Area Calculation of CombinedGeometry parts - wpf

Question

I need to calculate some areas based on Geometry intersection.
In my example I have the following Geometries:
Left RectangleGeometry
Right RectangleGeometry
EllipseGeometry
The Ellipse is in the middle of the Rectangles and I want two get the following data:
Area of the intersection between the Ellipse and left rectangle
Area of the intersection between the Ellipse and the right rectangle
Total Area of the Ellipse.
The issue is that the total area of the ellipse, EllipseGeometry.GetArea(), and the "LeftEllipseGeometry".GetArea() + "RightEllipseGeometry".GetArea() are different.
The sum of intersections areas have to be the same as the ellipe Area.
I made an example where you can test and see the problem.
MainWindow.xaml.cs
void MainWindow_Loaded(object sender, RoutedEventArgs e)
{
//LEFT
rectLeft = new RectangleGeometry();
rectLeft.Rect = new Rect(new Point(75, 100), new Point(700, 600));
Path pathRectLeft = new Path();
pathRectLeft.Stroke = Brushes.Red;
pathRectLeft.Data = rectLeft;
grdMain.Children.Add(pathRectLeft);
//RIGHT
rectRight = new RectangleGeometry();
rectRight.Rect = new Rect(new Point(700, 100), new Point(1300, 600));
Path pathRectRight = new Path();
pathRectRight.Stroke = Brushes.Green;
pathRectRight.Data = rectRight;
grdMain.Children.Add(pathRectRight);
//ELLIPSE
ellipseGeo = new EllipseGeometry();
ellipseGeo.RadiusX = 200;
ellipseGeo.RadiusY = 200;
ellipseGeo.Center = new Point(700, 350);
Path ellipsePath = new Path();
ellipsePath.Stroke = Brushes.Blue;
ellipsePath.Data = ellipseGeo;
grdMain.Children.Add(ellipsePath);
lblEllipseArea.Content = String.Concat("Area Ellipse = ", ellipseGeo.GetArea());
}
private void Button_Click(object sender, RoutedEventArgs e)
{
CombinedGeometry cgLeft = new CombinedGeometry();
cgLeft.Geometry1 = rectLeft;
cgLeft.Geometry2 = ellipseGeo;
cgLeft.GeometryCombineMode = GeometryCombineMode.Intersect;
Path cgLeftPath = new Path();
cgLeftPath.Stroke = Brushes.Yellow;
cgLeftPath.Data = cgLeft;
grdMain.Children.Add(cgLeftPath);
lblEllipseAreaLeft.Content = String.Concat("Area Left Ellipse = ", cgLeft.GetArea());
CombinedGeometry cgRight = new CombinedGeometry();
cgRight.Geometry1 = rectRight;
cgRight.Geometry2 = ellipseGeo;
cgRight.GeometryCombineMode = GeometryCombineMode.Intersect;
Path cgRightPath = new Path();
cgRightPath.Stroke = Brushes.White;
cgRightPath.Data = cgRight;
grdMain.Children.Add(cgRightPath);
lblEllipseAreaRight.Content = String.Concat("Area Right Ellipse = ", cgRight.GetArea());
lblEllipseTotal.Content = String.Concat("Area Ellipse Total = ", cgLeft.GetArea() + cgRight.GetArea());
}
MainWindow.xaml
<Grid>
<StackPanel Orientation="Vertical" Background="Black">
<Grid Background="Black" Height="700" Name="grdMain">
</Grid>
<Grid Background="Black" Height="150">
<StackPanel Orientation="Vertical">
<Button Height="30" Width="70" Click="Button_Click">Click Me!!!</Button>
<StackPanel Orientation="Horizontal">
<Label Foreground="White" Name="lblEllipseArea"></Label>
<Label Foreground="White" Name="lblEllipseArea2" Margin="20 0 0 0"></Label>
<Label Foreground="White" Name="lblEllipseAreaRight" Margin="20 0 0 0"></Label>
<Label Foreground="White" Name="lblEllipseAreaRight2" Margin="20 0 0 0"></Label>
<Label Foreground="White" Name="lblEllipseAreaLeft" Margin="20 0 0 0"></Label>
<Label Foreground="White" Name="lblEllipseAreaLeft2" Margin="20 0 0 0"></Label>
</StackPanel>
<StackPanel Orientation="Horizontal">
<Label Foreground="White" Name="lblEllipseTotal" Margin="20 0 0 0"></Label>
<Label Foreground="White" Name="lblEllipseTotal2" Margin="20 0 0 0"></Label>
</StackPanel>
</StackPanel>
</Grid>
</StackPanel>
</Grid>

Answer 1

I think you might never get the "exact" areas from the CombinedGeometry. As expected, WPF does not use the "ideal" method to calculate this values. From MSDN: "Some Geometry methods (such as GetArea) produce or use a polygonal approximation of the geometry".
Check MSDN