WPF Arc!

void setSegments() {
    if (Variant != EllipticalArcGeometryVariant.Sector)
        geometry.Figures[0] = segmentFigure;
    else
        geometry.Figures[0] = sectorFigure;
    double angleTo = AngularSize;
    bool fullEllipse = AngularSize >= Arcs.DefinitionSet.MaxAngle;
    if (fullEllipse)
        angleTo = Arcs.DefinitionSet.MaxAngle / 2;
    Point first = new Point(Center.X + RadiusX, Center.Y);
    Point second = new Point(Center.X + RadiusX * cos(angleTo), Center.Y - RadiusX * sin(angleTo));
    sectorFigure.StartPoint = Center;
    line.Point = first;
    arcSegment.Point = second;
    arcSegment.IsLargeArc = AngularSize > Arcs.DefinitionSet.MaxAngle / 2;
    if (Variant != EllipticalArcGeometryVariant.Sector)
        segmentFigure.StartPoint = first;
    if (fullEllipse) {
        ellipseFigure.StartPoint = first;
        augmentingArcSegment.Size = arcSegment.Size;
        augmentingArcSegment.Point = first;
        geometry.Figures[0] = ellipseFigure;
    } //if
} //setSegments

This entire exercise is done on a round shape and for the Angle value of 0. Other angles and different ellipse aspect ratio are obtained by two Transform operations: rotation followed by scale.

Having all that, the class EllipticalArcShape is quite trivially implemented based on EllipticalArcGeometry, without any need to deal with paths again. Please see the source code.

If it Looks Like Geometry, Swims Like Geometry…

…no, it is not a duck, and it does not even have to be Geometry. EllipticalArcGeometry just can be used where Geometry can be used; well, almost everywhere; this is the whole point of having this class.

For example, as with real Geometry types, it can be used to create a non-rectangular control, including Window. The picture at the top shows a ToolTip “Double click to see Non-Rectangular Window Demo”. Indeed, let’s click on it and see how it looks on the background of its own source code:

Sorry for somewhat predatory look of this picture. :-)

Note that this is not just transparency; it is a real window shape seen on the UIElement behavior. If you click it the area of the transparent elliptical-arc area in the bottom-right corner of the window, it will be deactivated to activate the window of some other application, such as Visual Studio. It you click in the opaque blue area, you can drag the window, close it, and so on.

Apparently, same thing can be done with any UIElement, as it is achieved by assigning some Geometry instance to the property System.Windows.UIElement.Clip.

Likewise, the Geometry instance coming from the EllipticalArcGeometry factory, can be used in other techniques, for example, in WPF Graphics Rendering through GeometryDrawing or rendered via DrawingContext by using the method DrawingContext.DrawGeometry.

Those who really ran the demo showing the non-rectangular window could see that the window is also animated; and the subject of this animation is the same very window clip: not only the window shape is not rectangular, but this shape is also changing with time. Is it a problem or not? It would not be a problem if EllipticalArcGeometry was actually a Geometry class, of if standard WPF animation was not used.

How can it be Animatable?

Coming back to the design of EllipticalArcGeometry, which works through a factory method providing access to some Geometry instance, but is not itself a Geometry. Would it be enough in all cases? Apparently not. There is always a way to see that some class is not derived from some other class, such as Geometry. For example, the method BeginAnimation accepts some dependency property as a first parameter, but properties of EllipticalArcGeometry are not the properties of its Geometry, so animation would not work. How to resolve this problem?

The main demo shows the animation on the class EllipticalArcShape, which is not a problem at all, because it derives from Shape, already Animatable. But we cannot do the same with Geometry. Pretty obviously, the problem can be solved if we derive from the Geometry base class, which is Animatable. Fortunately, in contrast to Geometry or PathSegment, this class is publicly extensible; and only one method is required to be overridden in a derived class. So, the solution is quite simple:

public partial class EllipticalArcGeometry : Animation.Animatable {
    // ...
    protected override Freezable CreateInstanceCore() {
        return this;
    }
    // ...
}

public partial class NonRectangularDemo : Window {

    // ...

    protected override void OnContentRendered(System.EventArgs e) {
        DoubleAnimation animation = new DoubleAnimation();
        // ...
        clip.BeginAnimation(EllipticalArcGeometry.AngularSizeProperty, animation);
    } //OnContentRendered

    // ...

}