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#region --- License ---

/*

Copyright (c) 2006 - 2008 The Open Toolkit library.

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.

*/

#endregion

using System;

using System.Runtime.InteropServices;

namespace OpenTK

{

    /// <summary>Represents a 2D vector using two double-precision floating-point numbers.</summary>

    [Serializable]

    [StructLayout(LayoutKind.Sequential)]

    public struct Vector2d : IEquatable<Vector2d>

    {

        #region Fields

        /// <summary>The X coordinate of this instance.</summary>

        public double X;

        /// <summary>The Y coordinate of this instance.</summary>

        public double Y;

        /// <summary>

        /// Defines a unit-length Vector2d that points towards the X-axis.

        /// </summary>

        public static Vector2d UnitX = new Vector2d(1, 0);

        /// <summary>

        /// Defines a unit-length Vector2d that points towards the Y-axis.

        /// </summary>

        public static Vector2d UnitY = new Vector2d(0, 1);

        /// <summary>

        /// Defines a zero-length Vector2d.

        /// </summary>

        public static Vector2d Zero = new Vector2d(0, 0);

        /// <summary>

        /// Defines an instance with all components set to 1.

        /// </summary>

        public static readonly Vector2d One = new Vector2d(1, 1);

        /// <summary>

        /// Defines the size of the Vector2d struct in bytes.

        /// </summary>

        public static readonly int SizeInBytes = Marshal.SizeOf(new Vector2d());

        #endregion

        #region Constructors

        /// <summary>Constructs left vector with the given coordinates.</summary>

        /// <param name="x">The X coordinate.</param>

        /// <param name="y">The Y coordinate.</param>

        public Vector2d(double x, double y)

        {

            this.X = x;

            this.Y = y;

        }

        #endregion

        #region Public Members

        #region Instance

        #region public void Add()

        /// <summary>Add the Vector passed as parameter to this instance.</summary>

        /// <param name="right">Right operand. This parameter is only read from.</param>

        [Obsolete("Use static Add() method instead.")]

        public void Add(Vector2d right)

        {

            this.X += right.X;

            this.Y += right.Y;

        }

        /// <summary>Add the Vector passed as parameter to this instance.</summary>

        /// <param name="right">Right operand. This parameter is only read from.</param>

        [CLSCompliant(false)]

        [Obsolete("Use static Add() method instead.")]

        public void Add(ref Vector2d right)

        {

            this.X += right.X;

            this.Y += right.Y;

        }

        #endregion public void Add()

        #region public void Sub()

        /// <summary>Subtract the Vector passed as parameter from this instance.</summary>

        /// <param name="right">Right operand. This parameter is only read from.</param>

        [Obsolete("Use static Subtract() method instead.")]

        public void Sub(Vector2d right)

        {

            this.X -= right.X;

            this.Y -= right.Y;

        }

        /// <summary>Subtract the Vector passed as parameter from this instance.</summary>

        /// <param name="right">Right operand. This parameter is only read from.</param>

        [CLSCompliant(false)]

        [Obsolete("Use static Subtract() method instead.")]

        public void Sub(ref Vector2d right)

        {

            this.X -= right.X;

            this.Y -= right.Y;

        }

        #endregion public void Sub()

        #region public void Mult()

        /// <summary>Multiply this instance by a scalar.</summary>

        /// <param name="f">Scalar operand.</param>

        [Obsolete("Use static Multiply() method instead.")]

        public void Mult(double f)

        {

            this.X *= f;

            this.Y *= f;

        }

        #endregion public void Mult()

        #region public void Div()

        /// <summary>Divide this instance by a scalar.</summary>

        /// <param name="f">Scalar operand.</param>

        [Obsolete("Use static Divide() method instead.")]

        public void Div(double f)

        {

            double mult = 1.0 / f;

            this.X *= mult;

            this.Y *= mult;

        }

        #endregion public void Div()

        #region public double Length

        /// <summary>

        /// Gets the length (magnitude) of the vector.

        /// </summary>

        /// <seealso cref="LengthSquared"/>

        public double Length

        {

            get

            {

                return System.Math.Sqrt(X * X + Y * Y);

            }

        }

        #endregion

        #region public double 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"/>

        public double LengthSquared

        {

            get

            {

                return X * X + Y * Y;

            }

        }

        #endregion

        #region public Vector2d PerpendicularRight

        /// <summary>

        /// Gets the perpendicular vector on the right side of this vector.

        /// </summary>

        public Vector2d PerpendicularRight

        {

            get

            {

                return new Vector2d(Y, -X);

            }

        }

        #endregion

        #region public Vector2d PerpendicularLeft

        /// <summary>

        /// Gets the perpendicular vector on the left side of this vector.

        /// </summary>

        public Vector2d PerpendicularLeft

        {

            get

            {

                return new Vector2d(-Y, X);

            }

        }

        #endregion

        #region public void Normalize()

        /// <summary>

        /// Scales the Vector2 to unit length.

        /// </summary>

        public void Normalize()

        {

            double scale = 1.0 / Length;

            X *= scale;

            Y *= scale;

        }

        #endregion

        #region public void Scale()

        /// <summary>

        /// Scales the current Vector2 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>

        [Obsolete("Use static Multiply() method instead.")]

        public void Scale(double sx, double sy)

        {

            X *= sx;

            Y *= sy;

        }

        /// <summary>Scales this instance by the given parameter.</summary>

        /// <param name="scale">The scaling of the individual components.</param>

        [Obsolete("Use static Multiply() method instead.")]

        public void Scale(Vector2d scale)

        {

            this.X *= scale.X;

            this.Y *= scale.Y;

        }

        /// <summary>Scales this instance by the given parameter.</summary>

        /// <param name="scale">The scaling of the individual components.</param>

        [CLSCompliant(false)]

        [Obsolete("Use static Multiply() method instead.")]

        public void Scale(ref Vector2d scale)

        {

            this.X *= scale.X;

            this.Y *= scale.Y;

        }

        #endregion public void Scale()

        #endregion

        #region Static

        #region Obsolete

        #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>

        [Obsolete("Use static Subtract() method instead.")]

        public static Vector2d Sub(Vector2d a, Vector2d b)

        {

            a.X -= b.X;

            a.Y -= b.Y;

            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>

        [Obsolete("Use static Subtract() method instead.")]

        public static void Sub(ref Vector2d a, ref Vector2d b, out Vector2d result)

        {

            result.X = a.X - b.X;

            result.Y = a.Y - b.Y;

        }

        #endregion

        #region Mult

        /// <summary>

        /// Multiply a vector and a scalar

        /// </summary>

        /// <param name="a">Vector operand</param>

        /// <param name="d">Scalar operand</param>

        /// <returns>Result of the multiplication</returns>

        [Obsolete("Use static Multiply() method instead.")]

        public static Vector2d Mult(Vector2d a, double d)

        {

            a.X *= d;

            a.Y *= d;

            return a;

        }

        /// <summary>

        /// Multiply a vector and a scalar

        /// </summary>

        /// <param name="a">Vector operand</param>

        /// <param name="d">Scalar operand</param>

        /// <param name="result">Result of the multiplication</param>

        [Obsolete("Use static Multiply() method instead.")]

        public static void Mult(ref Vector2d a, double d, out Vector2d result)

        {

            result.X = a.X * d;

            result.Y = a.Y * d;

        }

        #endregion

        #region Div

        /// <summary>

        /// Divide a vector by a scalar

        /// </summary>

        /// <param name="a">Vector operand</param>

        /// <param name="d">Scalar operand</param>

        /// <returns>Result of the division</returns>

        [Obsolete("Use static Divide() method instead.")]

        public static Vector2d Div(Vector2d a, double d)

        {

            double mult = 1.0 / d;

            a.X *= mult;

            a.Y *= mult;

            return a;

        }

        /// <summary>

        /// Divide a vector by a scalar

        /// </summary>

        /// <param name="a">Vector operand</param>

        /// <param name="d">Scalar operand</param>

        /// <param name="result">Result of the division</param>

        [Obsolete("Use static Divide() method instead.")]

        public static void Div(ref Vector2d a, double d, out Vector2d result)

        {

            double mult = 1.0 / d;

            result.X = a.X * mult;

            result.Y = a.Y * mult;

        }

        #endregion

        #endregion

        #region Add

        /// <summary>

        /// Adds two vectors.

        /// </summary>

        /// <param name="a">Left operand.</param>

        /// <param name="b">Right operand.</param>

        /// <returns>Result of operation.</returns>

        public static Vector2d Add(Vector2d a, Vector2d b)

        {

            Add(ref a, ref b, out a);

            return a;

        }

        /// <summary>

        /// Adds two vectors.

        /// </summary>

        /// <param name="a">Left operand.</param>

        /// <param name="b">Right operand.</param>

        /// <param name="result">Result of operation.</param>

        public static void Add(ref Vector2d a, ref Vector2d b, out Vector2d result)

        {

            result = new Vector2d(a.X + b.X, a.Y + b.Y);

        }

        #endregion

        #region Subtract

        /// <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 Vector2d Subtract(Vector2d a, Vector2d b)

        {

            Subtract(ref a, ref b, out a);

            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 Subtract(ref Vector2d a, ref Vector2d b, out Vector2d result)

        {

            result = new Vector2d(a.X - b.X, a.Y - b.Y);

        }

        #endregion

        #region Multiply

        /// <summary>

        /// Multiplies a vector by a scalar.

        /// </summary>

        /// <param name="vector">Left operand.</param>

        /// <param name="scale">Right operand.</param>

        /// <returns>Result of the operation.</returns>

        public static Vector2d Multiply(Vector2d vector, double scale)

        {

            Multiply(ref vector, scale, out vector);

            return vector;

        }

        /// <summary>

        /// Multiplies a vector by a scalar.

        /// </summary>

        /// <param name="vector">Left operand.</param>

        /// <param name="scale">Right operand.</param>

        /// <param name="result">Result of the operation.</param>

        public static void Multiply(ref Vector2d vector, double scale, out Vector2d result)

        {

            result = new Vector2d(vector.X * scale, vector.Y * scale);

        }

        /// <summary>

        /// Multiplies a vector by the components a vector (scale).

        /// </summary>

        /// <param name="vector">Left operand.</param>

        /// <param name="scale">Right operand.</param>

        /// <returns>Result of the operation.</returns>

        public static Vector2d Multiply(Vector2d vector, Vector2d scale)

        {

            Multiply(ref vector, ref scale, out vector);

            return vector;

        }

        /// <summary>

        /// Multiplies a vector by the components of a vector (scale).

        /// </summary>

        /// <param name="vector">Left operand.</param>

        /// <param name="scale">Right operand.</param>

        /// <param name="result">Result of the operation.</param>

        public static void Multiply(ref Vector2d vector, ref Vector2d scale, out Vector2d result)

        {

            result = new Vector2d(vector.X * scale.X, vector.Y * scale.Y);

        }

        #endregion

        #region Divide

        /// <summary>

        /// Divides a vector by a scalar.

        /// </summary>

        /// <param name="vector">Left operand.</param>

        /// <param name="scale">Right operand.</param>

        /// <returns>Result of the operation.</returns>

        public static Vector2d Divide(Vector2d vector, double scale)

        {

            Divide(ref vector, scale, out vector);

            return vector;

        }

        /// <summary>

        /// Divides a vector by a scalar.

        /// </summary>

        /// <param name="vector">Left operand.</param>

        /// <param name="scale">Right operand.</param>

        /// <param name="result">Result of the operation.</param>

        public static void Divide(ref Vector2d vector, double scale, out Vector2d result)

        {

            Multiply(ref vector, 1 / scale, out result);

        }

        /// <summary>

        /// Divides a vector by the components of a vector (scale).

        /// </summary>

        /// <param name="vector">Left operand.</param>

        /// <param name="scale">Right operand.</param>

        /// <returns>Result of the operation.</returns>

        public static Vector2d Divide(Vector2d vector, Vector2d scale)

        {

            Divide(ref vector, ref scale, out vector);

            return vector;

        }

        /// <summary>

        /// Divide a vector by the components of a vector (scale).

        /// </summary>

        /// <param name="vector">Left operand.</param>

        /// <param name="scale">Right operand.</param>

        /// <param name="result">Result of the operation.</param>

        public static void Divide(ref Vector2d vector, ref Vector2d scale, out Vector2d result)

        {

            result = new Vector2d(vector.X / scale.X, vector.Y / scale.Y);

        }

        #endregion

        #region Min

        /// <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 Vector2d Min(Vector2d a, Vector2d b)

        {

            a.X = a.X < b.X ? a.X : b.X;

            a.Y = a.Y < b.Y ? a.Y : b.Y;

            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 Min(ref Vector2d a, ref Vector2d b, out Vector2d result)

        {

            result.X = a.X < b.X ? a.X : b.X;

            result.Y = a.Y < b.Y ? a.Y : b.Y;

        }

        #endregion

        #region Max

        /// <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 Vector2d Max(Vector2d a, Vector2d b)

        {

            a.X = a.X > b.X ? a.X : b.X;

            a.Y = a.Y > b.Y ? a.Y : b.Y;

            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 Max(ref Vector2d a, ref Vector2d b, out Vector2d result)

        {

            result.X = a.X > b.X ? a.X : b.X;

            result.Y = a.Y > b.Y ? a.Y : b.Y;

        }

        #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 Vector2d Clamp(Vector2d vec, Vector2d min, Vector2d 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;

            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 Vector2d vec, ref Vector2d min, ref Vector2d max, out Vector2d 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;

        }

        #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 Vector2d Normalize(Vector2d vec)

        {

            double scale = 1.0 / vec.Length;

            vec.X *= scale;

            vec.Y *= 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 Vector2d vec, out Vector2d result)

        {

            double scale = 1.0 / vec.Length;

            result.X = vec.X * scale;

            result.Y = vec.Y * 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 Vector2d NormalizeFast(Vector2d vec)

        {

            double scale = MathHelper.InverseSqrtFast(vec.X * vec.X + vec.Y * vec.Y);

            vec.X *= scale;

            vec.Y *= 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 Vector2d vec, out Vector2d result)

        {

            double scale = MathHelper.InverseSqrtFast(vec.X * vec.X + vec.Y * vec.Y);

            result.X = vec.X * scale;

            result.Y = vec.Y * scale;

        }

        #endregion

        #region Dot

        /// <summary>

        /// Calculate 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 double Dot(Vector2d left, Vector2d right)

        {

            return left.X * right.X + left.Y * right.Y;

        }

        /// <summary>

        /// Calculate the dot (scalar) product of two vectors

        /// </summary>

        /// <param name="left">First operand</param>

        /// <param name="right">Second operand</param>

        /// <param name="result">The dot product of the two inputs</param>

        public static void Dot(ref Vector2d left, ref Vector2d right, out double result)

        {

            result = left.X * right.X + left.Y * right.Y;

        }

        #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. a when blend=0, b when blend=1.</param>

        /// <returns>a when blend=0, b when blend=1, and a linear combination otherwise</returns>

        public static Vector2d Lerp(Vector2d a, Vector2d b, double blend)

        {

            a.X = blend * (b.X - a.X) + a.X;

            a.Y = blend * (b.Y - a.Y) + a.Y;

            return a;

        }

        /// <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. a when blend=0, b when blend=1.</param>

        /// <param name="result">a when blend=0, b when blend=1, and a linear combination otherwise</param>

        public static void Lerp(ref Vector2d a, ref Vector2d b, double blend, out Vector2d result)

        {

            result.X = blend * (b.X - a.X) + a.X;

            result.Y = blend * (b.Y - a.Y) + a.Y;

        }

        #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 Vector2d BaryCentric(Vector2d a, Vector2d b, Vector2d c, double u, double v)

        {

            return a + u * (b - a) + v * (c - a);

        }

        /// <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>

        /// <param name="result">Output Vector. 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</param>

        public static void BaryCentric(ref Vector2d a, ref Vector2d b, ref Vector2d c, double u, double v, out Vector2d result)

        {

            result = a; // copy

            Vector2d temp = b; // copy

            Subtract(ref temp, ref a, out temp);

            Multiply(ref temp, u, out temp);

            Add(ref result, ref temp, out result);

            temp = c; // copy

            Subtract(ref temp, ref a, out temp);

            Multiply(ref temp, v, out temp);

            Add(ref result, ref temp, out result);

        }

        #endregion

        #region Transform

        /// <summary>

        /// Transforms a vector by a quaternion rotation.

        /// </summary>

        /// <param name="vec">The vector to transform.</param>

        /// <param name="quat">The quaternion to rotate the vector by.</param>

        /// <returns>The result of the operation.</returns>

        public static Vector2d Transform(Vector2d vec, Quaterniond quat)

        {

            Vector2d result;

            Transform(ref vec, ref quat, out result);

            return result;

        }

        /// <summary>

        /// Transforms a vector by a quaternion rotation.

        /// </summary>

        /// <param name="vec">The vector to transform.</param>

        /// <param name="quat">The quaternion to rotate the vector by.</param>

        /// <param name="result">The result of the operation.</param>

        public static void Transform(ref Vector2d vec, ref Quaterniond quat, out Vector2d result)

        {

            Quaterniond v = new Quaterniond(vec.X, vec.Y, 0, 0), i, t;

            Quaterniond.Invert(ref quat, out i);

            Quaterniond.Multiply(ref quat, ref v, out t);

            Quaterniond.Multiply(ref t, ref i, out v);

            result = new Vector2d(v.X, v.Y);

        }

        #endregion

        #endregion

        #region Operators

        /// <summary>

        /// Adds two instances.

        /// </summary>

        /// <param name="left">The left instance.</param>

        /// <param name="right">The right instance.</param>

        /// <returns>The result of the operation.</returns>

        public static Vector2d operator +(Vector2d left, Vector2d right)

        {

            left.X += right.X;

            left.Y += right.Y;

            return left;

        }

        /// <summary>

        /// Subtracts two instances.

        /// </summary>

        /// <param name="left">The left instance.</param>

        /// <param name="right">The right instance.</param>

        /// <returns>The result of the operation.</returns>

        public static Vector2d operator -(Vector2d left, Vector2d right)

        {

            left.X -= right.X;

            left.Y -= right.Y;

            return left;

        }

        /// <summary>

        /// Negates an instance.

        /// </summary>

        /// <param name="vec">The instance.</param>

        /// <returns>The result of the operation.</returns>

        public static Vector2d operator -(Vector2d vec)

        {

            vec.X = -vec.X;

            vec.Y = -vec.Y;

            return vec;

        }

        /// <summary>

        /// Multiplies an instance by a scalar.

        /// </summary>

        /// <param name="vec">The instance.</param>

        /// <param name="f">The scalar.</param>