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813 lines
25 KiB
C#
813 lines
25 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 4D vector using four double-precision floating-point numbers.</summary>
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[Serializable]
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[StructLayout(LayoutKind.Sequential)]
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public struct Vector4d : IEquatable<Vector4d>
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{
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#region Fields
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/// <summary>
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/// The X component of the Vector4d.
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/// </summary>
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public double X;
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/// <summary>
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/// The Y component of the Vector4d.
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/// </summary>
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public double Y;
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/// <summary>
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/// The Z component of the Vector4d.
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/// </summary>
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public double Z;
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/// <summary>
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/// The Z component of the Vector4d.
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/// </summary>
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public double W;
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/// <summary>
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/// Defines a unit-length Vector4d that points towards the X-axis.
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/// </summary>
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public static Vector4d UnitX = new Vector4d(1, 0, 0, 0);
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/// <summary>
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/// Defines a unit-length Vector4d that points towards the Y-axis.
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/// </summary>
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public static Vector4d UnitY = new Vector4d(0, 1, 0, 0);
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/// <summary>
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/// Defines a unit-length Vector4d that points towards the Z-axis.
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/// </summary>
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public static Vector4d UnitZ = new Vector4d(0, 0, 1, 0);
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/// <summary>
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/// Defines a unit-length Vector4d that points towards the W-axis.
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/// </summary>
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public static Vector4d UnitW = new Vector4d(0, 0, 0, 1);
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/// <summary>
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/// Defines a zero-length Vector4d.
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/// </summary>
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public static Vector4d Zero = new Vector4d(0, 0, 0, 0);
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/// <summary>
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/// Defines the size of the Vector4d struct in bytes.
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/// </summary>
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public static readonly int SizeInBytes = Marshal.SizeOf(new Vector4d());
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#endregion
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#region Constructors
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/// <summary>
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/// Constructs a new Vector4d.
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/// </summary>
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/// <param name="x">The x component of the Vector4d.</param>
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/// <param name="y">The y component of the Vector4d.</param>
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/// <param name="z">The z component of the Vector4d.</param>
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/// <param name="w">The z component of the Vector4d.</param>
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public Vector4d(double x, double y, double z, double w)
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{
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X = x;
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Y = y;
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Z = z;
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W = w;
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}
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/// <summary>
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/// Constructs a new Vector4d 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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public Vector4d(Vector2 v)
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{
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X = v.X;
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Y = v.Y;
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Z = 0.0f;
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W = 0.0f;
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}
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/// <summary>
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/// Constructs a new Vector4d from the given Vector3.
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/// </summary>
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/// <param name="v">The Vector3 to copy components from.</param>
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public Vector4d(Vector3 v)
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{
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X = v.X;
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Y = v.Y;
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Z = v.Z;
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W = 0.0f;
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}
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/// <summary>
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/// Constructs a new Vector4d from the given Vector4d.
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/// </summary>
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/// <param name="v">The Vector4d to copy components from.</param>
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public Vector4d(Vector4d v)
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{
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X = v.X;
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Y = v.Y;
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Z = v.Z;
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W = v.W;
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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 double 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 double Length
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{
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get
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{
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return (double)System.Math.Sqrt(X * X + Y * Y + Z * Z + W * W);
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}
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}
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#endregion
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#region public double 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 double 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 + Z * Z + W * W);
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}
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}
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#endregion
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#region public double 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 double LengthSquared
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{
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get
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{
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return X * X + Y * Y + Z * Z + W * W;
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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 Vector4d to unit length.
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/// </summary>
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public void Normalize()
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{
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double scale = 1.0f / this.Length;
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X *= scale;
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Y *= scale;
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Z *= scale;
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W *= 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 Vector4d to approximately unit length.
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/// </summary>
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public void NormalizeFast()
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{
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double scale = Functions.InverseSqrtFast(X * X + Y * Y + Z * Z + W * W);
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X *= scale;
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Y *= scale;
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Z *= scale;
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W *= scale;
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}
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#endregion
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#region public void Scale(double sx, double sy, double sz, double sw)
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/// <summary>
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/// Scales the current Vector4d 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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/// <param name="sz">The scale of the Z component.</param>
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/// <param name="sw">The scale of the Z component.</param>
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public void Scale(double sx, double sy, double sz, double sw)
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{
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this.X = X * sx;
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this.Y = Y * sy;
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this.Z = Z * sz;
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this.W = W * sw;
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}
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#endregion
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#endregion
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#region Static
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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 Vector4d Add(Vector4d a, Vector4d 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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a.Z += b.Z;
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a.W += b.W;
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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 Vector4d a, ref Vector4d b, out Vector4d 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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result.Z = a.Z + b.Z;
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result.W = a.W + b.W;
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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 Vector4d Sub(Vector4d a, Vector4d 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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a.Z -= b.Z;
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a.W -= b.W;
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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 Vector4d a, ref Vector4d b, out Vector4d 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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result.Z = a.Z - b.Z;
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result.W = a.W - b.W;
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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 Vector4d Mult(Vector4d a, double f)
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{
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a.X *= f;
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a.Y *= f;
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a.Z *= f;
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a.W *= 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 Vector4d a, double f, out Vector4d 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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result.Z = a.Z * f;
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result.W = a.W * 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 Vector4d Div(Vector4d a, double f)
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{
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double mult = 1.0f / f;
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a.X *= mult;
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a.Y *= mult;
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a.Z *= mult;
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a.W *= 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 Vector4d a, double f, out Vector4d result)
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{
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double 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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result.Z = a.Z * mult;
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result.W = a.W * mult;
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}
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#endregion
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#region Min
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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 Vector4d Min(Vector4d a, Vector4d 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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a.Z = a.Z < b.Z ? a.Z : b.Z;
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a.W = a.W < b.W ? a.W : b.W;
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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 Min(ref Vector4d a, ref Vector4d b, out Vector4d 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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result.Z = a.Z < b.Z ? a.Z : b.Z;
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result.W = a.W < b.W ? a.W : b.W;
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}
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#endregion
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#region Max
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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 Vector4d Max(Vector4d a, Vector4d 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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a.Z = a.Z > b.Z ? a.Z : b.Z;
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a.W = a.W > b.W ? a.W : b.W;
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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 Max(ref Vector4d a, ref Vector4d b, out Vector4d 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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result.Z = a.Z > b.Z ? a.Z : b.Z;
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result.W = a.W > b.W ? a.W : b.W;
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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 Vector4d Clamp(Vector4d vec, Vector4d min, Vector4d 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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vec.Z = vec.X < min.Z ? min.Z : vec.Z > max.Z ? max.Z : vec.Z;
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vec.W = vec.Y < min.W ? min.W : vec.W > max.W ? max.W : vec.W;
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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 Vector4d vec, ref Vector4d min, ref Vector4d max, out Vector4d 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;
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result.Y = vec.Y < min.Y ? min.Y : vec.Y > max.Y ? max.Y : vec.Y;
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result.Z = vec.X < min.Z ? min.Z : vec.Z > max.Z ? max.Z : vec.Z;
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result.W = vec.Y < min.W ? min.W : vec.W > max.W ? max.W : vec.W;
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}
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#endregion
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#region Normalize
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/// <summary>
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/// Scale a vector to unit length
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/// </summary>
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/// <param name="vec">The input vector</param>
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/// <returns>The normalized vector</returns>
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public static Vector4d Normalize(Vector4d vec)
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{
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double scale = 1.0f / vec.Length;
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vec.X *= scale;
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vec.Y *= scale;
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vec.Z *= scale;
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vec.W *= scale;
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return vec;
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}
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/// <summary>
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/// Scale a vector to unit length
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/// </summary>
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/// <param name="vec">The input vector</param>
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/// <param name="result">The normalized vector</param>
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public static void Normalize(ref Vector4d vec, out Vector4d result)
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{
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double scale = 1.0f / vec.Length;
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result.X = vec.X * scale;
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result.Y = vec.Y * scale;
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result.Z = vec.Z * scale;
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result.W = vec.W * scale;
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}
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#endregion
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#region NormalizeFast
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/// <summary>
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/// Scale a vector to approximately unit length
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/// </summary>
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/// <param name="vec">The input vector</param>
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/// <returns>The normalized vector</returns>
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public static Vector4d NormalizeFast(Vector4d vec)
|
|
{
|
|
double scale = Functions.InverseSqrtFast(vec.X * vec.X + vec.Y * vec.Y + vec.Z * vec.Z + vec.W * vec.W);
|
|
vec.X *= scale;
|
|
vec.Y *= scale;
|
|
vec.Z *= scale;
|
|
vec.W *= 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 Vector4d vec, out Vector4d result)
|
|
{
|
|
double scale = Functions.InverseSqrtFast(vec.X * vec.X + vec.Y * vec.Y + vec.Z * vec.Z + vec.W * vec.W);
|
|
result.X = vec.X * scale;
|
|
result.Y = vec.Y * scale;
|
|
result.Z = vec.Z * scale;
|
|
result.W = vec.W * scale;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Dot
|
|
|
|
/// <summary>
|
|
/// Calculate the dot 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(Vector4d left, Vector4d right)
|
|
{
|
|
return left.X * right.X + left.Y * right.Y + left.Z * right.Z + left.W * right.W;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculate the dot 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 Vector4d left, ref Vector4d right, out double result )
|
|
{
|
|
result = left.X * right.X + left.Y * right.Y + left.Z * right.Z + left.W * right.W;
|
|
}
|
|
|
|
#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 Vector4d Lerp(Vector4d a, Vector4d b, double 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;
|
|
a.W = blend * (b.W - a.W) + a.W;
|
|
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 Vector4d a, ref Vector4d b, double blend, out Vector4d result )
|
|
{
|
|
result.X = blend * ( b.X - a.X ) + a.X;
|
|
result.Y = blend * ( b.Y - a.Y ) + a.Y;
|
|
result.Z = blend * ( b.Z - a.Z ) + a.Z;
|
|
result.W = blend * ( b.W - a.W ) + a.W;
|
|
}
|
|
|
|
#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 Vector4d BaryCentric(Vector4d a, Vector4d b, Vector4d c, double u, double v)
|
|
{
|
|
return a + u * (b - a) + v * (c - a);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Transform
|
|
|
|
/// <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 Vector4d Transform(Vector4d vec, Matrix4d mat)
|
|
{
|
|
Vector4d result;
|
|
result.X = Vector4d.Dot(vec, mat.Column0);
|
|
result.Y = Vector4d.Dot(vec, mat.Column1);
|
|
result.Z = Vector4d.Dot(vec, mat.Column2);
|
|
result.W = Vector4d.Dot(vec, mat.Column3);
|
|
return result;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#region Operators
|
|
|
|
public static Vector4d operator +(Vector4d left, Vector4d right)
|
|
{
|
|
left.X += right.X;
|
|
left.Y += right.Y;
|
|
left.Z += right.Z;
|
|
left.W += right.W;
|
|
return left;
|
|
}
|
|
|
|
public static Vector4d operator -(Vector4d left, Vector4d right)
|
|
{
|
|
left.X -= right.X;
|
|
left.Y -= right.Y;
|
|
left.Z -= right.Z;
|
|
left.W -= right.W;
|
|
return left;
|
|
}
|
|
|
|
public static Vector4d operator -(Vector4d vec)
|
|
{
|
|
vec.X = -vec.X;
|
|
vec.Y = -vec.Y;
|
|
vec.Z = -vec.Z;
|
|
vec.W = -vec.W;
|
|
return vec;
|
|
}
|
|
|
|
public static Vector4d operator *(Vector4d vec, double f)
|
|
{
|
|
vec.X *= f;
|
|
vec.Y *= f;
|
|
vec.Z *= f;
|
|
vec.W *= f;
|
|
return vec;
|
|
}
|
|
|
|
public static Vector4d operator *(double f, Vector4d vec)
|
|
{
|
|
vec.X *= f;
|
|
vec.Y *= f;
|
|
vec.Z *= f;
|
|
vec.W *= f;
|
|
return vec;
|
|
}
|
|
|
|
public static Vector4d operator /(Vector4d vec, double f)
|
|
{
|
|
double mult = 1.0f / f;
|
|
vec.X *= mult;
|
|
vec.Y *= mult;
|
|
vec.Z *= mult;
|
|
vec.W *= mult;
|
|
return vec;
|
|
}
|
|
|
|
public static bool operator ==(Vector4d left, Vector4d right)
|
|
{
|
|
return left.Equals(right);
|
|
}
|
|
|
|
public static bool operator !=(Vector4d left, Vector4d right)
|
|
{
|
|
return !left.Equals(right);
|
|
}
|
|
|
|
[CLSCompliant(false)]
|
|
unsafe public static explicit operator double*(Vector4d v)
|
|
{
|
|
return &v.X;
|
|
}
|
|
|
|
public static explicit operator IntPtr(Vector4d v)
|
|
{
|
|
unsafe
|
|
{
|
|
return (IntPtr)(&v.X);
|
|
}
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Overrides
|
|
|
|
#region public override string ToString()
|
|
|
|
/// <summary>
|
|
/// Returns a System.String that represents the current Vector4d.
|
|
/// </summary>
|
|
/// <returns></returns>
|
|
public override string ToString()
|
|
{
|
|
return String.Format("({0}, {1}, {2}, {3})", X, Y, Z, W);
|
|
}
|
|
|
|
#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() ^ W.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 Vector4d))
|
|
return false;
|
|
|
|
return this.Equals((Vector4d)obj);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#region IEquatable<Vector4d> 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(Vector4d other)
|
|
{
|
|
return
|
|
X == other.X &&
|
|
Y == other.Y &&
|
|
Z == other.Z &&
|
|
W == other.W;
|
|
}
|
|
|
|
#endregion
|
|
}
|
|
} |