863 lines
26 KiB
C#
863 lines
26 KiB
C#
#region --- License ---
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/*
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Copyright (c) 2006 - 2008 The Open Toolkit library.
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Permission is hereby granted, free of charge, to any person obtaining a copy of
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this software and associated documentation files (the "Software"), to deal in
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the Software without restriction, including without limitation the rights to
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use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
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of the Software, and to permit persons to whom the Software is furnished to do
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so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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#endregion
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using System;
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using System.Runtime.InteropServices;
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namespace OpenTK.Math
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{
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/// <summary>Represents a 2D vector using two single-precision floating-point numbers.</summary>
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/// <remarks>
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/// The Vector2 structure is suitable for interoperation with unmanaged code requiring two consecutive floats.
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/// </remarks>
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[Serializable]
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[StructLayout(LayoutKind.Sequential)]
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public struct Vector2 : IEquatable<Vector2>
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{
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#region Fields
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/// <summary>
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/// The X component of the Vector2.
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/// </summary>
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public float X;
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/// <summary>
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/// The Y component of the Vector2.
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/// </summary>
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public float Y;
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#endregion
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#region Constructors
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/// <summary>
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/// Constructs a new Vector2.
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/// </summary>
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/// <param name="x">The x coordinate of the net Vector2.</param>
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/// <param name="y">The y coordinate of the net Vector2.</param>
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public Vector2(float x, float y)
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{
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X = x;
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Y = y;
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}
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/// <summary>
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/// Constructs a new Vector2 from the given Vector2.
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/// </summary>
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/// <param name="v">The Vector2 to copy components from.</param>
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[Obsolete]
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public Vector2(Vector2 v)
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{
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X = v.X;
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Y = v.Y;
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}
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/// <summary>
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/// Constructs a new Vector2 from the given Vector3.
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/// </summary>
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/// <param name="v">The Vector3 to copy components from. Z is discarded.</param>
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[Obsolete]
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public Vector2(Vector3 v)
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{
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X = v.X;
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Y = v.Y;
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}
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/// <summary>
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/// Constructs a new Vector2 from the given Vector4.
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/// </summary>
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/// <param name="v">The Vector4 to copy components from. Z and W are discarded.</param>
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[Obsolete]
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public Vector2(Vector4 v)
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{
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X = v.X;
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Y = v.Y;
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}
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#endregion
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#region Public Members
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#region Instance
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#region public void Add()
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/// <summary>Add the Vector passed as parameter to this instance.</summary>
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/// <param name="right">Right operand. This parameter is only read from.</param>
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public void Add( Vector2 right )
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{
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this.X += right.X;
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this.Y += right.Y;
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}
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/// <summary>Add the Vector passed as parameter to this instance.</summary>
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/// <param name="right">Right operand. This parameter is only read from.</param>
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[CLSCompliant(false)]
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public void Add( ref Vector2 right )
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{
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this.X += right.X;
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this.Y += right.Y;
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}
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#endregion public void Add()
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#region public void Sub()
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/// <summary>Subtract the Vector passed as parameter from this instance.</summary>
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/// <param name="right">Right operand. This parameter is only read from.</param>
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public void Sub( Vector2 right )
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{
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this.X -= right.X;
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this.Y -= right.Y;
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}
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/// <summary>Subtract the Vector passed as parameter from this instance.</summary>
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/// <param name="right">Right operand. This parameter is only read from.</param>
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[CLSCompliant(false)]
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public void Sub( ref Vector2 right )
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{
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this.X -= right.X;
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this.Y -= right.Y;
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}
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#endregion public void Sub()
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#region public void Mult()
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/// <summary>Multiply this instance by a scalar.</summary>
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/// <param name="f">Scalar operand.</param>
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public void Mult( float f )
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{
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this.X *= f;
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this.Y *= f;
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}
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#endregion public void Mult()
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#region public void Div()
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/// <summary>Divide this instance by a scalar.</summary>
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/// <param name="f">Scalar operand.</param>
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public void Div( float f )
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{
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float mult = 1.0f / f;
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this.X *= mult;
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this.Y *= mult;
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}
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#endregion public void Div()
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#region public float Length
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/// <summary>
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/// Gets the length (magnitude) of the vector.
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/// </summary>
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/// <see cref="FastLength"/>
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/// <seealso cref="LengthSquared"/>
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public float Length
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{
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get
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{
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return (float)System.Math.Sqrt(X * X + Y * Y);
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}
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}
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#endregion
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#region public float LengthFast
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/// <summary>
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/// Gets an approximation of the vector length (magnitude).
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/// </summary>
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/// <remarks>
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/// This property uses an approximation of the square root function to calculate vector magnitude, with
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/// an upper error bound of 0.001.
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/// </remarks>
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/// <see cref="Length"/>
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/// <seealso cref="LengthSquared"/>
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/// <seealso cref="OpenTK.Math.FastSqrt"/>
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public float LengthFast
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{
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get
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{
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return 1.0f / OpenTK.Math.Functions.InverseSqrtFast(X * X + Y * Y);
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}
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}
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#endregion
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#region public float LengthSquared
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/// <summary>
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/// Gets the square of the vector length (magnitude).
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/// </summary>
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/// <remarks>
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/// This property avoids the costly square root operation required by the Length property. This makes it more suitable
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/// for comparisons.
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/// </remarks>
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/// <see cref="Length"/>
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/// <seealso cref="FastLength"/>
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public float LengthSquared
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{
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get
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{
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return X * X + Y * Y;
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}
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}
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#endregion
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#region public Vector2 PerpendicularRight
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/// <summary>
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/// Gets the perpendicular vector on the right side of this vector.
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/// </summary>
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public Vector2 PerpendicularRight
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{
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get
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{
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return new Vector2(Y, -X);
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}
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}
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#endregion
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#region public Vector2 PerpendicularLeft
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/// <summary>
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/// Gets the perpendicular vector on the left side of this vector.
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/// </summary>
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public Vector2 PerpendicularLeft
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{
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get
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{
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return new Vector2(-Y, X);
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}
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}
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#endregion
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#region public void Normalize()
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/// <summary>
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/// Scales the Vector2 to unit length.
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/// </summary>
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public void Normalize()
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{
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float scale = 1.0f / this.Length;
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X *= scale;
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Y *= scale;
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}
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#endregion
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#region public void NormalizeFast()
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/// <summary>
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/// Scales the Vector2 to approximately unit length.
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/// </summary>
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public void NormalizeFast()
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{
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float scale = Functions.InverseSqrtFast(X * X + Y * Y);
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X *= scale;
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Y *= scale;
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}
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#endregion
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#region public void Scale()
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/// <summary>
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/// Scales the current Vector2 by the given amounts.
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/// </summary>
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/// <param name="sx">The scale of the X component.</param>
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/// <param name="sy">The scale of the Y component.</param>
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public void Scale(float sx, float sy)
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{
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this.X = X * sx;
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this.Y = Y * sy;
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}
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/// <summary>Scales this instance by the given parameter.</summary>
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/// <param name="scale">The scaling of the individual components.</param>
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public void Scale( Vector2 scale )
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{
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this.X *= scale.X;
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this.Y *= scale.Y;
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}
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/// <summary>Scales this instance by the given parameter.</summary>
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/// <param name="scale">The scaling of the individual components.</param>
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[CLSCompliant(false)]
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public void Scale( ref Vector2 scale )
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{
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this.X *= scale.X;
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this.Y *= scale.Y;
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}
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#endregion public void Scale()
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#endregion
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#region Static
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#region Fields
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/// <summary>
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/// Defines a unit-length Vector2 that points towards the X-axis.
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/// </summary>
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public static readonly Vector2 UnitX = new Vector2(1, 0);
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/// <summary>
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/// Defines a unit-length Vector2 that points towards the Y-axis.
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/// </summary>
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public static readonly Vector2 UnitY = new Vector2(0, 1);
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/// <summary>
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/// Defines a zero-length Vector2.
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/// </summary>
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public static readonly Vector2 Zero = new Vector2(0, 0);
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/// <summary>
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/// Defines the size of the Vector2 struct in bytes.
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/// </summary>
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public static readonly int SizeInBytes = Marshal.SizeOf(new Vector2());
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#endregion
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#region Add
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/// <summary>
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/// Add two Vectors
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <returns>Result of addition</returns>
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public static Vector2 Add(Vector2 a, Vector2 b)
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{
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a.X += b.X;
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a.Y += b.Y;
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return a;
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}
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/// <summary>
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/// Add two Vectors
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <param name="result">Result of addition</param>
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public static void Add(ref Vector2 a, ref Vector2 b, out Vector2 result)
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{
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result.X = a.X + b.X;
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result.Y = a.Y + b.Y;
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}
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#endregion
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#region Sub
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/// <summary>
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/// Subtract one Vector from another
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <returns>Result of subtraction</returns>
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public static Vector2 Sub(Vector2 a, Vector2 b)
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{
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a.X -= b.X;
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a.Y -= b.Y;
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return a;
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}
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/// <summary>
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/// Subtract one Vector from another
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <param name="result">Result of subtraction</param>
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public static void Sub(ref Vector2 a, ref Vector2 b, out Vector2 result)
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{
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result.X = a.X - b.X;
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result.Y = a.Y - b.Y;
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}
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#endregion
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#region Mult
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/// <summary>
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/// Multiply a vector and a scalar
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/// </summary>
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/// <param name="a">Vector operand</param>
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/// <param name="f">Scalar operand</param>
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/// <returns>Result of the multiplication</returns>
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public static Vector2 Mult(Vector2 a, float f)
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{
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a.X *= f;
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a.Y *= f;
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return a;
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}
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/// <summary>
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/// Multiply a vector and a scalar
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/// </summary>
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/// <param name="a">Vector operand</param>
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/// <param name="f">Scalar operand</param>
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/// <param name="result">Result of the multiplication</param>
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public static void Mult(ref Vector2 a, float f, out Vector2 result)
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{
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result.X = a.X * f;
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result.Y = a.Y * f;
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}
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#endregion
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#region Div
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/// <summary>
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/// Divide a vector by a scalar
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/// </summary>
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/// <param name="a">Vector operand</param>
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/// <param name="f">Scalar operand</param>
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/// <returns>Result of the division</returns>
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public static Vector2 Div(Vector2 a, float f)
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{
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float mult = 1.0f / f;
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a.X *= mult;
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a.Y *= mult;
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return a;
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}
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/// <summary>
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/// Divide a vector by a scalar
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/// </summary>
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/// <param name="a">Vector operand</param>
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/// <param name="f">Scalar operand</param>
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/// <param name="result">Result of the division</param>
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public static void Div(ref Vector2 a, float f, out Vector2 result)
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{
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float mult = 1.0f / f;
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result.X = a.X * mult;
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result.Y = a.Y * mult;
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}
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#endregion
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#region ComponentMin
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/// <summary>
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/// Calculate the component-wise minimum of two vectors
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <returns>The component-wise minimum</returns>
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public static Vector2 ComponentMin(Vector2 a, Vector2 b)
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{
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a.X = a.X < b.X ? a.X : b.X;
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a.Y = a.Y < b.Y ? a.Y : b.Y;
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return a;
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}
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/// <summary>
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/// Calculate the component-wise minimum of two vectors
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <param name="result">The component-wise minimum</param>
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public static void ComponentMin(ref Vector2 a, ref Vector2 b, out Vector2 result)
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{
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result.X = a.X < b.X ? a.X : b.X;
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result.Y = a.Y < b.Y ? a.Y : b.Y;
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}
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#endregion
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#region ComponentMax
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/// <summary>
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/// Calculate the component-wise maximum of two vectors
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <returns>The component-wise maximum</returns>
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public static Vector2 ComponentMax(Vector2 a, Vector2 b)
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{
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a.X = a.X > b.X ? a.X : b.X;
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a.Y = a.Y > b.Y ? a.Y : b.Y;
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return a;
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}
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/// <summary>
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/// Calculate the component-wise maximum of two vectors
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <param name="result">The component-wise maximum</param>
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public static void ComponentMax(ref Vector2 a, ref Vector2 b, out Vector2 result)
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{
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result.X = a.X > b.X ? a.X : b.X;
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result.Y = a.Y > b.Y ? a.Y : b.Y;
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}
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#endregion
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#region Min
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/// <summary>
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/// Returns the Vector3 with the minimum magnitude
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/// </summary>
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/// <param name="left">Left operand</param>
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/// <param name="right">Right operand</param>
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/// <returns>The minimum Vector3</returns>
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public static Vector2 Min(Vector2 left, Vector2 right)
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{
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return left.LengthSquared < right.LengthSquared ? left : right;
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}
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#endregion
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#region Max
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/// <summary>
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/// Returns the Vector3 with the minimum magnitude
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/// </summary>
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/// <param name="left">Left operand</param>
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/// <param name="right">Right operand</param>
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/// <returns>The minimum Vector3</returns>
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public static Vector2 Max(Vector2 left, Vector2 right)
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{
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return left.LengthSquared >= right.LengthSquared ? left : right;
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}
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#endregion
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#region Clamp
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/// <summary>
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/// Clamp a vector to the given minimum and maximum vectors
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/// </summary>
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/// <param name="vec">Input vector</param>
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/// <param name="min">Minimum vector</param>
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/// <param name="max">Maximum vector</param>
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/// <returns>The clamped vector</returns>
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public static Vector2 Clamp(Vector2 vec, Vector2 min, Vector2 max)
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{
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vec.X = vec.X < min.X ? min.X : vec.X > max.X ? max.X : vec.X;
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vec.Y = vec.Y < min.Y ? min.Y : vec.Y > max.Y ? max.Y : vec.Y;
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return vec;
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}
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/// <summary>
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/// Clamp a vector to the given minimum and maximum vectors
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/// </summary>
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/// <param name="vec">Input vector</param>
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/// <param name="min">Minimum vector</param>
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/// <param name="max">Maximum vector</param>
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/// <param name="result">The clamped vector</param>
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public static void Clamp(ref Vector2 vec, ref Vector2 min, ref Vector2 max, out Vector2 result)
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{
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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 Vector2 Normalize(Vector2 vec)
|
|
{
|
|
float scale = 1.0f / 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 Vector2 vec, out Vector2 result)
|
|
{
|
|
float scale = 1.0f / 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 Vector2 NormalizeFast(Vector2 vec)
|
|
{
|
|
float scale = Functions.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 Vector2 vec, out Vector2 result)
|
|
{
|
|
float scale = Functions.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 float Dot(Vector2 left, Vector2 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 Vector2 left, ref Vector2 right, out float 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 Vector2 Lerp(Vector2 a, Vector2 b, float 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 Vector2 a, ref Vector2 b, float blend, out Vector2 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 Vector2 BaryCentric(Vector2 a, Vector2 b, Vector2 c, float u, float 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 Vector2 a, ref Vector2 b, ref Vector2 c, float u, float v, out Vector2 result )
|
|
{
|
|
result = a; // copy
|
|
|
|
Vector2 temp = b; // copy
|
|
temp.Sub( ref a );
|
|
temp.Mult( u );
|
|
result.Add( ref temp );
|
|
|
|
temp = c; // copy
|
|
temp.Sub( ref a );
|
|
temp.Mult( v );
|
|
result.Add( ref temp );
|
|
}
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#region Operators
|
|
|
|
public static Vector2 operator +(Vector2 left, Vector2 right)
|
|
{
|
|
left.X += right.X;
|
|
left.Y += right.Y;
|
|
return left;
|
|
}
|
|
|
|
public static Vector2 operator -(Vector2 left, Vector2 right)
|
|
{
|
|
left.X -= right.X;
|
|
left.Y -= right.Y;
|
|
return left;
|
|
}
|
|
|
|
public static Vector2 operator -(Vector2 vec)
|
|
{
|
|
vec.X = -vec.X;
|
|
vec.Y = -vec.Y;
|
|
return vec;
|
|
}
|
|
|
|
public static Vector2 operator *(Vector2 vec, float f)
|
|
{
|
|
vec.X *= f;
|
|
vec.Y *= f;
|
|
return vec;
|
|
}
|
|
|
|
public static Vector2 operator *(float f, Vector2 vec)
|
|
{
|
|
vec.X *= f;
|
|
vec.Y *= f;
|
|
return vec;
|
|
}
|
|
|
|
public static Vector2 operator /(Vector2 vec, float f)
|
|
{
|
|
float mult = 1.0f / f;
|
|
vec.X *= mult;
|
|
vec.Y *= mult;
|
|
return vec;
|
|
}
|
|
|
|
public static bool operator ==(Vector2 left, Vector2 right)
|
|
{
|
|
return left.Equals(right);
|
|
}
|
|
|
|
public static bool operator !=(Vector2 left, Vector2 right)
|
|
{
|
|
return !left.Equals(right);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Overrides
|
|
|
|
#region public override string ToString()
|
|
|
|
/// <summary>
|
|
/// Returns a System.String that represents the current Vector2.
|
|
/// </summary>
|
|
/// <returns></returns>
|
|
public override string ToString()
|
|
{
|
|
return String.Format("({0}, {1})", X, Y);
|
|
}
|
|
|
|
#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();
|
|
}
|
|
|
|
#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 Vector2))
|
|
return false;
|
|
|
|
return this.Equals((Vector2)obj);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#region IEquatable<Vector2> 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(Vector2 other)
|
|
{
|
|
return
|
|
X == other.X &&
|
|
Y == other.Y;
|
|
}
|
|
|
|
#endregion
|
|
}
|
|
}
|