About the area filling problem formed by multiple Geometry elements

[PaperHammer]

This may involve computer graphics.

I plan to implement the paint feature based on WinUI3. I've made all sorts of lines on the Canvas with PathGeometry, and now I want to be able to click on a location to fill an enclosed area, but I don't know how to find an enclosed area where the click is located and fill it as PathGeometry data in a Path UIElement that is made up of PathGeometry data.
Is there some way to calculate that the de-area should be populated and can be populated as PathGeometry's data?

Here's some of the code for drawing and rendering lines:

// DataModel
[MessagePackObject]
[Union(0, typeof(VectorPath))]
[Union(1, typeof(VectorRectangle))]
public abstract class VectorShapeBase {
    [Key(0)]
    public Guid Id { get; set; } = Guid.NewGuid();
    [Key(1)]
    [MessagePackFormatter(typeof(BrushFormatter))]
    public Brush Stroke { get; set; }
    [Key(2)]
    [MessagePackFormatter(typeof(BrushFormatter))]
    public Brush Fill { get; set; }
    [Key(3)]
    public double StrokeThickness { get; set; } = 5;
    [Key(4)]
    [MessagePackFormatter(typeof(TransformFormatter))]
    public Transform RenderTransform { get; set; }
    [IgnoreMember]
    public abstract VectorShapeType ShapeType { get; }
    [IgnoreMember]
    public abstract Geometry GeometryData { get; }

    public abstract Shape ToXamlShape();
    public abstract bool HitTest(Vector2 point);
}

// Drawing
class PaintBrushTool : ITool {
    public PaintBrushTool(LayerManagerData managerData) {
        _managerData = managerData;
    }

    public void OnPointerEntered(ToolItemEventArgs e) {
        _isDrawable = _managerData.SelectedLayerData.IsEnable;
    }

    public void OnPointerPressed(ToolItemEventArgs e) {
        if (!_isDrawable || e.CurrentPointerPoint.Properties.IsMiddleButtonPressed)
            return;

        _isDrawing = true;
        _blendedColor = BlendColor(e.CurrentPointerPoint.Properties.IsRightButtonPressed ?
            _managerData.BackgroundColor : _managerData.ForegroundColor, _managerData.BrushOpacity / 100);
        _blendedBrush = new(_blendedColor);
        _lastPoint = e.CurrentPointerPoint.Position;

        _currentPath = new VectorPath {
            PathData = new PathGeometry(),
            Stroke = _blendedBrush,
            Fill = null, 
            StrokeThickness = _managerData.BrushThickness,
            StrokeLineJoin = PenLineJoin.Round,
            StrokeStartLineCap = PenLineCap.Round,
            StrokeEndLineCap = PenLineCap.Round,
        };

        var figure = new PathFigure {
            StartPoint = _lastPoint,
            IsClosed = false
        };

        figure.Segments.Add(new LineSegment { Point = _lastPoint });
        _currentPath.PathData.Figures.Add(figure);

        _managerData.SelectedLayerData.AddShape(_currentPath);
    }
}

// Render
private void AddShapeToVisualTree(VectorShapeBase shape) {
    var uiElement = shape.ToXamlShape();
    _shapeMap[shape] = uiElement;
    Children.Add(uiElement);
}