The right-angle triangle: Meet your new best friend

using System;
using System.Windows;
using System.Windows.Shapes;

namespace RedCell.Articles.RightAngleTriangle
{
    /// <summary>
    /// A ball
    /// </summary>
    public class Ball
    {
        #region Fields
        private Ellipse _ui;
        #endregion

        #region Initialization
        /// <summary>
        /// Initializes a new instance of the <see cref="Ball"/> class.
        /// </summary>
        public Ball()
        {
            Elasticity = 1;
        }
        #endregion

        #region Properties
        /// <summary>
        /// Gets or sets the X coordinate.
        /// </summary>
        /// <value>
        /// The X coordinate.
        /// </value>
        public double X { get; set; }

        /// <summary>
        /// Gets or sets the Y coordinate.
        /// </summary>
        /// <value>
        /// The Y coordinate.
        /// </value>
        public double Y { get; set; }

        /// <summary>
        /// Gets or sets the speed.
        /// </summary>
        /// <value>
        /// The speed.
        /// </value>
        public double Speed { get; set; }

        /// <summary>
        /// Gets or sets the angle.
        /// </summary>
        /// <value>
        /// The angle.
        /// </value>
        public double Angle { get; set; }

        /// <summary>
        /// Gets or sets the radius.
        /// </summary>
        /// <value>
        /// The radius.
        /// </value>
        public double Radius { get; set; }

        /// <summary>
        /// Gets the mass.
        /// </summary>
        public double Mass
        {
            get { return Math.PI*Math.Pow(Radius, 2); }
        }

        /// <summary>
        /// Gets the width.
        /// </summary>
        public double Width
        {
            get { return Radius*2; }
        }

        /// <summary>
        /// Gets the height.
        /// </summary>
        public double Height
        {
            get { return Radius * 2; }
        }

        /// <summary>
        /// Gets or sets the elasticity.
        /// </summary>
        /// <value>
        /// The elasticity.
        /// </value>
        public double Elasticity { get; set; }

        /// <summary>
        /// Gets or sets the UI element.
        /// </summary>
        /// <value>
        /// The UI element.
        /// </value>
        internal Ellipse UI
        {
            get
            {
                if (_ui == null)
                    _ui = new Ellipse
                                  {
                                      Width = Radius * 2,
                                      Height = Radius * 2,
                                      Margin = new Thickness(X - Radius, Y - Radius, 0, 0)
                                  };
                return _ui;
            }
        }

        /// <summary>
        /// Gets the location.
        /// </summary>
        public Point Location 
        { 
            get { return new Point(X, Y);}
        }

        /// <summary>
        /// Gets a value indicating whether this instance is moving.
        /// </summary>
        /// <value>
        ///   <c>true</c> if this instance is moving; otherwise, <c>false</c>.
        /// </value>
        public bool IsMoving { get; internal set; }
        #endregion

        #region Methods
        /// <summary>
        /// Determines whether the ball contains the specified ball.
        /// </summary>
        /// <param name="point">The ball.</param>
        /// <returns>
        ///   <c>true</c> if the ball contains the specified point; otherwise, <c>false</c>.
        /// </returns>
        public bool Contains(Ball point)
        {
            var cdx = point.X - X;
            var cdy = point.Y - Y;
            var cdh = Math.Sqrt(Math.Pow(cdx, 2) + Math.Pow(cdy, 2));
            return cdh <= Radius;
        }

        /// <summary>
        /// Collides the specified ball.
        /// </summary>
        /// <param name="ball">The ball.</param>
        public void Collide(Ball ball)
        {
            // Calculate angles.
            var cdx = ball.X - X;
            var cdy = ball.Y - Y;
            var oldAngle = ball.Angle;
            var incidence = Math.Atan(cdy/cdx);
            var newAngle = ball.Angle = incidence * 2;
            Angle = newAngle-oldAngle + Math.PI;
        }

        /// <summary>
        /// Moves the specified angle.
        /// </summary>
        public void Move()
        {
            X += Math.Cos(Angle) * Speed;
            Y += Math.Sin(Angle) * Speed;
            UI.Margin = new Thickness(X - Radius, Y - Radius, 0, 0);
        }
        #endregion
    }
}