public static void Draw(Canvas canvas, List<LinePoint> points, Brush stroke, bool clear = true)
        {
            if (clear)
            {
                canvas.Children.Clear();
            }

            PathFigureCollection myPathFigureCollection = new PathFigureCollection();
            PathGeometry myPathGeometry = new PathGeometry();

            foreach (LinePoint p in points)
            {
                PathFigure myPathFigure = new PathFigure();
                myPathFigure.StartPoint = p.StartPoint;

                LineSegment myLineSegment = new LineSegment();
                myLineSegment.Point = p.EndPoint;

                PathSegmentCollection myPathSegmentCollection = new PathSegmentCollection();
                myPathSegmentCollection.Add(myLineSegment);

                myPathFigure.Segments = myPathSegmentCollection;

                myPathFigureCollection.Add(myPathFigure);
            }

            myPathGeometry.Figures = myPathFigureCollection;
            Path myPath = new Path();
            myPath.Stroke = stroke == null ? Brushes.Black : stroke;
            myPath.StrokeThickness = 1;
            myPath.Data = myPathGeometry;

            canvas.Children.Add(myPath);
        }

        public void Setup()
        {
            m_StartSegment = Substitute.For <ITurnCircleArcSegment>();
            m_MiddleSegment = Substitute.For <ITurnCircleArcSegment>();
            m_EndSegment = Substitute.For <ITurnCircleArcSegment>();

            m_Path = Substitute.For <IPath>();
            var segments = new List <IPolylineSegment>
                           {
                               m_StartSegment,
                               m_MiddleSegment,
                               m_EndSegment
                           };

            m_Path.Segments.Returns(segments);

            m_ArcSegmentOne = new ArcSegment(new Point(10.0,
                                                       10.0),
                                             new Size(10.0,
                                                      10.0),
                                             45.0,
                                             false,
                                             SweepDirection.Clockwise,
                                             false);

            m_LineSegment = new LineSegment(new Point(20.0,
                                                      20.0),
                                            false);

            m_ArcSegmentTwo = new ArcSegment(new Point(30.0,
                                                       30.0),
                                             new Size(30.0,
                                                      30.0),
                                             90.0,
                                             false,
                                             SweepDirection.Counterclockwise,
                                             false);

            m_ArcSegmentThree = new ArcSegment(new Point(40.0,
                                                         40.0),
                                               new Size(40.0,
                                                        40.0),
                                               135.0,
                                               false,
                                               SweepDirection.Counterclockwise,
                                               false);


            m_Point = new Point(10.0,
                                10.0);

            m_Helper = Substitute.For <IPathSegmentHelper>();
            m_Helper.SegmentToLineSegment(Line.Unknown).ReturnsForAnyArgs(m_LineSegment);
            m_Helper.SegmentToArcSegment(TurnCircleArcSegment.Unknown).ReturnsForAnyArgs(m_ArcSegmentOne,
                                                                                         m_ArcSegmentTwo,
                                                                                         m_ArcSegmentThree);
            m_Helper.PointRelativeToOrigin(null).ReturnsForAnyArgs(m_Point);

            m_Converter = new RacetrackPathUTurnToFiguresConverter(m_Helper);
        }

        // Create the pen and triangle in a static constructor and freeze them to improve performance.
        static InsertionAdorner()
        {
            pen = new Pen
            {
                Brush = Brushes.Gray,
                Thickness = 2
            };
            pen.Freeze();

            LineSegment firstLine = new LineSegment(new Point(0, -5), false);
            firstLine.Freeze();
            LineSegment secondLine = new LineSegment(new Point(0, 5), false);
            secondLine.Freeze();

            PathFigure figure = new PathFigure
            {
                StartPoint = new Point(5, 0)
            };
            figure.Segments.Add(firstLine);
            figure.Segments.Add(secondLine);
            figure.Freeze();

            triangle = new PathGeometry();
            triangle.Figures.Add(figure);
            triangle.Freeze();
        }

        public Superposition()
        {
            InitializeComponent();
                        
            PathGeometry pathGeometry = new PathGeometry();
            PathFigure pathFigure = new PathFigure();
            
            pathFigure.StartPoint = new Point(0,0);

            PathSegmentCollection pathSegmentCollection = new PathSegmentCollection();

            int maxHeight = (int)this.Height;
            int maxWidth = (int)this.Width;
            Random rand = new Random();
            for (int i = 0; i < 500; i++)
            {
                LineSegment newSegment = new LineSegment();
                newSegment.Point = new Point(rand.Next(0, maxWidth), rand.Next(0, maxHeight));
                pathSegmentCollection.Add(newSegment);
            }

            pathFigure.Segments = pathSegmentCollection;
            pathGeometry.Figures.Add(pathFigure);

            pathBackground.Data = pathGeometry;


        }

        public void Draw(EasingFunctionBase easingFunction)
        {
            canvas1.Children.Clear();


            PathSegmentCollection pathSegments = new PathSegmentCollection();

            for (double i = 0; i < 1; i += _samplingInterval)
            {
                double x = i * canvas1.Width;
                double y = easingFunction.Ease(i) * canvas1.Height;

                var segment = new LineSegment();
                segment.Point = new Point(x, y);

                pathSegments.Add(segment);

            }
            var p = new Path();
            p.Stroke = new SolidColorBrush(Colors.Black);
            p.StrokeThickness = 3;
            PathFigureCollection figures = new PathFigureCollection();
            figures.Add(new PathFigure() { Segments = pathSegments });
            p.Data = new PathGeometry() { Figures = figures };
            canvas1.Children.Add(p);
        }

        public Triangle()
        {
            InitializeComponent();

            l1 = new LineSegment();
            l2 = new LineSegment();

            f = new PathFigure();
            f.Segments.Add(l1);
            f.Segments.Add(l2);
            f.IsClosed = true;

            PathGeometry g = new PathGeometry();
            g.Figures.Add(f);

            Path p = new Path();
            this.SetBinding(FillProperty, new Binding("Fill") { Source = p, Mode = BindingMode.TwoWay });
            this.SetBinding(StrokeProperty, new Binding("Stroke") { Source = p, Mode = BindingMode.TwoWay });
            this.SetBinding(StrokeThicknessProperty, new Binding("StrokeThickness") { Source = p, Mode = BindingMode.TwoWay });
            p.Data = g;

            this.Fill = new SolidColorBrush(Colors.White);
            this.Stroke = new SolidColorBrush(Colors.Black);

            this.LayoutRoot.Children.Add(p);
        }

        /// <summary>
        /// Add new point (line segment)
        /// </summary>
        public void AddPoint(Point point)
        {
            LineSegment segment = new LineSegment(point, true);
            segment.IsSmoothJoin = true;

            pathGeometry.Figures[0].Segments.Add(segment);

            MakePoints();   // keep points array up to date
        }

        private void DefineGeometry()
        {
            PointCollection points = Points;
            if (points == null)
            {
                _geometry = Geometry.Empty;
                return;
            }

            PathFigure figure = new PathFigure();
            if (points.Count > 0)
            {
                // start point
                figure.StartPoint = points[0];

                if (points.Count > 1)
                {
                    // points between
                    double desiredRadius = Radius;
                    for (int i = 1; i < (points.Count - 1); i++)
                    {
                        // adjust radius if points are too close
                        Vector v1 = points[i] - points[i - 1];
                        Vector v2 = points[i + 1] - points[i];
                        double radius = Math.Min(Math.Min(v1.Length, v2.Length) / 2, desiredRadius);

                        // draw the line, and stop before the next point
                        double len = v1.Length;
                        v1.Normalize();
                        v1 *= (len - radius);
                        LineSegment line = new LineSegment(points[i - 1] + v1, true);
                        figure.Segments.Add(line);

                        // draw the arc to the next point
                        v2.Normalize();
                        v2 *= radius;
                        SweepDirection direction = (Vector.AngleBetween(v1, v2) > 0) ? SweepDirection.Clockwise : SweepDirection.Counterclockwise;
                        ArcSegment arc = new ArcSegment(points[i] + v2, new Size(radius, radius), 0, false, direction, true);
                        figure.Segments.Add(arc);
                    }

                    // last point
                    figure.Segments.Add(new LineSegment(points[points.Count - 1], true));
                }
            }
            PathGeometry geometry = new PathGeometry();
            geometry.Figures.Add(figure);
            geometry.FillRule = FillRule;
            if (geometry.Bounds == Rect.Empty)
            {
                _geometry = Geometry.Empty;
            }
            else
            {
                _geometry = geometry;
            }
        }

 public Arc(Path path, LineSegment lineSegment, ArcSegment arcSegment, Point zeroPos, Color color)
 {
     Path = path;
     LineSegment = lineSegment;
     ArcSegment = arcSegment;
     ZeroPos = zeroPos;
     Path.Stroke = ToBrush(color);
     Path.Fill = ToBrush(color);
 }

        public LineSegment SegmentToLineSegment(ILine segment)
        {
            m_Converter.GeometryPoint = segment.EndPoint;
            m_Converter.Convert();

            var line = new LineSegment(m_Converter.Point,
                                       true);

            return line;
        }

        /// <summary>
        /// Adds a line to a <see cref="PathGeometry"/>.
        /// </summary>
        /// <param name="pathGeometry">The <see cref="PathGeometry"/>.</param>
        /// <param name="start">The start point of the line.</param>
        /// <param name="end">The end point of the line.</param>
        /// <exception cref="ArgumentNullException">
        /// <paramref name="pathGeometry"/> is <see langword="null"/>.
        /// </exception>
        public static void AddLine(this PathGeometry pathGeometry, Point start, Point end)
        {
            if (pathGeometry == null)
                throw new ArgumentNullException(nameof(pathGeometry));

            var pathFigure = new PathFigure { StartPoint = start };
            var lineSegment = new LineSegment { Point = end };
            pathFigure.Segments.Add(lineSegment);
            pathGeometry.Figures.Add(pathFigure);
        }

        public LineAndAreaShape(PathFigure figure)
        {
            Figure = figure;
            Right = new LineSegment(new Point(), false);
            Bottom = new LineSegment(new Point(), false);
            Left = new LineSegment(new Point(), false);

            Figure.Segments.Add(Right);
            Figure.Segments.Add(Bottom);
            Figure.Segments.Add(Left);
        }

        protected override void UpdateShape()
        {
            if (ShapeStart == ShapeEnd)
                return;
            figure.StartPoint = ShapeStart;

            LineSegment segment = new LineSegment();
            segment.Point = ShapeEnd;

            figure.Segments.Add(segment);
        }

        /// <summary>
        /// Paints on a pbgra32 WriteableBitmap with a stylized airbrush
        /// </summary>
        /// <param name="bmp">The bitmap to modify</param>
        /// <param name="from">The starting point of the stroke</param>
        /// <param name="to">The end point of the stroke</param>
        /// <param name="color">The color of the stroke</param>
        /// <param name="size">The size of the stroke</param>
        public static unsafe void Airbrush(WriteableBitmap bmp, Point from, Point to, Color color, int size)
        {
            Random r = new Random();

            if (bmp == null) return;

            bmp.Lock();

            // Create a line segment representation
            LineSegment segment = new LineSegment(from, to);

            // Get a bounding box for the painted area
            BoundingBox bitmapbounds = new BoundingBox();
            BoundingBox segmentbounds = new BoundingBox();

            bitmapbounds.AddPoint(0, 0, 0);
            bitmapbounds.AddPoint(bmp.PixelWidth - 1, bmp.PixelHeight - 1, 0);

            segmentbounds.AddPoint((int)from.X, (int)from.Y, size + AirbrushDotRadius);
            segmentbounds.AddPoint((int)to.X, (int)to.Y, size + AirbrushDotRadius);
            segmentbounds.Clip(bitmapbounds);

            UInt32* start = (UInt32*)bmp.BackBuffer.ToPointer();
            int stride = bmp.BackBufferStride / sizeof(UInt32);
            // Move from 'from' to 'to' along timestep intervals, with one dot painted per interval
            for (int i = 0; i < AirbrushDots; i++)
            {
                int x, y;
                segment.Interpolate(i, AirbrushDots, out x, out y);

                int dist = r.Next() % size;
                double angle = r.NextDouble() * 2 * Math.PI;

                double dx = Math.Cos(angle) * dist;
                double dy = Math.Sqrt(dist * dist - dx * dx);
                if(angle > Math.PI) dy = -dy;

                int bx = x + (int)dx;
                int by = y + (int)dy;

                BoundingBox dotbounds = new BoundingBox();

                dotbounds.AddPoint(bx,by,AirbrushDotRadius);
                dotbounds.Clip(bitmapbounds);

                for (int k = dotbounds.Top, row = 0; k < dotbounds.Bottom; k++, y++, row++)
                    for (int j = dotbounds.Left, col = 0; j < dotbounds.Right; j++, col++)
                        WriteAlphaBlended(start + stride * k + j, Color.FromArgb(AirbrushDotKernel[row][col], color.R, color.G, color.B));
            }

            bmp.AddDirtyRect(new Int32Rect(segmentbounds.Left, segmentbounds.Top, segmentbounds.Width, segmentbounds.Height));
            bmp.Unlock();
        }

 /// <summary>
 /// Create the pen and triangle in a static constructor and freeze them to improve performance.
 /// </summary>
 static InsertionAdorner()
 {
     Pen = new Pen { Brush = Brushes.SkyBlue, Thickness = LineThickness };
     Pen.Freeze();
     var firstLine = new LineSegment(new Point(0, -TriangleWidth), false);
     firstLine.Freeze();
     var secondLine = new LineSegment(new Point(0, TriangleWidth), false);
     secondLine.Freeze();
     var figure = new PathFigure {StartPoint = new Point(TriangleWidth, 0)};
     figure.Segments.Add(firstLine);
     figure.Segments.Add(secondLine);
     figure.Freeze();
     Triangle = new PathGeometry();
     Triangle.Figures.Add(figure);
     Triangle.Freeze();
 }

        public static PathGeometry GenerateBezierCurve(Point[] points)
        {
            PathFigure pathFigure = new PathFigure();
            PointCollection pointCollection = new PointCollection(points.Length);
            pathFigure.StartPoint = new Point(points[0].X, points[0].Y);

            PathGeometry myPathGeometry = new PathGeometry();
            PathSegment pathSegment;

            if (points.Length == 2)
            {
                pathSegment = new LineSegment();
                ((LineSegment)pathSegment).Point = new Point(points[1].X, points[1].Y);
            }
            else if (points.Length == 3)
            {
                pathSegment = new QuadraticBezierSegment();
                ((QuadraticBezierSegment)pathSegment).Point1 = new Point(points[1].X, points[1].Y);
                ((QuadraticBezierSegment)pathSegment).Point2 = new Point(points[2].X, points[2].Y);
            }
            else if (points.Length == 4)
            {
                for (int i = 1; i < points.Length; i++)
                {
                    pointCollection.Add(points[i]);
                }

                pathSegment = new PolyBezierSegment();
                ((PolyBezierSegment)pathSegment).Points = pointCollection;
            }
            else
            {
                return null;
            }

            PathSegmentCollection pathSegmentCollection = new PathSegmentCollection();
            pathSegmentCollection.Add(pathSegment);

            pathFigure.Segments = pathSegmentCollection;

            PathFigureCollection pathFigureCollection = new PathFigureCollection();
            pathFigureCollection.Add(pathFigure);

            myPathGeometry.Figures = pathFigureCollection;

            return myPathGeometry;
        }

        public void Show()
        {

            Color pixClr = new Color();
            pixClr.A = 255;
            pixClr.R = byte.Parse(PixelColor.Substring(0, 2), System.Globalization.NumberStyles.HexNumber);
            pixClr.G = byte.Parse(PixelColor.Substring(2, 2), System.Globalization.NumberStyles.HexNumber);
            pixClr.B = byte.Parse(PixelColor.Substring(4, 2), System.Globalization.NumberStyles.HexNumber);
            RandomNumber = new Random();
            for (int i = 0; i < 100; i++)
            {


                int xval = RandomNumber.Next((int)Width);
                int yval = RandomNumber.Next((int)Height);
                int xRval = xval+RandomNumber.Next(-20,20);
                int yRval = yval + RandomNumber.Next(-20, 20);
                int xR2val = xRval + RandomNumber.Next(-20, 20);
                int yR2val = yRval + RandomNumber.Next(-20, 20);
                Point startingPt = new Point(xval, yval);
                Point randomPt = new Point(xRval, yRval);
                Point randomPt2 = new Point(xR2val, yR2val);
                Path pixel = new Path();
                PathFigure pixelFigure = new PathFigure();
                GeometryGroup geometry = new GeometryGroup();
                LineSegment line1 = new LineSegment();
                pixelFigure.StartPoint = startingPt;
                line1.Point = randomPt;

                LineSegment line2 = new LineSegment();
                line2.Point = randomPt2;

                LineSegment line3 = new LineSegment();
                line3.Point = startingPt;
                pixelFigure.Segments.Add(line1);
                pixelFigure.Segments.Add(line2);
                pixelFigure.Segments.Add(line3);
                
                pixel.Stroke = new SolidColorBrush(pixClr);
                pixel.Fill = new SolidColorBrush(pixClr);
               // pixel.Stretch = Stretch.Fill;
                PathGeometry pathGeo = new PathGeometry();
                pathGeo.Figures.Add(pixelFigure);
                pixel.Data = pathGeo;
                ExplosionEffect.Children.Add(pixel);
            }
        }

        /// <summary>
        /// Adds a polygon to a <see cref="PathGeometry"/>.
        /// </summary>
        /// <param name="pathGeometry">The <see cref="PathGeometry"/>.</param>
        /// <param name="points">The points on the polygon.</param>
        /// <exception cref="ArgumentNullException">
        /// <paramref name="pathGeometry"/> is <see langword="null"/>.
        /// </exception>
        public static void AddPolygon(this PathGeometry pathGeometry, params Point[] points)
        {
            if (pathGeometry == null)
                throw new ArgumentNullException(nameof(pathGeometry));

            if (points == null || points.Length <= 1)
                return;

            var pathFigure = new PathFigure { StartPoint = points[0] };
            for (int i = 1; i < points.Length; i++)
            {
                var lineSegment = new LineSegment { Point = points[i] };
                pathFigure.Segments.Add(lineSegment);
            }

            pathGeometry.Figures.Add(pathFigure);
        }

 public override void OnApplyTemplate()
 {
     base.OnApplyTemplate();
     this.Root = base.GetTemplateChild("Root") as Border;
     this.ArrowRow = base.GetTemplateChild("ArrowRow") as RowDefinition;
     this.ToolTipPathFigure = base.GetTemplateChild("ToolTipPathFigure") as PathFigure;
     this.BottomCenterLeft = base.GetTemplateChild("BottomCenterLeft") as LineSegment;
     this.BottomLeftCorner1 = base.GetTemplateChild("BottomLeftCorner1") as LineSegment;
     this.BottomLeftCorner2 = base.GetTemplateChild("BottomLeftCorner2") as ArcSegment;
     this.TopLeftCorner1 = base.GetTemplateChild("TopLeftCorner1") as LineSegment;
     this.TopLeftCorner2 = base.GetTemplateChild("TopLeftCorner2") as ArcSegment;
     this.TopRightCorner1 = base.GetTemplateChild("TopRightCorner1") as LineSegment;
     this.TopRightCorner2 = base.GetTemplateChild("TopRightCorner2") as ArcSegment;
     this.BottomRightCorner1 = base.GetTemplateChild("BottomRightCorner1") as LineSegment;
     this.BottomRightCorner2 = base.GetTemplateChild("BottomRightCorner2") as ArcSegment;
     this.BottomCenterRight = base.GetTemplateChild("BottomCenterRight") as LineSegment;
 }

 public ArrowControl()
 {
     endPt1 = new BezierSegment();
       endPt2 = new LineSegment();
       arrowPt1 = new LineSegment();
       arrowPt2 = new LineSegment();
       headPt = new LineSegment();
       startPt2 = new BezierSegment();
       startPt1 = new PathFigure()
       {
     Segments = new PathSegmentCollection() { endPt1, arrowPt1, headPt, arrowPt2, endPt2, startPt2 },
     IsClosed = true
       };
       Shape = new Path() { Data = new PathGeometry() { Figures = new PathFigureCollection() { startPt1 } } };
       Shape.Stroke = Brushes.Red;
       Shape.Fill = fillBrush;
 }