public class Sphere : UIElement3D
{
    // OnUpdateModel is called in response to InvalidateModel and provides
    // a place to set the Visual3DModel property.
    // 
    // Setting Visual3DModel does not provide parenting information, which
    // is needed for data binding, styling, and other features. Similarly, creating render data
    // in 2-D does not provide the connections either.
    // 
    // To get around this, we create a Model dependency property which
    // sets this value.  The Model DP then causes the correct connections to occur
    // and the above features to work correctly.
    // 
    // In this update model we retessellate the sphere based on the current
    // dependency property values, and then set it as the model.  The brush
    // color is blue by default, but the code can easily be updated to let
    // this be set by the user.

    protected override void OnUpdateModel()
    {
        GeometryModel3D model = new GeometryModel3D();

        model.Geometry = Tessellate(ThetaDiv, PhiDiv, Radius);
        model.Material = new DiffuseMaterial(System.Windows.Media.Brushes.Blue);

        Model = model;
    }

    // The Model property for the sphere
    private static readonly DependencyProperty ModelProperty =
        DependencyProperty.Register("Model",
                                    typeof(Model3D),
                                    typeof(Sphere),
                                    new PropertyMetadata(ModelPropertyChanged));

    private static void ModelPropertyChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
    {
        Sphere s = (Sphere)d;
        s.Visual3DModel = s.Model;
    }

    private Model3D Model
    {
        get
        {
            return (Model3D)GetValue(ModelProperty);
        }

        set
        {
            SetValue(ModelProperty, value);
        }
    }

    // The number of divisions to make in the theta direction on the sphere
    public static readonly DependencyProperty ThetaDivProperty =
        DependencyProperty.Register("ThetaDiv",
                                    typeof(int),
                                    typeof(Sphere),
                                    new PropertyMetadata(15, ThetaDivPropertyChanged));

    private static void ThetaDivPropertyChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
    {
        Sphere s = (Sphere)d;
        s.InvalidateModel();
    }

    public int ThetaDiv
    {
        get
        {
            return (int)GetValue(ThetaDivProperty);
        }

        set
        {
            SetValue(ThetaDivProperty, value);
        }
    }

    // The number of divisions to make in the phi direction on the sphere
    public static readonly DependencyProperty PhiDivProperty =
        DependencyProperty.Register("PhiDiv",
                                    typeof(int),
                                    typeof(Sphere),
                                    new PropertyMetadata(15, PhiDivPropertyChanged));

    private static void PhiDivPropertyChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
    {
        Sphere s = (Sphere)d;
        s.InvalidateModel();
    }

    public int PhiDiv
    {
        get
        {
            return (int)GetValue(PhiDivProperty);
        }

        set
        {
            SetValue(PhiDivProperty, value);
        }
    }

    // The radius of the sphere
    public static readonly DependencyProperty RadiusProperty =
        DependencyProperty.Register("Radius",
                                    typeof(double),
                                    typeof(Sphere),
                                    new PropertyMetadata(1.0, RadiusPropertyChanged));

    private static void RadiusPropertyChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
    {
        Sphere s = (Sphere)d;
        s.InvalidateModel();
    }

    public double Radius
    {
        get
        {
            return (double)GetValue(RadiusProperty);
        }

        set
        {
            SetValue(RadiusProperty, value);
        }
    }

    // Private helper methods
    private static Point3D GetPosition(double theta, double phi, double radius)
    {
        double x = radius * Math.Sin(theta) * Math.Sin(phi);
        double y = radius * Math.Cos(phi);
        double z = radius * Math.Cos(theta) * Math.Sin(phi);

        return new Point3D(x, y, z);
    }

    private static Vector3D GetNormal(double theta, double phi)
    {
        return (Vector3D)GetPosition(theta, phi, 1.0);
    }

    private static double DegToRad(double degrees)
    {
        return (degrees / 180.0) * Math.PI;
    }

    private static System.Windows.Point GetTextureCoordinate(double theta, double phi)
    {
        System.Windows.Point p = new System.Windows.Point(theta / (2 * Math.PI),
                            phi / (Math.PI));

        return p;
    }

    // Tesselates the sphere and returns a MeshGeometry3D representing the 
    // tessellation based on the given parameters
    internal static MeshGeometry3D Tessellate(int tDiv, int pDiv, double radius)
    {            
        double dt = DegToRad(360.0) / tDiv;
        double dp = DegToRad(180.0) / pDiv;

        MeshGeometry3D mesh = new MeshGeometry3D();

        for (int pi = 0; pi <= pDiv; pi++)
        {
            double phi = pi * dp;

            for (int ti = 0; ti <= tDiv; ti++)
            {
                // we want to start the mesh on the x axis
                double theta = ti * dt;

                mesh.Positions.Add(GetPosition(theta, phi, radius));
                mesh.Normals.Add(GetNormal(theta, phi));
                mesh.TextureCoordinates.Add(GetTextureCoordinate(theta, phi));
            }
        }

        for (int pi = 0; pi < pDiv; pi++)
        {
            for (int ti = 0; ti < tDiv; ti++)
            {
                int x0 = ti;
                int x1 = (ti + 1);
                int y0 = pi * (tDiv + 1);
                int y1 = (pi + 1) * (tDiv + 1);

                mesh.TriangleIndices.Add(x0 + y0);
                mesh.TriangleIndices.Add(x0 + y1);
                mesh.TriangleIndices.Add(x1 + y0);

                mesh.TriangleIndices.Add(x1 + y0);
                mesh.TriangleIndices.Add(x0 + y1);
                mesh.TriangleIndices.Add(x1 + y1);
            }
        }

        mesh.Freeze();
        return mesh;
    }
}