WPF. GeometryDrawing's Brush is always only Transparent - wpf

Question

Here is a test app that just shows a hatched ellipse in a window. No matter how I write it, the background of the ellipse is transparent; not the color I'm setting the GeometryDrawing. I'm stumped. The resulting picture shows the background of the ellipse as transparent when it should be Green.
<Window x:Class="MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:local="clr-namespace:WpfApp2"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
Title="MainWindow"
Background="Red"
mc:Ignorable="d">
<Window.Resources>
<ResourceDictionary>
<DrawingBrush x:Key="HatchBrush"
Stretch="UniformToFill"
TileMode="Tile"
Viewbox="0 0 10 10"
ViewboxUnits="Absolute"
Viewport="0 0 10 10"
ViewportUnits="Absolute">
<DrawingBrush.Drawing>
<GeometryDrawing Brush="Green">
<GeometryDrawing.Geometry>
<GeometryGroup>
<LineGeometry StartPoint="0 0"
EndPoint="10 0" />
<LineGeometry StartPoint="0 0"
EndPoint="0 10" />
</GeometryGroup>
</GeometryDrawing.Geometry>
<GeometryDrawing.Pen>
<Pen Brush="Yellow"
EndLineCap="Square"
StartLineCap="Square"
Thickness="3" />
</GeometryDrawing.Pen>
</GeometryDrawing>
</DrawingBrush.Drawing>
</DrawingBrush>
</ResourceDictionary>
</Window.Resources>
<Grid Margin="5"
HorizontalAlignment="Stretch"
VerticalAlignment="Stretch">
<Ellipse x:Name="c_Ellipse"
HorizontalAlignment="Stretch"
VerticalAlignment="Stretch"
Fill="{StaticResource HatchBrush}"
Stroke="Black" />
</Grid>
</Window>
This is what I get:
The background of the ellipse should be Green:
<GeometryDrawing Brush="Green">

Answer 1

There is no filled geometry that uses the GeometryDrawing's Brush.
You may use a RectangleGeometry instead of two LineGeometries:
<GeometryDrawing Brush="Green">
<GeometryDrawing.Geometry>
<RectangleGeometry Rect="0,0,10,10"/>
</GeometryDrawing.Geometry>
<GeometryDrawing.Pen>
<Pen Brush="Yellow" Thickness="1.5"/>
</GeometryDrawing.Pen>
</GeometryDrawing>