  
  // We are only interested in the first PointCollection.
  ESRI.ArcGIS.Client.Geometry.PointCollection theFirstPointCollection = theCollectonOfPointCollections[0];
  
  // Loop through each MapPoint in the first PointCollection.
  foreach (ESRI.ArcGIS.Client.Geometry.MapPoint theMapPoint in theFirstPointCollection)
  {
    // Create a SimpleMarkerSymbol and set it's Color, Size, and Style.
    ESRI.ArcGIS.Client.Symbols.SimpleMarkerSymbol theSimpleMarkerSymbol = new ESRI.ArcGIS.Client.Symbols.SimpleMarkerSymbol();
    theSimpleMarkerSymbol.Color = new System.Windows.Media.SolidColorBrush(theColor);
    theSimpleMarkerSymbol.Size = theSize;
    theSimpleMarkerSymbol.Style = theSimpleMarkerSytle;
    
    // Create a new Graphic based upon the MapPoint's of the densified Geometry. Use the SimpleMarkerSymbol just defined.
    ESRI.ArcGIS.Client.Graphic theGraphic = new ESRI.ArcGIS.Client.Graphic();
    ESRI.ArcGIS.Client.Geometry.MapPoint densifyGeometry = new ESRI.ArcGIS.Client.Geometry.MapPoint(theMapPoint.X, theMapPoint.Y);
    theGraphic.Geometry = densifyGeometry;
    theGraphic.Symbol = theSimpleMarkerSymbol;
    
    // Add the new Graphic to the GraphicsLayer.
    theGraphicsLayer.Graphics.Add(theGraphic);
  }
}
            
#region Utility Functions
            
  public ESRI.ArcGIS.Client.Graphic GetAGraphicFromStaticSource(string theGraphicType)
  {
    // Create a new instance of one Graphic.
    ESRI.ArcGIS.Client.Graphic theGraphic = new ESRI.ArcGIS.Client.Graphic();
    
    // Create a SpatialReference for the Graphic using the Geographic Coordinate System of WKID=4326. 
    ESRI.ArcGIS.Client.Geometry.SpatialReference theSpatialReference = new ESRI.ArcGIS.Client.Geometry.SpatialReference(4326);
    
    // Create a new PointCollection used to add vertices to the Geometry.
    ESRI.ArcGIS.Client.Geometry.PointCollection thePointCollection = new ESRI.ArcGIS.Client.Geometry.PointCollection();
    
    // Generate a single Graphic based upon the user-specified type to be created. 
    if (theGraphicType == "Polyline")
    {
      // Add MapPoints into the PointCollection.
      AddMapPointsToPointCollection(14.94, 50.11, theSpatialReference, thePointCollection);
      AddMapPointsToPointCollection(-87.82, 30.65, theSpatialReference, thePointCollection);
      
      // The PointCollection needs to be added to a new instance of an ObservableCollection.
      System.Collections.ObjectModel.ObservableCollection<ESRI.ArcGIS.Client.Geometry.PointCollection> theObservableCollection = new System.Collections.ObjectModel.ObservableCollection<ESRI.ArcGIS.Client.Geometry.PointCollection>();
      theObservableCollection.Add(thePointCollection);
      
      // Create a new instance of a Polyline object and set the Paths and SpatialReference Properties.
      ESRI.ArcGIS.Client.Geometry.Polyline thePolyline = new ESRI.ArcGIS.Client.Geometry.Polyline();
      thePolyline.Paths = theObservableCollection;
      thePolyline.SpatialReference = theSpatialReference;
      
      // Create a new instance of a SimpleLineSymbol and set its Color, Style, and Width Properties.
      ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol theSimpleLineSymbol = CreateSimpleLineSymbol(Colors.Yellow, 
                                                                                               ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol.LineStyle.Solid, 
                                                                                               2);
      
      // Apply the Graphic's Geometry and Symbol Properties.
      theGraphic.Geometry = (ESRI.ArcGIS.Client.Geometry.Geometry)thePolyline;
      theGraphic.Symbol = (ESRI.ArcGIS.Client.Symbols.Symbol)theSimpleLineSymbol;
    }
    else if (theGraphicType == "Polygon")
    {
      // Add MapPoints into the PointCollection.
      AddMapPointsToPointCollection(23.66, 56.42, theSpatialReference, thePointCollection);
      AddMapPointsToPointCollection(13.39, 2.95, theSpatialReference, thePointCollection);
      AddMapPointsToPointCollection(-87.82, 38.58, theSpatialReference, thePointCollection);
      AddMapPointsToPointCollection(23.66, 56.42, theSpatialReference, thePointCollection);
      
      // The PointCollection needs to be added to a new instance of an ObservableCollection.
      System.Collections.ObjectModel.ObservableCollection<ESRI.ArcGIS.Client.Geometry.PointCollection> theObservableCollection = new System.Collections.ObjectModel.ObservableCollection<ESRI.ArcGIS.Client.Geometry.PointCollection>();
      theObservableCollection.Add(thePointCollection);
      
      // Create a new instance of a Polygon object and set the Rings and SpatialReference Properties.
      ESRI.ArcGIS.Client.Geometry.Polygon thePolygon = new ESRI.ArcGIS.Client.Geometry.Polygon();
      thePolygon.Rings = theObservableCollection;
      thePolygon.SpatialReference = theSpatialReference;
      
      // Create a new instance of a SimpleFillSymbol and set its Color, BorderBrush, BorderThickness, and Opacity Properties.
      ESRI.ArcGIS.Client.Symbols.SimpleFillSymbol theSimpleFillSymbol = CreateSimpleFillSymbol(Colors.Green, Colors.Yellow, 2, 1);
      
      // Apply the Graphic's Geometry and Symbol Properties.
      theGraphic.Geometry = (ESRI.ArcGIS.Client.Geometry.Geometry)thePolygon;
      theGraphic.Symbol = (ESRI.ArcGIS.Client.Symbols.Symbol)theSimpleFillSymbol;
    }
    
    // Return the created Graphic. 
    return theGraphic;
  }
  
  public void AddMapPointsToPointCollection(double theX, 
                                            double theY, 
                                            ESRI.ArcGIS.Client.Geometry.SpatialReference theSpatialReference, 
                                            ESRI.ArcGIS.Client.Geometry.PointCollection thePointCollection)
  {
    // Utility function to create and add a MapPoint to a PointCollection.
    ESRI.ArcGIS.Client.Geometry.MapPoint theMapPoint = new ESRI.ArcGIS.Client.Geometry.MapPoint(theX, theY, theSpatialReference);
    thePointCollection.Add(theMapPoint);
  }
  
  public ESRI.ArcGIS.Client.Symbols.SimpleFillSymbol CreateSimpleFillSymbol(System.Windows.Media.Color theFillColor, 
                                                                            System.Windows.Media.Color theBorderBrushColor, 
                                                                            double theBorderThickness, 
                                                                            double theOpacity)
  {
    // Utility function to create a SimpleFillSymbol with various Properties.
    ESRI.ArcGIS.Client.Symbols.SimpleFillSymbol theSimpleFillSymbol = new ESRI.ArcGIS.Client.Symbols.SimpleFillSymbol();
    theSimpleFillSymbol.Fill = new System.Windows.Media.SolidColorBrush(theFillColor);
    theSimpleFillSymbol.BorderBrush = new System.Windows.Media.SolidColorBrush(theBorderBrushColor);
    theSimpleFillSymbol.BorderThickness = theBorderThickness;
    theSimpleFillSymbol.Fill.Opacity = theOpacity;
    
    return (theSimpleFillSymbol);
  }
  
  public ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol CreateSimpleLineSymbol(System.Windows.Media.Color theColor, 
                                                                            ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol.LineStyle theStyle, 
                                                                            double theWidth)
  {
    // Utility function to create a SimpleLineSymbol with various Properties.
    ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol theSimpleLineSymbol = new ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol();
    theSimpleLineSymbol.Color = new System.Windows.Media.SolidColorBrush(theColor);
    theSimpleLineSymbol.Style = theStyle;
    theSimpleLineSymbol.Width = theWidth;
    
    return theSimpleLineSymbol;
  }
#endregion

Private Sub rb_Click(ByVal sender As System.Object, ByVal e As System.Windows.RoutedEventArgs)
  
  ' Cast the sender object to a RadioButton.
  Dim theRadioButton As System.Windows.Controls.RadioButton = CType(sender, System.Windows.Controls.RadioButton)
  
  ' Get the Tag Property (a String) of the RadioButton that was set in XAML. Possible options for the Tag
  ' Property are: "Polyline" and "Polygon".
  Dim theGraphicType As String = theRadioButton.Tag.ToString
  
  ' Remove any existing GraphicsLayer objects that are in the Map. This allows the user to choose the
  ' different RadioButtons over and over.
  If Map1.Layers.Count > 1 Then
    Map1.Layers.RemoveAt(1)
  End If
  
  ' Create a new instance of the GraphicsLayer object.
  Dim theGraphicsLayer As New ESRI.ArcGIS.Client.GraphicsLayer
  theGraphicsLayer.ID = "MyGraphicsLayer"
  
  ' Call the function that generates a single Graphic based upon the RadioButton Tag and add it to the GraphicsLayer.
  Dim theGraphic As ESRI.ArcGIS.Client.Graphic = GetAGraphicFromStaticSource(theGraphicType)
  theGraphicsLayer.Graphics.Add(theGraphic)
   
  ' Add the GraphicsLayer to the Layers collection of the Map. 
  Map1.Layers.Add(theGraphicsLayer)
  
  ' Make the Button to perform the Geodesic.Densify work visible.
  Button_Geometry_GeoDesicDensify.Visibility = Windows.Visibility.Visible
  
  ' Add the verticies that make up the Graphic to the Map for easy visualization.
  AddVisualVertices(theGraphic, 
                    theGraphicsLayer, 
                    ESRI.ArcGIS.Client.Symbols.SimpleMarkerSymbol.SimpleMarkerStyle.Square, 
                    Colors.Yellow, 
                    12)
  
End Sub
            
Private Sub Button_Geometry_GeoDesicDensify_Click(ByVal sender As System.Object, ByVal e As System.Windows.RoutedEventArgs)
  
  ' Get the GraphicsLayer.
  Dim theGraphicsLayer As ESRI.ArcGIS.Client.GraphicsLayer = CType(Map1.Layers("MyGraphicsLayer"), ESRI.ArcGIS.Client.GraphicsLayer)
  
  ' Create a new instance of one Graphic.
  Dim aGraphic As New ESRI.ArcGIS.Client.Graphic
  
  ' Loop through all of the Graphics in the GraphicsLayer.
  For Each theGraphic As ESRI.ArcGIS.Client.Graphic In theGraphicsLayer
    
    ' Get the Geometry from the Graphic.
    Dim theGeometry As ESRI.ArcGIS.Client.Geometry.Geometry = theGraphic.Geometry
    
    ' Create a placeholder for the new Geometry that will be created from the Shared/static Geometry.Geodesic.Densify Method.
    Dim theGeometry2 As ESRI.ArcGIS.Client.Geometry.Geometry
    
    If TypeOf (theGeometry) Is ESRI.ArcGIS.Client.Geometry.Polyline Then
      
      ' For Polyline Geometries do the following:
        
      ' Do the densification.
      theGeometry2 = ESRI.ArcGIS.Client.Geometry.Geodesic.Densify(theGeometry, 1000000) ' Examples: 10, 100, 1000, 10000, 100000
        
      ' Create a new instance of a SimpleLineSymbol and set its Color, Style, and Width Properties.
      Dim theSimpleLineSymbol As ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol = CreateSimpleLineSymbol(Colors.Red, 
                                                                                                      ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol.LineStyle.Solid, 
                                                                                                      2)
      
      ' Apply the Graphic's Geometry and Symbol Properties.
      aGraphic.Geometry = theGeometry2
      aGraphic.Symbol = CType(theSimpleLineSymbol, ESRI.ArcGIS.Client.Symbols.Symbol)
      
    ElseIf TypeOf (theGeometry) Is ESRI.ArcGIS.Client.Geometry.Polygon Then
      
      ' For Polygon Geometries do the following:
      
      ' Do the densification.
      theGeometry2 = ESRI.ArcGIS.Client.Geometry.Geodesic.Densify(theGeometry, 1000000) ' Examples: 10, 100, 1000, 10000, 100000
      
      ' Create a new instance of a SimpleFillSymbol and set its Color, BorderBrush, BorderThickness, and Opacity Properties.
      Dim theSimpleFillSymbol As ESRI.ArcGIS.Client.Symbols.SimpleFillSymbol = CreateSimpleFillSymbol(Colors.Blue, 
                                                                                                      Colors.Red, 
                                                                                                      2, 
                                                                                                      0.5)
        
      ' Apply the Graphic's Geometry and Symbol Properties.
      aGraphic.Geometry = theGeometry2
      aGraphic.Symbol = CType(theSimpleFillSymbol, ESRI.ArcGIS.Client.Symbols.Symbol)
      
    End If
    
  Next
  
  ' Add the 'densified' Graphics into the GraphicsLayer.
  theGraphicsLayer.Graphics.Add(aGraphic)
  
  ' Add the verticies that make up the Graphic to the Map for easy visualization.
  AddVisualVertices(aGraphic, 
                    theGraphicsLayer, 
                    ESRI.ArcGIS.Client.Symbols.SimpleMarkerSymbol.SimpleMarkerStyle.Circle, 
                    Colors.Red, 
                    6)
  
End Sub
            
Public Sub AddVisualVertices(aGraphic As ESRI.ArcGIS.Client.Graphic, 
                             theGraphicsLayer As ESRI.ArcGIS.Client.GraphicsLayer, 
                             theSimpleMarkerSytle As ESRI.ArcGIS.Client.Symbols.SimpleMarkerSymbol.SimpleMarkerStyle, 
                             theColor As System.Windows.Media.Color, 
                             theSize As Double)
  
  ' This function displays the verticies of the Densifiy Geometry.
    
  ' Create an ObservableCollection(Of PointCollection)
  Dim theCollectonOfPointCollections As Collections.ObjectModel.ObservableCollection(Of ESRI.ArcGIS.Client.Geometry.PointCollection) = Nothing
  
  If TypeOf aGraphic.Geometry Is ESRI.ArcGIS.Client.Geometry.Polyline Then
    
    ' For Polyline Geometries do the following:
    
    ' Cast the generic Geometry into a Polyline.
    Dim theDensifiedPolyline As ESRI.ArcGIS.Client.Geometry.Polyline = CType(aGraphic.Geometry, ESRI.ArcGIS.Client.Geometry.Polyline)
    
    ' Set the ObservableCollecton(Of PointCollection) to the Polyline.Paths 
    theCollectonOfPointCollections = theDensifiedPolyline.Paths
    
  ElseIf TypeOf aGraphic.Geometry Is ESRI.ArcGIS.Client.Geometry.Polygon Then
    
    ' For Polygon Geometries do the following:
    
    ' Cast the generic Geometry into a Polygon.
    Dim theDensifiedPolygon As ESRI.ArcGIS.Client.Geometry.Polygon = CType(aGraphic.Geometry, ESRI.ArcGIS.Client.Geometry.Polygon)
    
    ' Set the ObservableCollecton(Of PointCollection) to the Polygon.Rings 
    theCollectonOfPointCollections = theDensifiedPolygon.Rings
    
  End If
  
  ' We are only interested in the first PointCollection.
  Dim theFirstPointCollection As ESRI.ArcGIS.Client.Geometry.PointCollection = theCollectonOfPointCollections.Item(0)
  
  ' Loop through each MapPoint in the first PointCollection.
  For Each theMapPoint As ESRI.ArcGIS.Client.Geometry.MapPoint In theFirstPointCollection
  
    ' Create a SimpleMarkerSymbol and set it's Color, Size, and Style.
    Dim theSimpleMarkerSymbol As New ESRI.ArcGIS.Client.Symbols.SimpleMarkerSymbol
    theSimpleMarkerSymbol.Color = New System.Windows.Media.SolidColorBrush(theColor)
    theSimpleMarkerSymbol.Size = theSize
    theSimpleMarkerSymbol.Style = theSimpleMarkerSytle
    
    ' Create a new Graphic based upon the MapPoint's of the densified Geometry. Use the SimpleMarkerSymbol just defined.
    Dim theGraphic As New ESRI.ArcGIS.Client.Graphic
    Dim densifyGeometry As New ESRI.ArcGIS.Client.Geometry.MapPoint(theMapPoint.X, theMapPoint.Y)
    theGraphic.Geometry = densifyGeometry
    theGraphic.Symbol = theSimpleMarkerSymbol
    
    ' Add the new Graphic to the GraphicsLayer.
    theGraphicsLayer.Graphics.Add(theGraphic)
    
  Next
  
End Sub
            
#Region "Utility Functions"
            
  Public Function GetAGraphicFromStaticSource(ByVal theGraphicType As String) As ESRI.ArcGIS.Client.Graphic
            
    ' Create a new instance of one Graphic.
    Dim theGraphic As New ESRI.ArcGIS.Client.Graphic
    
    ' Create a SpatialReference for the Graphic using the Geographic Coordinate System of WKID=4326. 
    Dim theSpatialReference As New ESRI.ArcGIS.Client.Geometry.SpatialReference(4326)
    
    ' Create a new PointCollection used to add vertices to the Geometry.
    Dim thePointCollection As New ESRI.ArcGIS.Client.Geometry.PointCollection
    
    ' Generate a single Graphic based upon the user-specified type to be created. 
    If theGraphicType = "Polyline" Then
      
      ' Add MapPoints into the PointCollection.
      AddMapPointsToPointCollection(14.94, 50.11, theSpatialReference, thePointCollection)
      AddMapPointsToPointCollection(-87.82, 30.65, theSpatialReference, thePointCollection)
      
      ' The PointCollection needs to be added to a new instance of an ObservableCollection.
      Dim theObservableCollection As New System.Collections.ObjectModel.ObservableCollection(Of ESRI.ArcGIS.Client.Geometry.PointCollection)
      theObservableCollection.Add(thePointCollection)
      
      ' Create a new instance of a Polyline object and set the Paths and SpatialReference Properties.
      Dim thePolyline As New ESRI.ArcGIS.Client.Geometry.Polyline
      thePolyline.Paths = theObservableCollection
      thePolyline.SpatialReference = theSpatialReference
      
      ' Create a new instance of a SimpleLineSymbol and set its Color, Style, and Width Properties.
      Dim theSimpleLineSymbol As ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol = CreateSimpleLineSymbol(Colors.Yellow, 
                                                                                                      ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol.LineStyle.Solid, 
                                                                                                      2)
      
      ' Apply the Graphic's Geometry and Symbol Properties.
      theGraphic.Geometry = CType(thePolyline, ESRI.ArcGIS.Client.Geometry.Geometry)
      theGraphic.Symbol = CType(theSimpleLineSymbol, ESRI.ArcGIS.Client.Symbols.Symbol)
      
    ElseIf theGraphicType = "Polygon" Then
      
      ' Add MapPoints into the PointCollection.
      AddMapPointsToPointCollection(23.66, 56.42, theSpatialReference, thePointCollection)
      AddMapPointsToPointCollection(13.39, 2.95, theSpatialReference, thePointCollection)
      AddMapPointsToPointCollection(-87.82, 38.58, theSpatialReference, thePointCollection)
      AddMapPointsToPointCollection(23.66, 56.42, theSpatialReference, thePointCollection)
      
      ' The PointCollection needs to be added to a new instance of an ObservableCollection.
      Dim theObservableCollection As New System.Collections.ObjectModel.ObservableCollection(Of ESRI.ArcGIS.Client.Geometry.PointCollection)
      theObservableCollection.Add(thePointCollection)
      
      ' Create a new instance of a Polygon object and set the Rings and SpatialReference Properties.
      Dim thePolygon As New ESRI.ArcGIS.Client.Geometry.Polygon
      thePolygon.Rings = theObservableCollection
      thePolygon.SpatialReference = theSpatialReference
      
      ' Create a new instance of a SimpleFillSymbol and set its Color, BorderBrush, BorderThickness, and Opacity Properties.
      Dim theSimpleFillSymbol As ESRI.ArcGIS.Client.Symbols.SimpleFillSymbol = CreateSimpleFillSymbol(Colors.Green, 
                                                                                                      Colors.Yellow, 
                                                                                                      2, 
                                                                                                      1)
      
      ' Apply the Graphic's Geometry and Symbol Properties.
      theGraphic.Geometry = CType(thePolygon, ESRI.ArcGIS.Client.Geometry.Geometry)
      theGraphic.Symbol = CType(theSimpleFillSymbol, ESRI.ArcGIS.Client.Symbols.Symbol)
      
    End If
      
    ' Return the created Graphic. 
    Return theGraphic
    
  End Function
  
  Public Sub AddMapPointsToPointCollection(theX As Double,
                                           theY As Double,
                                           theSpatialReference As ESRI.ArcGIS.Client.Geometry.SpatialReference,
                                           thePointCollection As ESRI.ArcGIS.Client.Geometry.PointCollection)
    
    ' Utility function to create and add a MapPoint to a PointCollection.
    Dim theMapPoint As New ESRI.ArcGIS.Client.Geometry.MapPoint(theX, theY, theSpatialReference)
    thePointCollection.Add(theMapPoint)
    
  End Sub
  
  Public Function CreateSimpleFillSymbol(theFillColor As System.Windows.Media.Color,
                                         theBorderBrushColor As System.Windows.Media.Color,
                                         theBorderThickness As Double,
                                         theOpacity As Double) As ESRI.ArcGIS.Client.Symbols.SimpleFillSymbol
    
    ' Utility function to create a SimpleFillSymbol with various Properties.
    Dim theSimpleFillSymbol As New ESRI.ArcGIS.Client.Symbols.SimpleFillSymbol
    theSimpleFillSymbol.Fill = New System.Windows.Media.SolidColorBrush(theFillColor)
    theSimpleFillSymbol.BorderBrush = New System.Windows.Media.SolidColorBrush(theBorderBrushColor)
    theSimpleFillSymbol.BorderThickness = theBorderThickness
    theSimpleFillSymbol.Fill.Opacity = theOpacity
    
    Return (theSimpleFillSymbol)
    
  End Function
  
  Public Function CreateSimpleLineSymbol(theColor As System.Windows.Media.Color,
                                         theStyle As ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol.LineStyle,
                                         theWidth As Double) As ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol
    
    ' Utility function to create a SimpleLineSymbol with various Properties.
    Dim theSimpleLineSymbol As New ESRI.ArcGIS.Client.Symbols.SimpleLineSymbol
    theSimpleLineSymbol.Color = New System.Windows.Media.SolidColorBrush(theColor)
    theSimpleLineSymbol.Style = theStyle
    theSimpleLineSymbol.Width = theWidth
    
    Return theSimpleLineSymbol
    
  End Function
  
#End Region