// 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 three dimensional mathematical vector.
    /// </summary>
    [DataContract( Name = "Int3" )]
    [DataStyle( DataStyle.Compact )]
    [StructLayout( LayoutKind.Sequential, Pack = 4 )]
    public struct Int3 : IEquatable<Int3>, IFormattable
    {
        /// <summary>
        /// The size of the <see cref="Int3"/> type, in bytes.
        /// </summary>
        public static readonly int SizeInBytes = lib.Util.SizeOf<Int3>();

        /// <summary>
        /// A <see cref="Int3"/> with all of its components set to zero.
        /// </summary>
        public static readonly Int3 Zero = new Int3();

        /// <summary>
        /// The X unit <see cref="Int3"/> (1, 0, 0).
        /// </summary>
        public static readonly Int3 UnitX = new Int3( 1, 0, 0 );

        /// <summary>
        /// The Y unit <see cref="Int3"/> (0, 1, 0).
        /// </summary>
        public static readonly Int3 UnitY = new Int3( 0, 1, 0 );

        /// <summary>
        /// The Z unit <see cref="Int3"/> (0, 0, 1).
        /// </summary>
        public static readonly Int3 UnitZ = new Int3( 0, 0, 1 );

        /// <summary>
        /// A <see cref="Int3"/> with all of its components set to one.
        /// </summary>
        public static readonly Int3 One = new Int3( 1, 1, 1 );

        /// <summary>
        /// The X component of the vector.
        /// </summary>
        [DataMember( Order = 0 )]
        public int X;

        /// <summary>
        /// The Y component of the vector.
        /// </summary>
        [DataMember( Order = 1 )]
        public int Y;

        /// <summary>
        /// The Z component of the vector.
        /// </summary>
        [DataMember( Order = 2 )]
        public int Z;

        /// <summary>
        /// Initializes a new instance of the <see cref="Int3"/> struct.
        /// </summary>
        /// <param name="value">The value that will be assigned to all components.</param>
        public Int3( int value )
        {
            X = value;
            Y = value;
            Z = value;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Int3"/> struct.
        /// </summary>
        /// <param name="x">Initial value for the X component of the vector.</param>
        /// <param name="y">Initial value for the Y component of the vector.</param>
        /// <param name="z">Initial value for the Z component of the vector.</param>
        public Int3( int x, int y, int z )
        {
            X = x;
            Y = y;
            Z = z;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Int3"/> struct.
        /// </summary>
        /// <param name="value">A vector containing the values with which to initialize the X and Y components.</param>
        /// <param name="z">Initial value for the Z component of the vector.</param>
        public Int3( Vec2 value, int z )
        {
            X = (int)value.X;
            Y = (int)value.Y;
            Z = z;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Int3"/> struct.
        /// </summary>
        /// <param name="values">The values to assign to the X, Y, and Z components of the vector. This must be an array with three 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 three elements.</exception>
        public Int3( int[] values )
        {
            if( values == null )
                throw new ArgumentNullException( "values" );
            if( values.Length != 3 )
                throw new ArgumentOutOfRangeException( "values", "There must be three and only three input values for Int3." );

            X = values[0];
            Y = values[1];
            Z = values[2];
        }

        /// <summary>
        /// Gets or sets the component at the specified index.
        /// </summary>
        /// <value>The value of the X, Y, or Z component, depending on the index.</value>
        /// <param name="index">The index of the component to access. Use 0 for the X component, 1 for the Y component, and 2 for the Z 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, 2].</exception>
        public int this[int index]
        {
            get
            {
                switch( index )
                {
                    case 0:
                        return X;
                    case 1:
                        return Y;
                    case 2:
                        return Z;
                }

                throw new ArgumentOutOfRangeException( "index", "Indices for Int3 run from 0 to 2, inclusive." );
            }

            set
            {
                switch( index )
                {
                    case 0:
                        X = value;
                        break;
                    case 1:
                        Y = value;
                        break;
                    case 2:
                        Z = value;
                        break;
                    default:
                        throw new ArgumentOutOfRangeException( "index", "Indices for Int3 run from 0 to 2, inclusive." );
                }
            }
        }

        /// <summary>
        /// Calculates the length of the vector.
        /// </summary>
        /// <returns>The length of the vector.</returns>
        /// <remarks>
        /// <see cref="Int3.LengthSquared"/> may be preferred when only the relative length is needed
        /// and speed is of the essence.
        /// </remarks>
        public int Length()
        {
            return (int)Math.Sqrt( ( X * X ) + ( Y * Y ) + ( Z * Z ) );
        }

        /// <summary>
        /// Calculates the squared length of the vector.
        /// </summary>
        /// <returns>The squared length of the vector.</returns>
        /// <remarks>
        /// This method may be preferred to <see cref="Int3.Length"/> when only a relative length is needed
        /// and speed is of the essence.
        /// </remarks>
        public int LengthSquared()
        {
            return ( X * X ) + ( Y * Y ) + ( Z * Z );
        }

        /// <summary>
        /// Raises the exponent for each components.
        /// </summary>
        /// <param name="exponent">The exponent.</param>
        public void Pow( int exponent )
        {
            X = (int)Math.Pow( X, exponent );
            Y = (int)Math.Pow( Y, exponent );
            Z = (int)Math.Pow( Z, exponent );
        }

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

        /// <summary>
        /// Adds two vectors.
        /// </summary>
        /// <param name="left">The first vector to add.</param>
        /// <param name="right">The second vector to add.</param>
        /// <param name="result">When the method completes, contains the sum of the two vectors.</param>
        public static void Add( ref Int3 left, ref Int3 right, out Int3 result )
        {
            result = new Int3( left.X + right.X, left.Y + right.Y, left.Z + right.Z );
        }

        /// <summary>
        /// Adds two vectors.
        /// </summary>
        /// <param name="left">The first vector to add.</param>
        /// <param name="right">The second vector to add.</param>
        /// <returns>The sum of the two vectors.</returns>
        public static Int3 Add( Int3 left, Int3 right )
        {
            return new Int3( left.X + right.X, left.Y + right.Y, left.Z + right.Z );
        }

        /// <summary>
        /// Subtracts two vectors.
        /// </summary>
        /// <param name="left">The first vector to subtract.</param>
        /// <param name="right">The second vector to subtract.</param>
        /// <param name="result">When the method completes, contains the difference of the two vectors.</param>
        public static void Subtract( ref Int3 left, ref Int3 right, out Int3 result )
        {
            result = new Int3( left.X - right.X, left.Y - right.Y, left.Z - right.Z );
        }

        /// <summary>
        /// Subtracts two vectors.
        /// </summary>
        /// <param name="left">The first vector to subtract.</param>
        /// <param name="right">The second vector to subtract.</param>
        /// <returns>The difference of the two vectors.</returns>
        public static Int3 Subtract( Int3 left, Int3 right )
        {
            return new Int3( left.X - right.X, left.Y - right.Y, left.Z - right.Z );
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <param name="result">When the method completes, contains the scaled vector.</param>
        public static void Multiply( ref Int3 value, int scale, out Int3 result )
        {
            result = new Int3( value.X * scale, value.Y * scale, value.Z * scale );
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The scaled vector.</returns>
        public static Int3 Multiply( Int3 value, int scale )
        {
            return new Int3( value.X * scale, value.Y * scale, value.Z * scale );
        }

        /// <summary>
        /// Modulates a vector with another by performing component-wise multiplication.
        /// </summary>
        /// <param name="left">The first vector to modulate.</param>
        /// <param name="right">The second vector to modulate.</param>
        /// <param name="result">When the method completes, contains the modulated vector.</param>
        public static void Modulate( ref Int3 left, ref Int3 right, out Int3 result )
        {
            result = new Int3( left.X * right.X, left.Y * right.Y, left.Z * right.Z );
        }

        /// <summary>
        /// Modulates a vector with another by performing component-wise multiplication.
        /// </summary>
        /// <param name="left">The first vector to modulate.</param>
        /// <param name="right">The second vector to modulate.</param>
        /// <returns>The modulated vector.</returns>
        public static Int3 Modulate( Int3 left, Int3 right )
        {
            return new Int3( left.X * right.X, left.Y * right.Y, left.Z * right.Z );
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <param name="result">When the method completes, contains the scaled vector.</param>
        public static void Divide( ref Int3 value, int scale, out Int3 result )
        {
            result = new Int3( value.X / scale, value.Y / scale, value.Z / scale );
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The scaled vector.</returns>
        public static Int3 Divide( Int3 value, int scale )
        {
            return new Int3( value.X / scale, value.Y / scale, value.Z / scale );
        }

        /// <summary>
        /// Reverses the direction of a given vector.
        /// </summary>
        /// <param name="value">The vector to negate.</param>
        /// <param name="result">When the method completes, contains a vector facing in the opposite direction.</param>
        public static void Negate( ref Int3 value, out Int3 result )
        {
            result = new Int3( -value.X, -value.Y, -value.Z );
        }

        /// <summary>
        /// Reverses the direction of a given vector.
        /// </summary>
        /// <param name="value">The vector to negate.</param>
        /// <returns>A vector facing in the opposite direction.</returns>
        public static Int3 Negate( Int3 value )
        {
            return new Int3( -value.X, -value.Y, -value.Z );
        }

        /// <summary>
        /// Restricts a value to be within a specified range.
        /// </summary>
        /// <param name="value">The value to clamp.</param>
        /// <param name="min">The minimum value.</param>
        /// <param name="max">The maximum value.</param>
        /// <param name="result">When the method completes, contains the clamped value.</param>
        public static void Clamp( ref Int3 value, ref Int3 min, ref Int3 max, out Int3 result )
        {
            int x = value.X;
            x = ( x > max.X ) ? max.X : x;
            x = ( x < min.X ) ? min.X : x;

            int y = value.Y;
            y = ( y > max.Y ) ? max.Y : y;
            y = ( y < min.Y ) ? min.Y : y;

            int z = value.Z;
            z = ( z > max.Z ) ? max.Z : z;
            z = ( z < min.Z ) ? min.Z : z;

            result = new Int3( x, y, z );
        }

        /// <summary>
        /// Restricts a value to be within a specified range.
        /// </summary>
        /// <param name="value">The value to clamp.</param>
        /// <param name="min">The minimum value.</param>
        /// <param name="max">The maximum value.</param>
        /// <returns>The clamped value.</returns>
        public static Int3 Clamp( Int3 value, Int3 min, Int3 max )
        {
            Int3 result;
            Clamp( ref value, ref min, ref max, out result );
            return result;
        }

        /// <summary>
        /// Calculates the dot product of two vectors.
        /// </summary>
        /// <param name="left">First source vector.</param>
        /// <param name="right">Second source vector.</param>
        /// <param name="result">When the method completes, contains the dot product of the two vectors.</param>
        public static void Dot( ref Int3 left, ref Int3 right, out int result )
        {
            result = ( left.X * right.X ) + ( left.Y * right.Y ) + ( left.Z * right.Z );
        }

        /// <summary>
        /// Calculates the dot product of two vectors.
        /// </summary>
        /// <param name="left">First source vector.</param>
        /// <param name="right">Second source vector.</param>
        /// <returns>The dot product of the two vectors.</returns>
        public static int Dot( Int3 left, Int3 right )
        {
            return ( left.X * right.X ) + ( left.Y * right.Y ) + ( left.Z * right.Z );
        }

        /// <summary>
        /// Performs a linear interpolation between two vectors.
        /// </summary>
        /// <param name="start">Start vector.</param>
        /// <param name="end">End vector.</param>
        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
        /// <param name="result">When the method completes, contains the linear interpolation of the two vectors.</param>
        /// <remarks>
        /// This method performs the linear interpolation based on the following formula.
        /// <code>start + (end - start) * amount</code>
        /// Passing <paramref name="amount"/> a value of 0 will cause <paramref name="start"/> to be returned; a value of 1 will cause <paramref name="end"/> to be returned.
        /// </remarks>
        public static void Lerp( ref Int3 start, ref Int3 end, float amount, out Int3 result )
        {
            result.X = (int)( start.X + ( ( end.X - start.X ) * amount ) );
            result.Y = (int)( start.Y + ( ( end.Y - start.Y ) * amount ) );
            result.Z = (int)( start.Z + ( ( end.Z - start.Z ) * amount ) );
        }

        /// <summary>
        /// Performs a linear interpolation between two vectors.
        /// </summary>
        /// <param name="start">Start vector.</param>
        /// <param name="end">End vector.</param>
        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
        /// <returns>The linear interpolation of the two vectors.</returns>
        /// <remarks>
        /// This method performs the linear interpolation based on the following formula.
        /// <code>start + (end - start) * amount</code>
        /// Passing <paramref name="amount"/> a value of 0 will cause <paramref name="start"/> to be returned; a value of 1 will cause <paramref name="end"/> to be returned.
        /// </remarks>
        public static Int3 Lerp( Int3 start, Int3 end, float amount )
        {
            Int3 result;
            Lerp( ref start, ref end, amount, out result );
            return result;
        }

        /// <summary>
        /// Performs a cubic interpolation between two vectors.
        /// </summary>
        /// <param name="start">Start vector.</param>
        /// <param name="end">End vector.</param>
        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
        /// <param name="result">When the method completes, contains the cubic interpolation of the two vectors.</param>
        public static void SmoothStep( ref Int3 start, ref Int3 end, float amount, out Int3 result )
        {
            amount = ( amount > 1 ) ? 1 : ( ( amount < 0 ) ? 0 : amount );
            amount = ( amount * amount ) * ( 3 - ( 2 * amount ) );

            result.X = (int)( start.X + ( ( end.X - start.X ) * amount ) );
            result.Y = (int)( start.Y + ( ( end.Y - start.Y ) * amount ) );
            result.Z = (int)( start.Z + ( ( end.Z - start.Z ) * amount ) );
        }

        /// <summary>
        /// Performs a cubic interpolation between two vectors.
        /// </summary>
        /// <param name="start">Start vector.</param>
        /// <param name="end">End vector.</param>
        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
        /// <returns>The cubic interpolation of the two vectors.</returns>
        public static Int3 SmoothStep( Int3 start, Int3 end, float amount )
        {
            Int3 result;
            SmoothStep( ref start, ref end, amount, out result );
            return result;
        }

        /// <summary>
        /// Returns a vector containing the smallest components of the specified vectors.
        /// </summary>
        /// <param name="left">The first source vector.</param>
        /// <param name="right">The second source vector.</param>
        /// <param name="result">When the method completes, contains an new vector composed of the largest components of the source vectors.</param>
        public static void Max( ref Int3 left, ref Int3 right, out Int3 result )
        {
            result.X = ( left.X > right.X ) ? left.X : right.X;
            result.Y = ( left.Y > right.Y ) ? left.Y : right.Y;
            result.Z = ( left.Z > right.Z ) ? left.Z : right.Z;
        }

        /// <summary>
        /// Returns a vector containing the largest components of the specified vectors.
        /// </summary>
        /// <param name="left">The first source vector.</param>
        /// <param name="right">The second source vector.</param>
        /// <returns>A vector containing the largest components of the source vectors.</returns>
        public static Int3 Max( Int3 left, Int3 right )
        {
            Int3 result;
            Max( ref left, ref right, out result );
            return result;
        }

        /// <summary>
        /// Returns a vector containing the smallest components of the specified vectors.
        /// </summary>
        /// <param name="left">The first source vector.</param>
        /// <param name="right">The second source vector.</param>
        /// <param name="result">When the method completes, contains an new vector composed of the smallest components of the source vectors.</param>
        public static void Min( ref Int3 left, ref Int3 right, out Int3 result )
        {
            result.X = ( left.X < right.X ) ? left.X : right.X;
            result.Y = ( left.Y < right.Y ) ? left.Y : right.Y;
            result.Z = ( left.Z < right.Z ) ? left.Z : right.Z;
        }

        /// <summary>
        /// Returns a vector containing the smallest components of the specified vectors.
        /// </summary>
        /// <param name="left">The first source vector.</param>
        /// <param name="right">The second source vector.</param>
        /// <returns>A vector containing the smallest components of the source vectors.</returns>
        public static Int3 Min( Int3 left, Int3 right )
        {
            Int3 result;
            Min( ref left, ref right, out result );
            return result;
        }

        /// <summary>
        /// Adds two vectors.
        /// </summary>
        /// <param name="left">The first vector to add.</param>
        /// <param name="right">The second vector to add.</param>
        /// <returns>The sum of the two vectors.</returns>
        public static Int3 operator +( Int3 left, Int3 right )
        {
            return new Int3( left.X + right.X, left.Y + right.Y, left.Z + right.Z );
        }

        /// <summary>
        /// Assert a vector (return it unchanged).
        /// </summary>
        /// <param name="value">The vector to assert (unchange).</param>
        /// <returns>The asserted (unchanged) vector.</returns>
        public static Int3 operator +( Int3 value )
        {
            return value;
        }

        /// <summary>
        /// Subtracts two vectors.
        /// </summary>
        /// <param name="left">The first vector to subtract.</param>
        /// <param name="right">The second vector to subtract.</param>
        /// <returns>The difference of the two vectors.</returns>
        public static Int3 operator -( Int3 left, Int3 right )
        {
            return new Int3( left.X - right.X, left.Y - right.Y, left.Z - right.Z );
        }

        /// <summary>
        /// Reverses the direction of a given vector.
        /// </summary>
        /// <param name="value">The vector to negate.</param>
        /// <returns>A vector facing in the opposite direction.</returns>
        public static Int3 operator -( Int3 value )
        {
            return new Int3( -value.X, -value.Y, -value.Z );
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The scaled vector.</returns>
        public static Int3 operator *( float scale, Int3 value )
        {
            return new Int3( (int)( value.X * scale ), (int)( value.Y * scale ), (int)( value.Z * scale ) );
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The scaled vector.</returns>
        public static Int3 operator *( Int3 value, float scale )
        {
            return new Int3( (int)( value.X * scale ), (int)( value.Y * scale ), (int)( value.Z * scale ) );
        }

        /// <summary>
        /// Scales a vector by the given value.
        /// </summary>
        /// <param name="value">The vector to scale.</param>
        /// <param name="scale">The amount by which to scale the vector.</param>
        /// <returns>The scaled vector.</returns>
        public static Int3 operator /( Int3 value, float scale )
        {
            return new Int3( (int)( value.X / scale ), (int)( value.Y / scale ), (int)( value.Z / scale ) );
        }

        /// <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 ==( Int3 left, Int3 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 !=( Int3 left, Int3 right )
        {
            return !left.Equals( right );
        }

        /// <summary>
        /// Performs an explicit conversion from <see cref="Int3"/> to <see cref="Vec2"/>.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static explicit operator Vec2( Int3 value )
        {
            return new Vec2( value.X, value.Y );
        }

        /// <summary>
        /// Performs an explicit conversion from <see cref="Int3"/> to <see cref="Vec3"/>.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static explicit operator Vec3( Int3 value )
        {
            return new Vec3( value.X, value.Y, value.Z );
        }

        /// <summary>
        /// Performs an explicit conversion from <see cref="Int3"/> to <see cref="Vec4"/>.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static explicit operator Vec4( Int3 value )
        {
            return new Vec4( value.X, value.Y, value.Z, 0 );
        }

        /// <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, "X:{0} Y:{1} Z:{2}", X, Y, Z );
        }

        /// <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 )
        {
            if( format == null )
                return ToString();

            return string.Format( CultureInfo.CurrentCulture, "X:{0} Y:{1} Z:{2}", X.ToString( format, CultureInfo.CurrentCulture ),
                Y.ToString( format, CultureInfo.CurrentCulture ), Z.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, "X:{0} Y:{1} Z:{2}", X, Y, Z );
        }

        /// <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 )
        {
            if( format == null )
                return ToString( formatProvider );

            return string.Format( formatProvider, "X:{0} Y:{1} Z:{2}", X.ToString( format, formatProvider ),
                Y.ToString( format, formatProvider ), Z.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 X.GetHashCode() + Y.GetHashCode() + Z.GetHashCode();
        }

        /// <summary>
        /// Determines whether the specified <see cref="Int3"/> is equal to this instance.
        /// </summary>
        /// <param name="other">The <see cref="Int3"/> to compare with this instance.</param>
        /// <returns>
        /// <c>true</c> if the specified <see cref="Int3"/> is equal to this instance; otherwise, <c>false</c>.
        /// </returns>
        public bool Equals( Int3 other )
        {
            return ( (float)Math.Abs( other.X - X ) < MathUtil.ZeroTolerance &&
                (float)Math.Abs( other.Y - Y ) < MathUtil.ZeroTolerance &&
                (float)Math.Abs( other.Z - Z ) < MathUtil.ZeroTolerance );
        }

        /// <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( (Int3)value );
        }
#if WPFInterop
        /// <summary>
        /// Performs an implicit conversion from <see cref="math.Int3"/> to <see cref="System.Windows.Media.Media3D.Int3D"/>.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static implicit operator System.Windows.Media.Media3D.Int3D(Int3 value)
        {
            return new System.Windows.Media.Media3D.Int3D(value.X, value.Y, value.Z);
        }

        /// <summary>
        /// Performs an explicit conversion from <see cref="System.Windows.Media.Media3D.Int3D"/> to <see cref="math.Int3"/>.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static explicit operator Int3(System.Windows.Media.Media3D.Int3D value)
        {
            return new Int3((float)value.X, (float)value.Y, (float)value.Z);
        }
#endif

#if XnaInterop
        /// <summary>
        /// Performs an implicit conversion from <see cref="math.Int3"/> to <see cref="Microsoft.Xna.Framework.Int3"/>.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static implicit operator Microsoft.Xna.Framework.Int3(Int3 value)
        {
            return new Microsoft.Xna.Framework.Int3(value.X, value.Y, value.Z);
        }

        /// <summary>
        /// Performs an implicit conversion from <see cref="Microsoft.Xna.Framework.Int3"/> to <see cref="math.Int3"/>.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static implicit operator Int3(Microsoft.Xna.Framework.Int3 value)
        {
            return new Int3(value.X, value.Y, value.Z);
        }
#endif
    }
}