// Copyright (c) Xenko contributors (https://xenko.com) and Silicon Studio Corp. (https://www.siliconstudio.co.jp)
// Distributed under the MIT license. See the LICENSE.md file in the project root for more information.
//
// -----------------------------------------------------------------------------
// Original code from SlimMath project. http://code.google.com/p/slimmath/
// Greetings to SlimDX Group. Original code published with the following license:
// -----------------------------------------------------------------------------
/*
* Copyright (c) 2007-2011 SlimDX Group
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
using System;
using System.Globalization;
using System.Runtime.InteropServices;
using System.Runtime.Serialization;

namespace math
{
    /// <summary>
    /// Represents a plane in three dimensional space.
    /// </summary>
    [DataContract]
    [StructLayout( LayoutKind.Sequential, Pack = 4 )]
    public struct Plane : IEquatable<Plane>, IFormattable
    {
        /// <summary>
        /// The normal vector of the plane.
        /// </summary>
        public Vec3 Normal;

        /// <summary>
        /// The distance of the plane along its normal from the origin.
        /// </summary>
        public float D;

        /// <summary>
        /// Initializes a new instance of the <see cref="math.Plane"/> struct.
        /// </summary>
        /// <param name="value">The value that will be assigned to all components.</param>
        public Plane( float value )
        {
            Normal.X = Normal.Y = Normal.Z = D = value;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="math.Plane"/> struct.
        /// </summary>
        /// <param name="a">The X component of the normal.</param>
        /// <param name="b">The Y component of the normal.</param>
        /// <param name="c">The Z component of the normal.</param>
        /// <param name="d">The distance of the plane along its normal from the origin.</param>
        public Plane( float a, float b, float c, float d )
        {
            Normal.X = a;
            Normal.Y = b;
            Normal.Z = c;
            D = d;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Plane"/> struct.
        /// </summary>
        /// <param name="point">Any point that lies along the plane.</param>
        /// <param name="normal">The normal vector to the plane.</param>
        public Plane( Vec3 point, Vec3 normal )
        {
            this.Normal = normal;
            this.D = Vec3.Dot( normal, point );
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="math.Plane"/> struct.
        /// </summary>
        /// <param name="value">The normal of the plane.</param>
        /// <param name="d">The distance of the plane along its normal from the origin</param>
        public Plane( Vec3 value, float d )
        {
            Normal = value;
            D = d;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="math.Plane"/> struct.
        /// </summary>
        /// <param name="point1">First point of a triangle defining the plane.</param>
        /// <param name="point2">Second point of a triangle defining the plane.</param>
        /// <param name="point3">Third point of a triangle defining the plane.</param>
        public Plane( Vec3 point1, Vec3 point2, Vec3 point3 )
        {
            float x1 = point2.X - point1.X;
            float y1 = point2.Y - point1.Y;
            float z1 = point2.Z - point1.Z;
            float x2 = point3.X - point1.X;
            float y2 = point3.Y - point1.Y;
            float z2 = point3.Z - point1.Z;
            float yz = ( y1 * z2 ) - ( z1 * y2 );
            float xz = ( z1 * x2 ) - ( x1 * z2 );
            float xy = ( x1 * y2 ) - ( y1 * x2 );
            float invPyth = 1.0f / (float)( Math.Sqrt( ( yz * yz ) + ( xz * xz ) + ( xy * xy ) ) );

            Normal.X = yz * invPyth;
            Normal.Y = xz * invPyth;
            Normal.Z = xy * invPyth;
            D = -( ( Normal.X * point1.X ) + ( Normal.Y * point1.Y ) + ( Normal.Z * point1.Z ) );
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="math.Plane"/> struct.
        /// </summary>
        /// <param name="values">The values to assign to the A, B, C, and D components of the plane. This must be an array with four elements.</param>
        /// <exception cref="ArgumentNullException">Thrown when <paramref name="values"/> is <c>null</c>.</exception>
        /// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="values"/> contains more or less than four elements.</exception>
        public Plane( float[] values )
        {
            if( values == null )
                throw new ArgumentNullException( "values" );
            if( values.Length != 4 )
                throw new ArgumentOutOfRangeException( "values", "There must be four and only four input values for Plane." );

            Normal.X = values[0];
            Normal.Y = values[1];
            Normal.Z = values[2];
            D = values[3];
        }

        /// <summary>
        /// Gets or sets the component at the specified index.
        /// </summary>
        /// <value>The value of the A, B, C, or D component, depending on the index.</value>
        /// <param name="index">The index of the component to access. Use 0 for the A component, 1 for the B component, 2 for the C component, and 3 for the D component.</param>
        /// <returns>The value of the component at the specified index.</returns>
        /// <exception cref="System.ArgumentOutOfRangeException">Thrown when the <paramref name="index"/> is out of the range [0, 3].</exception>
        public float this[int index]
        {
            get
            {
                switch( index )
                {
                    case 0:
                        return Normal.X;
                    case 1:
                        return Normal.Y;
                    case 2:
                        return Normal.Z;
                    case 3:
                        return D;
                }

                throw new ArgumentOutOfRangeException( "index", "Indices for Plane run from 0 to 3, inclusive." );
            }

            set
            {
                switch( index )
                {
                    case 0:
                        Normal.X = value;
                        break;
                    case 1:
                        Normal.Y = value;
                        break;
                    case 2:
                        Normal.Z = value;
                        break;
                    case 3:
                        D = value;
                        break;
                    default:
                        throw new ArgumentOutOfRangeException( "index", "Indices for Plane run from 0 to 3, inclusive." );
                }
            }
        }

        /// <summary>
        /// Negates a plane by negating all its coefficients, which result in a plane in opposite direction.
        /// </summary>
        public void Negate()
        {
            Normal.X = -Normal.X;
            Normal.Y = -Normal.Y;
            Normal.Z = -Normal.Z;
            D = -D;
        }

        /// <summary>
        /// Changes the coefficients of the normal vector of the plane to make it of unit length.
        /// </summary>
        public void Normalize()
        {
            float magnitude = 1.0f / (float)( Math.Sqrt( ( Normal.X * Normal.X ) + ( Normal.Y * Normal.Y ) + ( Normal.Z * Normal.Z ) ) );

            Normal.X *= magnitude;
            Normal.Y *= magnitude;
            Normal.Z *= magnitude;
            D *= magnitude;
        }

        /// <summary>
        /// Creates an array containing the elements of the plane.
        /// </summary>
        /// <returns>A four-element array containing the components of the plane.</returns>
        public float[] ToArray()
        {
            return new float[] { Normal.X, Normal.Y, Normal.Z, D };
        }

        /// <summary>
        /// Determines if there is an intersection between the current object and a point.
        /// </summary>
        /// <param name="point">The point to test.</param>
        /// <returns>Whether the two objects intersected.</returns>
        public PlaneIntersectionType Intersects( ref Vec3 point )
        {
            return CollisionHelper.PlaneIntersectsPoint( ref this, ref point );
        }

        /// <summary>
        /// Determines if there is an intersection between the current object and a <see cref="math.Ray"/>.
        /// </summary>
        /// <param name="ray">The ray to test.</param>
        /// <returns>Whether the two objects intersected.</returns>
        public bool Intersects( ref Ray ray )
        {
            float distance;
            return CollisionHelper.RayIntersectsPlane( ref ray, ref this, out distance );
        }

        /// <summary>
        /// Determines if there is an intersection between the current object and a <see cref="math.Ray"/>.
        /// </summary>
        /// <param name="ray">The ray to test.</param>
        /// <param name="distance">When the method completes, contains the distance of the intersection,
        /// or 0 if there was no intersection.</param>
        /// <returns>Whether the two objects intersected.</returns>
        public bool Intersects( ref Ray ray, out float distance )
        {
            return CollisionHelper.RayIntersectsPlane( ref ray, ref this, out distance );
        }

        /// <summary>
        /// Determines if there is an intersection between the current object and a <see cref="math.Ray"/>.
        /// </summary>
        /// <param name="ray">The ray to test.</param>
        /// <param name="point">When the method completes, contains the point of intersection,
        /// or <see cref="math.Vec3.Zero"/> if there was no intersection.</param>
        /// <returns>Whether the two objects intersected.</returns>
        public bool Intersects( ref Ray ray, out Vec3 point )
        {
            return CollisionHelper.RayIntersectsPlane( ref ray, ref this, out point );
        }

        /// <summary>
        /// Determines if there is an intersection between the current object and a <see cref="math.Plane"/>.
        /// </summary>
        /// <param name="plane">The plane to test.</param>
        /// <returns>Whether the two objects intersected.</returns>
        public bool Intersects( ref Plane plane )
        {
            return CollisionHelper.PlaneIntersectsPlane( ref this, ref plane );
        }

        /// <summary>
        /// Determines if there is an intersection between the current object and a <see cref="math.Plane"/>.
        /// </summary>
        /// <param name="plane">The plane to test.</param>
        /// <param name="line">When the method completes, contains the line of intersection
        /// as a <see cref="math.Ray"/>, or a zero ray if there was no intersection.</param>
        /// <returns>Whether the two objects intersected.</returns>
        public bool Intersects( ref Plane plane, out Ray line )
        {
            return CollisionHelper.PlaneIntersectsPlane( ref this, ref plane, out line );
        }

        /// <summary>
        /// Determines if there is an intersection between the current object and a triangle.
        /// </summary>
        /// <param name="vertex1">The first vertex of the triangle to test.</param>
        /// <param name="vertex2">The second vertex of the triagnle to test.</param>
        /// <param name="vertex3">The third vertex of the triangle to test.</param>
        /// <returns>Whether the two objects intersected.</returns>
        public PlaneIntersectionType Intersects( ref Vec3 vertex1, ref Vec3 vertex2, ref Vec3 vertex3 )
        {
            return CollisionHelper.PlaneIntersectsTriangle( ref this, ref vertex1, ref vertex2, ref vertex3 );
        }

        /// <summary>
        /// Determines if there is an intersection between the current object and a <see cref="math.BoundingBox"/>.
        /// </summary>
        /// <param name="box">The box to test.</param>
        /// <returns>Whether the two objects intersected.</returns>
        public PlaneIntersectionType Intersects( ref BoundingBox box )
        {
            return CollisionHelper.PlaneIntersectsBox( ref this, ref box );
        }

        /// <summary>
        /// Determines if there is an intersection between the current object and a <see cref="math.BoundingSphere"/>.
        /// </summary>
        /// <param name="sphere">The sphere to test.</param>
        /// <returns>Whether the two objects intersected.</returns>
        public PlaneIntersectionType Intersects( ref BoundingSphere sphere )
        {
            return CollisionHelper.PlaneIntersectsSphere( ref this, ref sphere );
        }

        /// <summary>
        /// Scales the plane by the given scaling factor.
        /// </summary>
        /// <param name="value">The plane to scale.</param>
        /// <param name="scale">The amount by which to scale the plane.</param>
        /// <param name="result">When the method completes, contains the scaled plane.</param>
        public static void Multiply( ref Plane value, float scale, out Plane result )
        {
            result.Normal.X = value.Normal.X * scale;
            result.Normal.Y = value.Normal.Y * scale;
            result.Normal.Z = value.Normal.Z * scale;
            result.D = value.D * scale;
        }

        /// <summary>
        /// Scales the plane by the given scaling factor.
        /// </summary>
        /// <param name="value">The plane to scale.</param>
        /// <param name="scale">The amount by which to scale the plane.</param>
        /// <returns>The scaled plane.</returns>
        public static Plane Multiply( Plane value, float scale )
        {
            return new Plane( value.Normal.X * scale, value.Normal.Y * scale, value.Normal.Z * scale, value.D * scale );
        }

        /// <summary>
        /// Calculates the dot product of the specified vector and plane.
        /// </summary>
        /// <param name="left">The source plane.</param>
        /// <param name="right">The source vector.</param>
        /// <param name="result">When the method completes, contains the dot product of the specified plane and vector.</param>
        public static void Dot( ref Plane left, ref Vec4 right, out float result )
        {
            result = ( left.Normal.X * right.X ) + ( left.Normal.Y * right.Y ) + ( left.Normal.Z * right.Z ) + ( left.D * right.W );
        }

        /// <summary>
        /// Calculates the dot product of the specified vector and plane.
        /// </summary>
        /// <param name="left">The source plane.</param>
        /// <param name="right">The source vector.</param>
        /// <returns>The dot product of the specified plane and vector.</returns>
        public static float Dot( Plane left, Vec4 right )
        {
            return ( left.Normal.X * right.X ) + ( left.Normal.Y * right.Y ) + ( left.Normal.Z * right.Z ) + ( left.D * right.W );
        }

        /// <summary>
        /// Calculates the dot product of a specified vector and the normal of the plane plus the distance value of the plane.
        /// </summary>
        /// <param name="left">The source plane.</param>
        /// <param name="right">The source vector.</param>
        /// <param name="result">When the method completes, contains the dot product of a specified vector and the normal of the Plane plus the distance value of the plane.</param>
        public static void DotCoordinate( ref Plane left, ref Vec3 right, out float result )
        {
            result = ( left.Normal.X * right.X ) + ( left.Normal.Y * right.Y ) + ( left.Normal.Z * right.Z ) + left.D;
        }

        /// <summary>
        /// Calculates the dot product of a specified vector and the normal of the plane plus the distance value of the plane.
        /// </summary>
        /// <param name="left">The source plane.</param>
        /// <param name="right">The source vector.</param>
        /// <returns>The dot product of a specified vector and the normal of the Plane plus the distance value of the plane.</returns>
        public static float DotCoordinate( Plane left, Vec3 right )
        {
            return ( left.Normal.X * right.X ) + ( left.Normal.Y * right.Y ) + ( left.Normal.Z * right.Z ) + left.D;
        }

        /// <summary>
        /// Calculates the dot product of the specified vector and the normal of the plane.
        /// </summary>
        /// <param name="left">The source plane.</param>
        /// <param name="right">The source vector.</param>
        /// <param name="result">When the method completes, contains the dot product of the specified vector and the normal of the plane.</param>
        public static void DotNormal( ref Plane left, ref Vec3 right, out float result )
        {
            result = ( left.Normal.X * right.X ) + ( left.Normal.Y * right.Y ) + ( left.Normal.Z * right.Z );
        }

        /// <summary>
        /// Calculates the dot product of the specified vector and the normal of the plane.
        /// </summary>
        /// <param name="left">The source plane.</param>
        /// <param name="right">The source vector.</param>
        /// <returns>The dot product of the specified vector and the normal of the plane.</returns>
        public static float DotNormal( Plane left, Vec3 right )
        {
            return ( left.Normal.X * right.X ) + ( left.Normal.Y * right.Y ) + ( left.Normal.Z * right.Z );
        }

        /// <summary>
        /// Projects a point onto a plane.
        /// </summary>
        /// <param name="plane">The plane to project the point to.</param>
        /// <param name="point">The point to project.</param>
        /// <param name="result">The projected point.</param>
        public static void Project( ref Plane plane, ref Vec3 point, out Vec3 result )
        {
            float distance;
            DotCoordinate( ref plane, ref point, out distance );

            // compute: point - distance * plane.Normal
            Vec3.Multiply( ref plane.Normal, distance, out result );
            Vec3.Subtract( ref point, ref result, out result );
        }

        /// <summary>
        /// Projects a point onto a plane.
        /// </summary>
        /// <param name="plane">The plane to project the point to.</param>
        /// <param name="point">The point to project.</param>
        /// <returns>The projected point.</returns>
        public static Vec3 Project( Plane plane, Vec3 point )
        {
            Vec3 result;
            Project( ref plane, ref point, out result );
            return result;
        }

        /// <summary>
        /// Changes the coefficients of the normal vector of the plane to make it of unit length.
        /// </summary>
        /// <param name="plane">The source plane.</param>
        /// <param name="result">When the method completes, contains the normalized plane.</param>
        public static void Normalize( ref Plane plane, out Plane result )
        {
            float magnitude = 1.0f / (float)( Math.Sqrt( ( plane.Normal.X * plane.Normal.X ) + ( plane.Normal.Y * plane.Normal.Y ) + ( plane.Normal.Z * plane.Normal.Z ) ) );

            result.Normal.X = plane.Normal.X * magnitude;
            result.Normal.Y = plane.Normal.Y * magnitude;
            result.Normal.Z = plane.Normal.Z * magnitude;
            result.D = plane.D * magnitude;
        }

        /// <summary>
        /// Changes the coefficients of the normal vector of the plane to make it of unit length.
        /// </summary>
        /// <param name="plane">The source plane.</param>
        /// <returns>The normalized plane.</returns>
        public static Plane Normalize( Plane plane )
        {
            float magnitude = 1.0f / (float)( Math.Sqrt( ( plane.Normal.X * plane.Normal.X ) + ( plane.Normal.Y * plane.Normal.Y ) + ( plane.Normal.Z * plane.Normal.Z ) ) );
            return new Plane( plane.Normal.X * magnitude, plane.Normal.Y * magnitude, plane.Normal.Z * magnitude, plane.D * magnitude );
        }

        /// <summary>
        /// Negates a plane by negating all its coefficients, which result in a plane in opposite direction.
        /// </summary>
        /// <param name="plane">The source plane.</param>
        /// <param name="result">When the method completes, contains the flipped plane.</param>
        public static void Negate( ref Plane plane, out Plane result )
        {
            result.Normal.X = -plane.Normal.X;
            result.Normal.Y = -plane.Normal.Y;
            result.Normal.Z = -plane.Normal.Z;
            result.D = -plane.D;
        }

        /// <summary>
        /// Negates a plane by negating all its coefficients, which result in a plane in opposite direction.
        /// </summary>
        /// <param name="plane">The source plane.</param>
        /// <returns>The flipped plane.</returns>
        public static Plane Negate( Plane plane )
        {
            float magnitude = 1.0f / (float)( Math.Sqrt( ( plane.Normal.X * plane.Normal.X ) + ( plane.Normal.Y * plane.Normal.Y ) + ( plane.Normal.Z * plane.Normal.Z ) ) );
            return new Plane( plane.Normal.X * magnitude, plane.Normal.Y * magnitude, plane.Normal.Z * magnitude, plane.D * magnitude );
        }

        /// <summary>
        /// Transforms a normalized plane by a quaternion rotation.
        /// </summary>
        /// <param name="plane">The normalized source plane.</param>
        /// <param name="rotation">The quaternion rotation.</param>
        /// <param name="result">When the method completes, contains the transformed plane.</param>
        public static void Transform( ref Plane plane, ref Quaternion rotation, out Plane result )
        {
            float x2 = rotation.X + rotation.X;
            float y2 = rotation.Y + rotation.Y;
            float z2 = rotation.Z + rotation.Z;
            float wx = rotation.W * x2;
            float wy = rotation.W * y2;
            float wz = rotation.W * z2;
            float xx = rotation.X * x2;
            float xy = rotation.X * y2;
            float xz = rotation.X * z2;
            float yy = rotation.Y * y2;
            float yz = rotation.Y * z2;
            float zz = rotation.Z * z2;

            float x = plane.Normal.X;
            float y = plane.Normal.Y;
            float z = plane.Normal.Z;

            result.Normal.X = ( ( x * ( ( 1.0f - yy ) - zz ) ) + ( y * ( xy - wz ) ) ) + ( z * ( xz + wy ) );
            result.Normal.Y = ( ( x * ( xy + wz ) ) + ( y * ( ( 1.0f - xx ) - zz ) ) ) + ( z * ( yz - wx ) );
            result.Normal.Z = ( ( x * ( xz - wy ) ) + ( y * ( yz + wx ) ) ) + ( z * ( ( 1.0f - xx ) - yy ) );
            result.D = plane.D;
        }

        /// <summary>
        /// Transforms a normalized plane by a quaternion rotation.
        /// </summary>
        /// <param name="plane">The normalized source plane.</param>
        /// <param name="rotation">The quaternion rotation.</param>
        /// <returns>The transformed plane.</returns>
        public static Plane Transform( Plane plane, Quaternion rotation )
        {
            Plane result;
            float x2 = rotation.X + rotation.X;
            float y2 = rotation.Y + rotation.Y;
            float z2 = rotation.Z + rotation.Z;
            float wx = rotation.W * x2;
            float wy = rotation.W * y2;
            float wz = rotation.W * z2;
            float xx = rotation.X * x2;
            float xy = rotation.X * y2;
            float xz = rotation.X * z2;
            float yy = rotation.Y * y2;
            float yz = rotation.Y * z2;
            float zz = rotation.Z * z2;

            float x = plane.Normal.X;
            float y = plane.Normal.Y;
            float z = plane.Normal.Z;

            result.Normal.X = ( ( x * ( ( 1.0f - yy ) - zz ) ) + ( y * ( xy - wz ) ) ) + ( z * ( xz + wy ) );
            result.Normal.Y = ( ( x * ( xy + wz ) ) + ( y * ( ( 1.0f - xx ) - zz ) ) ) + ( z * ( yz - wx ) );
            result.Normal.Z = ( ( x * ( xz - wy ) ) + ( y * ( yz + wx ) ) ) + ( z * ( ( 1.0f - xx ) - yy ) );
            result.D = plane.D;

            return result;
        }

        /// <summary>
        /// Transforms an array of normalized planes by a quaternion rotation.
        /// </summary>
        /// <param name="planes">The array of normalized planes to transform.</param>
        /// <param name="rotation">The quaternion rotation.</param>
        /// <exception cref="ArgumentNullException">Thrown when <paramref name="planes"/> is <c>null</c>.</exception>
        public static void Transform( Plane[] planes, ref Quaternion rotation )
        {
            if( planes == null )
                throw new ArgumentNullException( "planes" );

            float x2 = rotation.X + rotation.X;
            float y2 = rotation.Y + rotation.Y;
            float z2 = rotation.Z + rotation.Z;
            float wx = rotation.W * x2;
            float wy = rotation.W * y2;
            float wz = rotation.W * z2;
            float xx = rotation.X * x2;
            float xy = rotation.X * y2;
            float xz = rotation.X * z2;
            float yy = rotation.Y * y2;
            float yz = rotation.Y * z2;
            float zz = rotation.Z * z2;

            for( int i = 0; i < planes.Length; ++i )
            {
                float x = planes[i].Normal.X;
                float y = planes[i].Normal.Y;
                float z = planes[i].Normal.Z;

                /*
                 * Note:
                 * Factor common arithmetic out of loop.
                */
                planes[i].Normal.X = ( ( x * ( ( 1.0f - yy ) - zz ) ) + ( y * ( xy - wz ) ) ) + ( z * ( xz + wy ) );
                planes[i].Normal.Y = ( ( x * ( xy + wz ) ) + ( y * ( ( 1.0f - xx ) - zz ) ) ) + ( z * ( yz - wx ) );
                planes[i].Normal.Z = ( ( x * ( xz - wy ) ) + ( y * ( yz + wx ) ) ) + ( z * ( ( 1.0f - xx ) - yy ) );
            }
        }

        /// <summary>
        /// Transforms a normalized plane by a matrix.
        /// </summary>
        /// <param name="plane">The normalized source plane.</param>
        /// <param name="transformation">The transformation matrix.</param>
        /// <param name="result">When the method completes, contains the transformed plane.</param>
        public static void Transform( ref Plane plane, ref Matrix transformation, out Plane result )
        {
            float x = plane.Normal.X;
            float y = plane.Normal.Y;
            float z = plane.Normal.Z;
            float d = plane.D;

            Matrix inverse;
            Matrix.Invert( ref transformation, out inverse );

            result.Normal.X = ( ( ( x * inverse.M11 ) + ( y * inverse.M12 ) ) + ( z * inverse.M13 ) ) + ( d * inverse.M14 );
            result.Normal.Y = ( ( ( x * inverse.M21 ) + ( y * inverse.M22 ) ) + ( z * inverse.M23 ) ) + ( d * inverse.M24 );
            result.Normal.Z = ( ( ( x * inverse.M31 ) + ( y * inverse.M32 ) ) + ( z * inverse.M33 ) ) + ( d * inverse.M34 );
            result.D = ( ( ( x * inverse.M41 ) + ( y * inverse.M42 ) ) + ( z * inverse.M43 ) ) + ( d * inverse.M44 );
        }

        /// <summary>
        /// Transforms a normalized plane by a matrix.
        /// </summary>
        /// <param name="plane">The normalized source plane.</param>
        /// <param name="transformation">The transformation matrix.</param>
        /// <returns>When the method completes, contains the transformed plane.</returns>
        public static Plane Transform( Plane plane, Matrix transformation )
        {
            Plane result;
            float x = plane.Normal.X;
            float y = plane.Normal.Y;
            float z = plane.Normal.Z;
            float d = plane.D;

            transformation.Invert();
            result.Normal.X = ( ( ( x * transformation.M11 ) + ( y * transformation.M12 ) ) + ( z * transformation.M13 ) ) + ( d * transformation.M14 );
            result.Normal.Y = ( ( ( x * transformation.M21 ) + ( y * transformation.M22 ) ) + ( z * transformation.M23 ) ) + ( d * transformation.M24 );
            result.Normal.Z = ( ( ( x * transformation.M31 ) + ( y * transformation.M32 ) ) + ( z * transformation.M33 ) ) + ( d * transformation.M34 );
            result.D = ( ( ( x * transformation.M41 ) + ( y * transformation.M42 ) ) + ( z * transformation.M43 ) ) + ( d * transformation.M44 );

            return result;
        }

        /// <summary>
        /// Transforms an array of normalized planes by a matrix.
        /// </summary>
        /// <param name="planes">The array of normalized planes to transform.</param>
        /// <param name="transformation">The transformation matrix.</param>
        /// <exception cref="ArgumentNullException">Thrown when <paramref name="planes"/> is <c>null</c>.</exception>
        public static void Transform( Plane[] planes, ref Matrix transformation )
        {
            if( planes == null )
                throw new ArgumentNullException( "planes" );

            Matrix inverse;
            Matrix.Invert( ref transformation, out inverse );

            for( int i = 0; i < planes.Length; ++i )
            {
                Transform( ref planes[i], ref transformation, out planes[i] );
            }
        }

        /// <summary>
        /// Scales a plane by the given value.
        /// </summary>
        /// <param name="scale">The amount by which to scale the plane.</param>
        /// <param name="plane">The plane to scale.</param>
        /// <returns>The scaled plane.</returns>
        public static Plane operator *( float scale, Plane plane )
        {
            return new Plane( plane.Normal.X * scale, plane.Normal.Y * scale, plane.Normal.Z * scale, plane.D * scale );
        }

        /// <summary>
        /// Scales a plane by the given value.
        /// </summary>
        /// <param name="plane">The plane to scale.</param>
        /// <param name="scale">The amount by which to scale the plane.</param>
        /// <returns>The scaled plane.</returns>
        public static Plane operator *( Plane plane, float scale )
        {
            return new Plane( plane.Normal.X * scale, plane.Normal.Y * scale, plane.Normal.Z * scale, plane.D * scale );
        }

        /// <summary>
        /// Negates a plane by negating all its coefficients, which result in a plane in opposite direction.
        /// </summary>
        /// <returns>The negated plane.</returns>
        public static Plane operator -( Plane plane )
        {
            return new Plane( -plane.Normal.X, -plane.Normal.Y, -plane.Normal.Z, -plane.D );
        }

        /// <summary>
        /// Tests for equality between two objects.
        /// </summary>
        /// <param name="left">The first value to compare.</param>
        /// <param name="right">The second value to compare.</param>
        /// <returns><c>true</c> if <paramref name="left"/> has the same value as <paramref name="right"/>; otherwise, <c>false</c>.</returns>
        public static bool operator ==( Plane left, Plane right )
        {
            return left.Equals( right );
        }

        /// <summary>
        /// Tests for inequality between two objects.
        /// </summary>
        /// <param name="left">The first value to compare.</param>
        /// <param name="right">The second value to compare.</param>
        /// <returns><c>true</c> if <paramref name="left"/> has a different value than <paramref name="right"/>; otherwise, <c>false</c>.</returns>
        public static bool operator !=( Plane left, Plane right )
        {
            return !left.Equals( right );
        }

        /// <summary>
        /// Returns a <see cref="string"/> that represents this instance.
        /// </summary>
        /// <returns>
        /// A <see cref="string"/> that represents this instance.
        /// </returns>
        public override string ToString()
        {
            return string.Format( CultureInfo.CurrentCulture, "A:{0} B:{1} C:{2} D:{3}", Normal.X, Normal.Y, Normal.Z, D );
        }

        /// <summary>
        /// Returns a <see cref="string"/> that represents this instance.
        /// </summary>
        /// <param name="format">The format.</param>
        /// <returns>
        /// A <see cref="string"/> that represents this instance.
        /// </returns>
        public string ToString( string format )
        {
            return string.Format( CultureInfo.CurrentCulture, "A:{0} B:{1} C:{2} D:{3}", Normal.X.ToString( format, CultureInfo.CurrentCulture ),
                Normal.Y.ToString( format, CultureInfo.CurrentCulture ), Normal.Z.ToString( format, CultureInfo.CurrentCulture ), D.ToString( format, CultureInfo.CurrentCulture ) );
        }

        /// <summary>
        /// Returns a <see cref="string"/> that represents this instance.
        /// </summary>
        /// <param name="formatProvider">The format provider.</param>
        /// <returns>
        /// A <see cref="string"/> that represents this instance.
        /// </returns>
        public string ToString( IFormatProvider formatProvider )
        {
            return string.Format( formatProvider, "A:{0} B:{1} C:{2} D:{3}", Normal.X, Normal.Y, Normal.Z, D );
        }

        /// <summary>
        /// Returns a <see cref="string"/> that represents this instance.
        /// </summary>
        /// <param name="format">The format.</param>
        /// <param name="formatProvider">The format provider.</param>
        /// <returns>
        /// A <see cref="string"/> that represents this instance.
        /// </returns>
        public string ToString( string format, IFormatProvider formatProvider )
        {
            return string.Format( formatProvider, "A:{0} B:{1} C:{2} D:{3}", Normal.X.ToString( format, formatProvider ),
                Normal.Y.ToString( format, formatProvider ), Normal.Z.ToString( format, formatProvider ), D.ToString( format, formatProvider ) );
        }

        /// <summary>
        /// Returns a hash code for this instance.
        /// </summary>
        /// <returns>
        /// A hash code for this instance, suitable for use in hashing algorithms and data structures like a hash table.
        /// </returns>
        public override int GetHashCode()
        {
            return Normal.GetHashCode() + D.GetHashCode();
        }

        /// <summary>
        /// Determines whether the specified <see cref="math.Vec4"/> is equal to this instance.
        /// </summary>
        /// <param name="value">The <see cref="math.Vec4"/> to compare with this instance.</param>
        /// <returns>
        /// <c>true</c> if the specified <see cref="math.Vec4"/> is equal to this instance; otherwise, <c>false</c>.
        /// </returns>
        public bool Equals( Plane value )
        {
            return Normal == value.Normal && D == value.D;
        }

        /// <summary>
        /// Determines whether the specified <see cref="object"/> is equal to this instance.
        /// </summary>
        /// <param name="value">The <see cref="object"/> to compare with this instance.</param>
        /// <returns>
        /// <c>true</c> if the specified <see cref="object"/> is equal to this instance; otherwise, <c>false</c>.
        /// </returns>
        public override bool Equals( object value )
        {
            if( value == null )
                return false;

            if( value.GetType() != GetType() )
                return false;

            return Equals( (Plane)value );
        }

#if SlimDX1xInterop
        /// <summary>
        /// Performs an implicit conversion from <see cref="math.Plane"/> to <see cref="SlimDX.Plane"/>.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static implicit operator SlimDX.Plane(Plane value)
        {
            return new SlimDX.Plane(value.Normal, value.D);
        }

        /// <summary>
        /// Performs an implicit conversion from <see cref="SlimDX.Plane"/> to <see cref="math.Plane"/>.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static implicit operator Plane(SlimDX.Plane value)
        {
            return new Plane(value.Normal, value.D);
        }
#endif

#if XnaInterop
        /// <summary>
        /// Performs an implicit conversion from <see cref="math.Plane"/> to <see cref="Microsoft.Xna.Framework.Plane"/>.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static implicit operator Microsoft.Xna.Framework.Plane(Plane value)
        {
            return new Microsoft.Xna.Framework.Plane(value.Normal, value.D);
        }

        /// <summary>
        /// Performs an implicit conversion from <see cref="Microsoft.Xna.Framework.Plane"/> to <see cref="math.Plane"/>.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static implicit operator Plane(Microsoft.Xna.Framework.Plane value)
        {
            return new Plane(value.Normal, value.D);
        }
#endif
    }
}