Int3.cs

Go to the documentation of this file.

// Copyright (c) 2014 Silicon Studio Corp. (http://siliconstudio.co.jp)
// This file is distributed under MIT License. See LICENSE.md for details.
//
// -----------------------------------------------------------------------------
// 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;

namespace SiliconStudio.Core.Mathematics
{
    /// <summary>
    /// Represents a three dimensional mathematical vector.
    /// </summary>
    [DataContract("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 = Marshal.SizeOf(typeof(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(0)]
        public int X;

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

        /// <summary>
        /// The Z component of the vector.
        /// </summary>
        [DataMember(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(Vector2 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 a value indicting whether this instance is normalized.
        /// </summary>
        public bool IsNormalized
        {
            get { return Math.Abs((X * X) + (Y * Y) + (Z * Z) - 1f) < MathUtil.ZeroTolerance; }
        }

        /// <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>
        /// Converts the vector into a unit vector.
        /// </summary>
        public void Normalize()
        {
            int length = Length();
            if (length > MathUtil.ZeroTolerance)
            {
                int inv = 1 / length;
                X *= inv;
                Y *= inv;
                Z *= inv;
            }
        }

        /// <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>
        /// Converts the vector into a unit vector.
        /// </summary>
        /// <param name="value">The vector to normalize.</param>
        /// <param name="result">When the method completes, contains the normalized vector.</param>
        public static void Normalize(ref Int3 value, out Int3 result)
        {
            result = value;
            result.Normalize();
        }

        /// <summary>
        /// Converts the vector into a unit vector.
        /// </summary>
        /// <param name="value">The vector to normalize.</param>
        /// <returns>The normalized vector.</returns>
        public static Int3 Normalize(Int3 value)
        {
            value.Normalize();
            return value;
        }

        /// <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="Vector2"/>.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static explicit operator Vector2(Int3 value)
        {
            return new Vector2(value.X, value.Y);
        }

        /// <summary>
        /// Performs an explicit conversion from <see cref="Int3"/> to <see cref="Vector4"/>.
        /// </summary>
        /// <param name="value">The value.</param>
        /// <returns>The result of the conversion.</returns>
        public static explicit operator Vector4(Int3 value)
        {
            return new Vector4(value.X, value.Y, value.Z, 0);
        }

        /// <summary>
        /// Returns a <see cref="System.String"/> that represents this instance.
        /// </summary>
        /// <returns>
        /// A <see cref="System.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="System.String"/> that represents this instance.
        /// </summary>
        /// <param name="format">The format.</param>
        /// <returns>
        /// A <see cref="System.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="System.String"/> that represents this instance.
        /// </summary>
        /// <param name="formatProvider">The format provider.</param>
        /// <returns>
        /// A <see cref="System.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="System.String"/> that represents this instance.
        /// </summary>
        /// <param name="format">The format.</param>
        /// <param name="formatProvider">The format provider.</param>
        /// <returns>
        /// A <see cref="System.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="System.Object"/> is equal to this instance.
        /// </summary>
        /// <param name="value">The <see cref="System.Object"/> to compare with this instance.</param>
        /// <returns>
        ///     <c>true</c> if the specified <see cref="System.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="SiliconStudio.Core.Mathematics.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="SiliconStudio.Core.Mathematics.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="SiliconStudio.Core.Mathematics.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="SiliconStudio.Core.Mathematics.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
    }
}