Opentk/Source/OpenTK/Math/Vector3.cs

#region --- License ---
/* Copyright (c) 2006, 2007 Stefanos Apostolopoulos
 * See license.txt for license info
 * 
 * Contributions by Andy Gill.
 */
#endregion

using System;
using System.Collections.Generic;
using System.Text;
using System.Runtime.InteropServices;

namespace OpenTK.Math
{
	/// <summary>
	/// Represents a three-dimensional vector.
	/// </summary>
    [Serializable]
	[StructLayout(LayoutKind.Sequential)]
	public struct Vector3 : IEquatable<Vector3>
	{
		#region Fields

		/// <summary>
		/// The X component of the Vector3.
		/// </summary>
		public float X;

		/// <summary>
		/// The Y component of the Vector3.
		/// </summary>
		public float Y;

		/// <summary>
		/// The Z component of the Vector3.
		/// </summary>
		public float Z;

        /// <summary>
        /// Defines a unit-length Vector3 that points towards the X-axis.
        /// </summary>
        public static readonly Vector3 UnitX = new Vector3(1, 0, 0);

        /// <summary>
        /// Defines a unit-length Vector3 that points towards the Y-axis.
        /// </summary>
        public static readonly Vector3 UnitY = new Vector3(0, 1, 0);

        /// <summary>
        /// /// Defines a unit-length Vector3 that points towards the Z-axis.
        /// </summary>
        public static readonly Vector3 UnitZ = new Vector3(0, 0, 1);

        /// <summary>
        /// Defines a zero-length Vector3.
        /// </summary>
        public static readonly Vector3 Zero = new Vector3(0, 0, 0);

        /// <summary>
        /// Defines the size of the Vector3 struct in bytes.
        /// </summary>
        public static readonly int SizeInBytes = Marshal.SizeOf(new Vector3());

        #endregion

		#region Constructors

		/// <summary>
		/// Constructs a new Vector3.
		/// </summary>
		/// <param name="x">The x component of the Vector3.</param>
		/// <param name="y">The y component of the Vector3.</param>
		/// <param name="z">The z component of the Vector3.</param>
		public Vector3(float x, float y, float z)
		{
			X = x;
			Y = y;
			Z = z;
		}

        /// <summary>
        /// Constructs a new Vector3 from the given Vector2.
        /// </summary>
        /// <param name="v">The Vector2 to copy components from.</param>
        public Vector3(Vector2 v)
        {
            X = v.X;
            Y = v.Y;
            Z = 0.0f;
        }

        /// <summary>
        /// Constructs a new Vector3 from the given Vector3.
        /// </summary>
        /// <param name="v">The Vector3 to copy components from.</param>
        public Vector3(Vector3 v)
        {
            X = v.X;
            Y = v.Y;
            Z = v.Z;
        }

        /// <summary>
        /// Constructs a new Vector3 from the given Vector4.
        /// </summary>
        /// <param name="v">The Vector4 to copy components from.</param>
        public Vector3(Vector4 v)
        {
            X = v.X;
            Y = v.Y;
            Z = v.Z;
        }

        #endregion

        #region Functions

        #region This property

        public float this[int index]
        {
            get
            {
                switch (index)
                {
                    case 0: return X;
                    case 1: return Y;
                    case 2: return Z;
                    default: throw new ArgumentOutOfRangeException("index", index, "Should be 0, 1 or 2.");
                }
                /*
                unsafe
                {
                    fixed (float* ptr = &this.X)
                        return *(ptr + index);
                }

                */
            }
        }

        #endregion

        #region public float Length

        /// <summary>
        /// Gets the length (magnitude) of the vector.
        /// </summary>
        /// <see cref="FastLength"/>
        /// <seealso cref="LengthSquared"/>
        public float Length
        {
            get
            {
                return (float)System.Math.Sqrt(X * X + Y * Y + Z * Z);
            }
        }

        #endregion

        #region public float LengthFast

        /// <summary>
        /// Gets an approximation of the vector length (magnitude).
        /// </summary>
        /// <remarks>
        /// This property uses an approximation of the square root function to calculate vector magnitude, with
        /// an upper error bound of 0.001.
        /// </remarks>
        /// <see cref="Length"/>
        /// <seealso cref="LengthSquared"/>
        /// <seealso cref="OpenTK.Math.FastSqrt"/>
        public float LengthFast
        {
            get
            {
                return 1.0f / OpenTK.Math.Functions.InverseSqrtFast(X * X + Y * Y + Z * Z);
            }
        }

        #endregion

        #region public float LengthSquared

        /// <summary>
        /// Gets the square of the vector length (magnitude).
        /// </summary>
        /// <remarks>
        /// This property avoids the costly square root operation required by the Length property. This makes it more suitable
        /// for comparisons.
        /// </remarks>
        /// <see cref="Length"/>
        /// <seealso cref="FastLength"/>
        public float LengthSquared
        {
            get
            {
                return X * X + Y * Y + Z * Z;
            }
        }

        #endregion

        #region public void Normalize()

        /// <summary>
        /// Scales the Vector3 to unit length.
        /// </summary>
        public void Normalize()
        {
            float scale = 1.0f / this.Length;
            X *= scale;
            Y *= scale;
            Z *= scale;
        }

        #endregion

        #region public void NormalizeFast()

        /// <summary>
        /// Scales the Vector3 to approximately unit length.
        /// </summary>
        public void NormalizeFast()
        {
            float scale = Functions.InverseSqrtFast(X * X + Y * Y + Z * Z);
            X *= scale;
            Y *= scale;
            Z *= scale;
        }

        #endregion

        #region public void Scale(float sx, float sy, float sz)

        /// <summary>
        /// Scales the current Vector3 by the given amounts.
        /// </summary>
        /// <param name="sx">The scale of the X component.</param>
        /// <param name="sy">The scale of the Y component.</param>
        /// <param name="sz">The scale of the Z component.</param>
        public void Scale(float sx, float sy, float sz)
        {
            this.X = X * sx;
            this.Y = Y * sy;
            this.Z = Z * sz;
        }

        #endregion

        #endregion

        #region Operator overloads

        public static Vector3 operator +(Vector3 left, Vector3 right)
        {
			left.X += right.X;
			left.Y += right.Y;
			left.Z += right.Z;
			return left;
        }

        public static Vector3 operator -(Vector3 left, Vector3 right)
        {
			left.X -= right.X;
			left.Y -= right.Y;
			left.Z -= right.Z;
			return left;
        }

		public static Vector3 operator -(Vector3 vec)
		{
			vec.X = -vec.X;
			vec.Y = -vec.Y;
			vec.Z = -vec.Z;
			return vec;
		}

		public static Vector3 operator *(Vector3 vec, float f)
		{
			vec.X *= f;
			vec.Y *= f;
			vec.Z *= f;
			return vec;
		}

		public static Vector3 operator *(float f, Vector3 vec)
		{
			vec.X *= f;
			vec.Y *= f;
			vec.Z *= f;
			return vec;
		}

		public static Vector3 operator /(Vector3 vec, float f)
		{
			float mult = 1.0f / f;
			vec.X *= mult;
			vec.Y *= mult;
			vec.Z *= mult;
			return vec;
		}

        public static bool operator ==(Vector3 left, Vector3 right)
        {
            return left.Equals(right);
        }

        public static bool operator !=(Vector3 left, Vector3 right)
        {
            return !left.Equals(right);
        }

        #endregion

        #region Static functions

		#region Add

		/// <summary>
		/// Add two Vectors
		/// </summary>
		/// <param name="a">First operand</param>
		/// <param name="b">Second operand</param>
		/// <returns>Result of addition</returns>
		public static Vector3 Add(Vector3 a, Vector3 b)
		{
			a.X += b.X;
			a.Y += b.Y;
			a.Z += b.Z;
			return a;
		}

		/// <summary>
		/// Add two Vectors
		/// </summary>
		/// <param name="a">First operand</param>
		/// <param name="b">Second operand</param>
		/// <param name="result">Result of addition</param>
		public static void Add(ref Vector3 a, ref Vector3 b, out Vector3 result)
		{
			result.X = a.X + b.X;
			result.Y = a.Y + b.Y;
			result.Z = a.Z + b.Z;
		}

		#endregion

		#region Sub

		/// <summary>
		/// Subtract one Vector from another
		/// </summary>
		/// <param name="a">First operand</param>
		/// <param name="b">Second operand</param>
		/// <returns>Result of subtraction</returns>
		public static Vector3 Sub(Vector3 a, Vector3 b)
		{
			a.X -= b.X;
			a.Y -= b.Y;
			a.Z -= b.Z;
			return a;
		}

		/// <summary>
		/// Subtract one Vector from another
		/// </summary>
		/// <param name="a">First operand</param>
		/// <param name="b">Second operand</param>
		/// <param name="result">Result of subtraction</param>
		public static void Sub(ref Vector3 a, ref Vector3 b, out Vector3 result)
		{
			result.X = a.X - b.X;
			result.Y = a.Y - b.Y;
			result.Z = a.Z - b.Z;
		}

		#endregion

		#region Mult

		/// <summary>
		/// Multiply a vector and a scalar
		/// </summary>
		/// <param name="a">Vector operand</param>
		/// <param name="f">Scalar operand</param>
		/// <returns>Result of the multiplication</returns>
		public static Vector3 Mult(Vector3 a, float f)
		{
			a.X *= f;
			a.Y *= f;
			a.Z *= f;
			return a;
		}

		/// <summary>
		/// Multiply a vector and a scalar
		/// </summary>
		/// <param name="a">Vector operand</param>
		/// <param name="f">Scalar operand</param>
		/// <param name="result">Result of the multiplication</param>
		public static void Mult(ref Vector3 a, float f, out Vector3 result)
		{
			result.X = a.X * f;
			result.Y = a.Y * f;
			result.Z = a.Z * f;
		}

		#endregion

		#region Div

		/// <summary>
		/// Divide a vector by a scalar
		/// </summary>
		/// <param name="a">Vector operand</param>
		/// <param name="f">Scalar operand</param>
		/// <returns>Result of the division</returns>
		public static Vector3 Div(Vector3 a, float f)
		{
			float mult = 1.0f / f;
			a.X *= mult;
			a.Y *= mult;
			a.Z *= mult;
			return a;
		}

		/// <summary>
		/// Divide a vector by a scalar
		/// </summary>
		/// <param name="a">Vector operand</param>
		/// <param name="f">Scalar operand</param>
		/// <param name="result">Result of the division</param>
		public static void Div(ref Vector3 a, float f, out Vector3 result)
		{
			float mult = 1.0f / f;
			result.X = a.X * mult;
			result.Y = a.Y * mult;
			result.Z = a.Z * mult;
		}

		#endregion

        #region ComponentMin

        /// <summary>
        /// Calculate the component-wise minimum of two vectors
        /// </summary>
        /// <param name="a">First operand</param>
        /// <param name="b">Second operand</param>
        /// <returns>The component-wise minimum</returns>
        public static Vector3 ComponentMin(Vector3 a, Vector3 b)
        {
            a.X = a.X < b.X ? a.X : b.X;
            a.Y = a.Y < b.Y ? a.Y : b.Y;
            a.Z = a.Z < b.Z ? a.Z : b.Z;
            return a;
        }

        /// <summary>
        /// Calculate the component-wise minimum of two vectors
        /// </summary>
        /// <param name="a">First operand</param>
        /// <param name="b">Second operand</param>
        /// <param name="result">The component-wise minimum</param>
        public static void ComponentMin(ref Vector3 a, ref Vector3 b, out Vector3 result)
        {
            result.X = a.X < b.X ? a.X : b.X;
            result.Y = a.Y < b.Y ? a.Y : b.Y;
            result.Z = a.Z < b.Z ? a.Z : b.Z;
        }

        #endregion

        #region ComponentMax

        /// <summary>
        /// Calculate the component-wise maximum of two vectors
        /// </summary>
        /// <param name="a">First operand</param>
        /// <param name="b">Second operand</param>
        /// <returns>The component-wise maximum</returns>
        public static Vector3 ComponentMax(Vector3 a, Vector3 b)
        {
            a.X = a.X > b.X ? a.X : b.X;
            a.Y = a.Y > b.Y ? a.Y : b.Y;
            a.Z = a.Z > b.Z ? a.Z : b.Z;
            return a;
        }

        /// <summary>
        /// Calculate the component-wise maximum of two vectors
        /// </summary>
        /// <param name="a">First operand</param>
        /// <param name="b">Second operand</param>
        /// <param name="result">The component-wise maximum</param>
        public static void ComponentMax(ref Vector3 a, ref Vector3 b, out Vector3 result)
        {
            result.X = a.X > b.X ? a.X : b.X;
            result.Y = a.Y > b.Y ? a.Y : b.Y;
            result.Z = a.Z > b.Z ? a.Z : b.Z;
        }

        #endregion

        #region Min

        /// <summary>
        /// Returns the Vector3 with the minimum magnitude
        /// </summary>
        /// <param name="left">Left operand</param>
        /// <param name="right">Right operand</param>
        /// <returns>The minimum Vector3</returns>
        public static Vector3 Min(Vector3 left, Vector3 right)
        {
            return left.LengthSquared < right.LengthSquared ? left : right;
        }

        #endregion

        #region Max

        /// <summary>
        /// Returns the Vector3 with the minimum magnitude
        /// </summary>
        /// <param name="left">Left operand</param>
        /// <param name="right">Right operand</param>
        /// <returns>The minimum Vector3</returns>
        public static Vector3 Max(Vector3 left, Vector3 right)
        {
            return left.LengthSquared >= right.LengthSquared ? left : right;
        }

        #endregion

		#region Clamp

		/// <summary>
		/// Clamp a vector to the given minimum and maximum vectors
		/// </summary>
		/// <param name="vec">Input vector</param>
		/// <param name="min">Minimum vector</param>
		/// <param name="max">Maximum vector</param>
		/// <returns>The clamped vector</returns>
		public static Vector3 Clamp(Vector3 vec, Vector3 min, Vector3 max)
		{
			vec.X = vec.X < min.X ? min.X : vec.X > max.X ? max.X : vec.X;
			vec.Y = vec.Y < min.Y ? min.Y : vec.Y > max.Y ? max.Y : vec.Y;
			vec.Z = vec.Z < min.Z ? min.Z : vec.Z > max.Z ? max.Z : vec.Z;
			return vec;
		}

		/// <summary>
		/// Clamp a vector to the given minimum and maximum vectors
		/// </summary>
		/// <param name="vec">Input vector</param>
		/// <param name="min">Minimum vector</param>
		/// <param name="max">Maximum vector</param>
		/// <param name="result">The clamped vector</param>
		public static void Clamp(ref Vector3 vec, ref Vector3 min, ref Vector3 max, out Vector3 result)
		{
			result.X = vec.X < min.X ? min.X : vec.X > max.X ? max.X : vec.X;
			result.Y = vec.Y < min.Y ? min.Y : vec.Y > max.Y ? max.Y : vec.Y;
			result.Z = vec.Z < min.Z ? min.Z : vec.Z > max.Z ? max.Z : vec.Z;
		}

		#endregion

		#region Normalize

		/// <summary>
		/// Scale a vector to unit length
		/// </summary>
		/// <param name="vec">The input vector</param>
		/// <returns>The normalized vector</returns>
		public static Vector3 Normalize(Vector3 vec)
        {
            float scale = 1.0f / vec.Length;
            vec.X *= scale;
            vec.Y *= scale;
            vec.Z *= scale;
			return vec;
        }

		/// <summary>
		/// Scale a vector to unit length
		/// </summary>
		/// <param name="vec">The input vector</param>
		/// <param name="result">The normalized vector</param>
		public static void Normalize(ref Vector3 vec, out Vector3 result)
		{
            float scale = 1.0f / vec.Length;
            result.X = vec.X * scale;
            result.Y = vec.Y * scale;
            result.Z = vec.Z * scale;
		}

		#endregion

		#region NormalizeFast

		/// <summary>
		/// Scale a vector to approximately unit length
		/// </summary>
		/// <param name="vec">The input vector</param>
		/// <returns>The normalized vector</returns>
		public static Vector3 NormalizeFast(Vector3 vec)
        {
            float scale = Functions.InverseSqrtFast(vec.X * vec.X + vec.Y * vec.Y + vec.Z * vec.Z);
            vec.X *= scale;
            vec.Y *= scale;
            vec.Z *= scale;
			return vec;
        }

		/// <summary>
		/// Scale a vector to approximately unit length
		/// </summary>
		/// <param name="vec">The input vector</param>
		/// <param name="result">The normalized vector</param>
		public static void NormalizeFast(ref Vector3 vec, out Vector3 result)
		{
            float scale = Functions.InverseSqrtFast(vec.X * vec.X + vec.Y * vec.Y + vec.Z * vec.Z);
            result.X = vec.X * scale;
            result.Y = vec.Y * scale;
            result.Z = vec.Z * scale;
		}

		#endregion

		#region Dot

		/// <summary>
		/// Caclulate the dot (scalar) product of two vectors
		/// </summary>
		/// <param name="left">First operand</param>
		/// <param name="right">Second operand</param>
		/// <returns>The dot product of the two inputs</returns>
		public static float Dot(Vector3 left, Vector3 right)
        {
            return left.X * right.X + left.Y * right.Y + left.Z * right.Z;
		}

		#endregion

		#region Cross

		/// <summary>
		/// Caclulate the cross (vector) product of two vectors
		/// </summary>
		/// <param name="left">First operand</param>
		/// <param name="right">Second operand</param>
		/// <returns>The cross product of the two inputs</returns>
		public static Vector3 Cross(Vector3 left, Vector3 right)
        {
            float
                x = left.Y * right.Z - left.Z * right.Y,
                y = left.Z * right.X - left.X * right.Z,
                z = left.X * right.Y - left.Y * right.X;
            left.X = x;
            left.Y = y;
            left.Z = z;
            return left;
        }

		/// <summary>
		/// Caclulate the cross (vector) product of two vectors
		/// </summary>
		/// <param name="left">First operand</param>
		/// <param name="right">Second operand</param>
		/// <returns>The cross product of the two inputs</returns>
		/// <param name="result">The cross product of the two inputs</param>
        public static void Cross(ref Vector3 left, ref Vector3 right, out Vector3 result)
        {
			result.X = left.Y * right.Z - left.Z * right.Y;
            result.Y = left.Z * right.X - left.X * right.Z;
            result.Z = left.X * right.Y - left.Y * right.X;
		}

		#endregion

		#region Lerp

		/// <summary>
		/// Returns a new Vector that is the linear blend of the 2 given Vectors
		/// </summary>
		/// <param name="a">First input vector</param>
		/// <param name="b">Second input vector</param>
		/// <param name="blend">The blend factor</param>
		/// <returns>a when blend=0, b when blend=1, and a linear combination otherwise</returns>
		public static Vector3 Lerp(Vector3 a, Vector3 b, float blend)
		{
			a.X = blend * (b.X - a.X) + a.X;
			a.Y = blend * (b.Y - a.Y) + a.Y;
			a.Z = blend * (b.Z - a.Z) + a.Z;
			return a;
		}

		#endregion

		#region Barycentric

		/// <summary>
		/// Interpolate 3 Vectors using Barycentric coordinates
		/// </summary>
		/// <param name="a">First input Vector</param>
		/// <param name="b">Second input Vector</param>
		/// <param name="c">Third input Vector</param>
		/// <param name="u">First Barycentric Coordinate</param>
		/// <param name="v">Second Barycentric Coordinate</param>
		/// <returns>a when u=v=0, b when u=1,v=0, c when u=0,v=1, and a linear combination of a,b,c otherwise</returns>
		public static Vector3 BaryCentric(Vector3 a, Vector3 b, Vector3 c, float u, float v)
		{
			return a + u * (b - a) + v * (c - a);
		}

		#endregion

		#region Transform

		/// <summary>
		/// Transform a direction vector by the given Matrix
		/// Assumes the matrix has a bottom row of (0,0,0,1), that is the translation part is ignored.
		/// </summary>
		/// <param name="vec">The vector to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <returns>The transformed vector</returns>
		public static Vector3 TransformVector(Vector3 vec, Matrix4 mat)
		{
			Vector3 v;
			v.X = Vector3.Dot(vec, new Vector3(mat.Column0));
			v.Y = Vector3.Dot(vec, new Vector3(mat.Column1));
			v.Z = Vector3.Dot(vec, new Vector3(mat.Column2));
			return v;
		}

		/// <summary>
		/// Transform a Normal by the given Matrix
		/// </summary>
		/// <remarks>
		/// This calculates the inverse of the given matrix, use TransformNormalInverse if you
		/// already have the inverse to avoid this extra calculation
		/// </remarks>
		/// <param name="norm">The normal to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <returns>The transformed normal</returns>
		public static Vector3 TransformNormal(Vector3 norm, Matrix4 mat)
		{
			mat.Invert();
			return TransformNormalInverse(norm, mat);
		}

		/// <summary>
		/// Transform a Normal by the (transpose of the) given Matrix
		/// </summary>
		/// <remarks>
		/// This version doesn't calculate the inverse matrix.
		/// Use this version if you already have the inverse of the desired transform to hand
		/// </remarks>
		/// <param name="norm">The normal to transform</param>
		/// <param name="mat">The inverse of the desired transformation</param>
		/// <returns>The transformed normal</returns>
		public static Vector3 TransformNormalInverse(Vector3 norm, Matrix4 invMat)
		{
			Vector3 n;
			n.X = Vector3.Dot(norm, new Vector3(invMat.Row0));
			n.Y = Vector3.Dot(norm, new Vector3(invMat.Row1));
			n.Z = Vector3.Dot(norm, new Vector3(invMat.Row2));
			return n;
		}

		/// <summary>
		/// Transform a Position by the given Matrix
		/// </summary>
		/// <param name="pos">The position to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <returns>The transformed position</returns>
		public static Vector3 TransformPosition(Vector3 pos, Matrix4 mat)
		{
			Vector3 p;
			p.X = Vector3.Dot(pos, new Vector3(mat.Column0)) + mat.Row3.X;
			p.Y = Vector3.Dot(pos, new Vector3(mat.Column1)) + mat.Row3.Y;
			p.Z = Vector3.Dot(pos, new Vector3(mat.Column2)) + mat.Row3.Z;
			return p;
		}

		/// <summary>
		/// Transform a Vector by the given Matrix
		/// </summary>
		/// <param name="pos">The vector to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <returns>The transformed vector</returns>
		public static Vector4 Transform(Vector3 vec, Matrix4 mat)
		{
			Vector4 v4 = new Vector4(vec.X, vec.Y, vec.Z, 1.0f);
			Vector4 result;
			result.X = Vector4.Dot(v4, mat.Column0);
			result.Y = Vector4.Dot(v4, mat.Column1);
			result.Z = Vector4.Dot(v4, mat.Column2);
			result.W = Vector4.Dot(v4, mat.Column3);
			return result;
		}

		/// <summary>
		/// Transform a Vector3 by the given Matrix, and project the resulting Vector4 back to a Vector3
		/// </summary>
		/// <param name="pos">The vector to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <returns>The transformed vector</returns>
		public static Vector3 TransformPerspective(Vector3 vec, Matrix4 mat)
		{
			Vector4 h = Transform(vec, mat);
			return new Vector3(h.X / h.W, h.Y / h.W, h.Z / h.W);
		}

		#endregion

		#region CalculateAngle

		/// <summary>
		/// Calculates the angle (in radians) between two vectors.
		/// </summary>
		/// <param name="first">The first vector.</param>
		/// <param name="second">The second vector.</param>
		/// <returns>Angle (in radians) between the vectors.</returns>
		/// <remarks>Note that the returned angle is never bigger than the constant Pi.</remarks>
		public static float CalculateAngle(Vector3 first, Vector3 second)
		{
			return (float)System.Math.Acos((Vector3.Dot(first, second)) / (first.Length * second.Length));
		}

		#endregion

		#endregion

		#region public override string ToString()

		/// <summary>
		/// Returns a System.String that represents the current Vector3.
		/// </summary>
		/// <returns></returns>
		public override string ToString()
        {
            return String.Format("({0}, {1}, {2})", X, Y, Z);
		}

		#endregion

        #region public override int GetHashCode()

        /// <summary>
        /// Returns the hashcode for this instance.
        /// </summary>
        /// <returns>A System.Int32 containing the unique hashcode for this instance.</returns>
        public override int GetHashCode()
        {
            return X.GetHashCode() ^ Y.GetHashCode() ^ Z.GetHashCode();
        }

        #endregion

        #region public override bool Equals(object obj)

        /// <summary>
        /// Indicates whether this instance and a specified object are equal.
        /// </summary>
        /// <param name="obj">The object to compare to.</param>
        /// <returns>True if the instances are equal; false otherwise.</returns>
        public override bool Equals(object obj)
        {
            if (!(obj is Vector3))
                return false;

            return this.Equals((Vector3)obj);
        }

        #endregion

        #region IEquatable<Vector3> Members

        /// <summary>Indicates whether the current vector is equal to another vector.</summary>
        /// <param name="vector">A vector to compare with this vector.</param>
        /// <returns>true if the current vector is equal to the vector parameter; otherwise, false.</returns>
        public bool Equals(Vector3 other)
        {
            return
                X == other.X &&
                Y == other.Y &&
                Z == other.Z;
        }

        #endregion
    }
}