An Oriented Bounding Box object with intersection methods for use in 2D projects under the XNA framework

OBB.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using Microsoft.Xna.Framework;
using Microsoft.Xna.Framework.Graphics;
using Extensions;

namespace OBBTest
{
    public class OBB
    {
        #region members and properties
        Vector2 _origin;//centre point of the OBB
        public Vector2 Origin
        {
            get { return _origin; }
            set { _origin = value; }
        }
        Vector2[] _axis;//2d orientation matrix
        public Vector2[] Axis
        {
            get { return _axis; }
        }
        Vector2 _halfWidths;//the +ve extents along each axis
        public Vector2 HalfWidths
        {
            get { return _halfWidths; }
            set { _halfWidths = value; }
        }
        float _angleInRadians;//used for drawing a visuaisation of the OBB
        public float AngleInRadians
        {
            get { return _angleInRadians; }
            set
            {
                if (value < Math.PI && value > -Math.PI) //in the range [-PI..PI]
                    UpdateAxis(value);
                if (value >= Math.PI)
                    UpdateAxis((float)(Math.Abs((value % Math.PI * 2)) - Math.PI));
                if (value <= -Math.PI)
                    UpdateAxis((float)(Math.Abs((value % Math.PI * 2)) + Math.PI));
            }
        }

        public Color DebugColor = Color.White;
        //an epsilon value to counter floating point errors in a parallel situation
        const float EPSILON = 0.00001f; 
        #endregion

        /// <summary>
        /// Creates an oriented bounding box for collision detection
        /// </summary>
        /// <param name="Origin">The center of the box</param>
        /// <param name="AngleInRadians">The rotation of the box in the xy plane</param>
        /// <param name="HalfWidths">The half extents of the box in it's X and Y axis</param>
        public OBB(Vector2 Origin, float AngleInRadians, Vector2 HalfWidths)
        {
            _origin = Origin;
            _angleInRadians = AngleInRadians;
            _halfWidths = HalfWidths;

            _axis = new Vector2[2];
            _axis[0] = new Vector2();
            _axis[1] = new Vector2();

            UpdateAxis(AngleInRadians);
        }

        /// <summary>
        /// Returns whether this OBB is intersecting a second
        /// </summary>
        /// <param name="OtherOBB"></param>
        /// <returns></returns>
        public bool Intersects(OBB OtherOBB)
        {
            return OBB.Intersects(this, OtherOBB);
        }

        /// <summary>
        /// Finds where we would draw our debug texture without rotation.
        /// </summary>
        /// <returns>A rectangle corresponging to the unrotated position of the AABB</returns>
        private Rectangle GetDestinationRect()
        {
            int x = (int)( _origin.X );
            int y = (int)(_origin.Y );
            int width = (int)(_halfWidths.X*2);
            int height = (int)(_halfWidths.Y*2);
            return new Rectangle(x, y, width, height);
        }

        /// <summary>
        /// Updates the orientation of the OBB
        /// </summary>
        /// <param name="AngleInRadians">The new rotation in radians</param>
        public void UpdateAxis(float AngleInRadians)
        {
            //Standard rotation matrix equation
            _axis[0].X = (float) Math.Cos(AngleInRadians);
            _axis[0].Y = (float)Math.Sin(AngleInRadians);
            _axis[1].Y = (float)Math.Cos(AngleInRadians);
            _axis[1].X = -(float)Math.Sin(AngleInRadians);

            _angleInRadians = AngleInRadians;
        }

        /// <summary>
        /// Prints the properties of the OBB to the console
        /// </summary>
        public void Print()
        {
            Console.WriteLine("origin : "+_origin+"\nAngle : "+_angleInRadians+
            "\nX Axis : "+_axis[0]+"\nY Axis : "+_axis[1]);
        }

        /// <summary>
        /// Draws a visualisation of the OBB, useful for debug purposes
        /// </summary>
        /// <param name="sb">The spritebatch instance to draw with</param>
        /// <param name="NullTexture">A reference to a 1x1 texture which will be draw over the OBB</param>
        public void Draw(Texture2D NullTexture,SpriteBatch sb)
        {
            //OBB's are only ever going to be drawn in debug mode
            //so performance from repeated Begin() End() calls is acceptable

            sb.Begin();
            
            Vector2 g = _halfWidths;
            g.Normalize();
            sb.Draw(NullTexture, GetDestinationRect(), null, DebugColor,
                _angleInRadians,
                Vector2.One/2,//the origin of the 1x1 texture i.e. (0.5f,0.5f)
                SpriteEffects.None, 1f);

            sb.End();

        }

        /// <summary>
        /// Tests whether two OBBs intersect. Uses a separating axis implementation.
        /// </summary>
        /// <param name="First">The first OBB</param>
        /// <param name="Second">The second OBB</param>
        /// <returns></returns>
        public static bool Intersects(OBB First, OBB Second)
        {
            #region pre test calcs and declarations
            float rf, rs;
            float[,] R = new float[2, 2];
            float[,] AbsR = new float[2, 2];

            //compuet rotation matrix by expressing second in terms of first
            //also create common sub expressions
            for (int i = 0; i < 2; i++)
                for (int j = 0; j < 2; j++)
                {
                    R[i, j] = Vector2.Dot(First.Axis[i], Second.Axis[j]);
                    AbsR[i, j] = Math.Abs(R[i, j]) + EPSILON;
                }

            //create translation vector
            Vector2 translation = Second.Origin - First.Origin;

            //bring translation into First's local coordinate system
            translation = new Vector2(Vector2.Dot(translation, First.Axis[0]),
                Vector2.Dot(translation, First.Axis[1])); 
            #endregion

           //Test if axes FirstX or FirstY separate the OBBs
            for (int i = 0; i < 2; i++ )
            {
                rf = First.HalfWidths.Index(i);
                rs = Second.HalfWidths.X * AbsR[i,0] + Second.HalfWidths.Y * AbsR[i,1];
                
                if(Math.Abs(translation.Index(i)) > (rf + rs))
                    return false;
            }

            //Test if axes SecondX or SecondY separate the OBBs
            for (int i = 0; i < 2; i++)
            {
                rf = First.HalfWidths.Index(0) * AbsR[0, i] + First.HalfWidths.Index(1) * AbsR[1, i];
                rs = Second.HalfWidths.Index(i);

                if(Math.Abs(translation.Index(0) * R[0,i] + translation.Index(1) * R[1,i]) > (rf + rs))
                    return false;
            }

            //no separating axis - OBBs must therefore be intersecting
            return true;
        }
    }
    
}

namespace Extensions
{
    /// <summary>
    /// Adds the ability to index a Vector2 for cheeky code saving
    /// </summary>
    public static class Vector2Extensions
    {
        public static float Index(this Vector2 v, int i)
        {
             switch(i)
            {
                case 0:
                    return v.X;
                case 1:
                    return v.Y;
                default:
                    throw new IndexOutOfRangeException();
            }
        }
    }
}