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286 lines
10 KiB
C#
286 lines
10 KiB
C#
#region --- License ---
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/* Licensed under the MIT/X11 license.
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* Copyright (c) 2006-2008 the OpenTK Team.
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* This notice may not be removed from any source distribution.
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* See license.txt for licensing detailed licensing details.
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*
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* Contributions by Andy Gill, James Talton and Georg Wächter.
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*/
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#endregion
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using System;
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using System.Collections.Generic;
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using System.Text;
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namespace OpenTK.Math
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{
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/// <summary>
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/// Contains mathematical functions for the OpenTK.Math toolkit.
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/// </summary>
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public static class Functions
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{
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#region public static long NextPowerOfTwo(long n)
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/// <summary>
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/// Returns the next power of two that is larger than the specified number.
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/// </summary>
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/// <param name="n">The specified number.</param>
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/// <returns>The next power of two.</returns>
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public static long NextPowerOfTwo(long n)
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{
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if (n < 0) throw new ArgumentOutOfRangeException("n", "Must be positive.");
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return (long)System.Math.Pow(2, System.Math.Ceiling(System.Math.Log((double)n, 2)));
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}
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#endregion
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#region public static int NextPowerOfTwo(int n)
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/// <summary>
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/// Returns the next power of two that is larger than the specified number.
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/// </summary>
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/// <param name="n">The specified number.</param>
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/// <returns>The next power of two.</returns>
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public static int NextPowerOfTwo(int n)
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{
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if (n < 0) throw new ArgumentOutOfRangeException("n", "Must be positive.");
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return (int)System.Math.Pow(2, System.Math.Ceiling(System.Math.Log((double)n, 2)));
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}
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#endregion
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/// <summary>
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/// Calculates the factorial of a given natural number.
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/// </summary>
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/// <param name="n">The number.</param>
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/// <returns>n!</returns>
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public static long Factorial(int n)
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{
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long result = 1;
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for (; n > 1; n--)
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result *= n;
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return result;
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}
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/// <summary>
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/// Calculates the binomial coefficient <paramref name="n"/> above <paramref name="k"/>.
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/// </summary>
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/// <param name="n">The n.</param>
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/// <param name="k">The k.</param>
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/// <returns>n! / (k! * (n - k)!)</returns>
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public static long BinomialCoefficient(int n, int k)
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{
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return Factorial(n) / (Factorial(k) * Factorial(n - k));
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}
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/// <summary>
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/// Returns an approximation of the inverse square root of left number.
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/// </summary>
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/// <param name="x">A number.</param>
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/// <returns>An approximation of the inverse square root of the specified number, with an upper error bound of 0.001</returns>
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/// <remarks>
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/// This is an improved implementation of the the method known as Carmack's inverse square root
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/// which is found in the Quake III source code. This implementation comes from
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/// http://www.codemaestro.com/reviews/review00000105.html. For the history of this method, see
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/// http://www.beyond3d.com/content/articles/8/
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/// </remarks>
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public static float InverseSqrtFast(float x)
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{
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unsafe
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{
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float xhalf = 0.5f * x;
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int i = *(int*)&x; // Read bits as integer.
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i = 0x5f375a86 - (i >> 1); // Make an initial guess for Newton-Raphson approximation
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x = *(float*)&i; // Convert bits back to float
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x = x * (1.5f - xhalf * x * x); // Perform left single Newton-Raphson step.
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return x;
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}
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}
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public static double InverseSqrtFast(double x)
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{
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return InverseSqrtFast((float)x);
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// TODO: The following code is wrong. Fix it, to improve precision.
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#if false
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unsafe
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{
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double xhalf = 0.5f * x;
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int i = *(int*)&x; // Read bits as integer.
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i = 0x5f375a86 - (i >> 1); // Make an initial guess for Newton-Raphson approximation
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x = *(float*)&i; // Convert bits back to float
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x = x * (1.5f - xhalf * x * x); // Perform left single Newton-Raphson step.
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return x;
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}
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#endif
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}
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/// <summary>
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/// Convert degrees to radians
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/// </summary>
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/// <param name="degrees">An angle in degrees</param>
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/// <returns>The angle expressed in radians</returns>
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public static float DegreesToRadians(float degrees)
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{
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const float degToRad = (float)System.Math.PI / 180.0f;
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return degrees * degToRad;
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}
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/// <summary>
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/// Convert radians to degrees
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/// </summary>
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/// <param name="degrees">An angle in radians</param>
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/// <returns>The angle expressed in degrees</returns>
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public static float RadiansToDegrees(float radians)
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{
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const float radToDeg = 180.0f / (float)System.Math.PI;
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return radians * radToDeg;
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}
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public static readonly float PIF = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930382f;
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public static readonly float RTODF = 180.0f / PIF;
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public static readonly float DTORF = PIF / 180.0f;
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public static readonly double PI = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930382d;
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public static readonly double RTOD = 180.0d / PIF;
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public static readonly double DTOR = PIF / 180.0d;
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public static void Swap(ref double a, ref double b)
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{
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double temp = a;
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a = b;
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b = temp;
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}
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public static void Swap(ref float a, ref float b)
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{
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float temp = a;
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a = b;
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b = temp;
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}
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}
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#if false
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public static partial class Math
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{
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#region --- Vectors ---
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#region --- Addition ---
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/// <summary>
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/// Adds the given Vector2 to the current Vector3.
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/// </summary>
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/// <param name="right">The right operand of the addition.</param>
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/// <returns>A new Vector3 containing the result of the addition.</returns>
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public static Vector2 Add(Vector2 left, Vector2 right)
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{
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return new Vector2(left).Add(right);
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}
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/// <summary>
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/// Adds the given Vector3 to the current Vector3.
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/// </summary>
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/// <param name="right">The right operand of the addition.</param>
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/// <returns>A new Vector3 containing the result of the addition.</returns>
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public static Vector3 Add(Vector2 left, Vector3 right)
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{
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return new Vector3(left).Add(right);
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}
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/// <summary>
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/// Adds the given Vector4 to the current Vector3. W-coordinate remains unaffected.
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/// </summary>
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/// <param name="right">The right operand of the addition.</param>
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/// <returns>A new Vector4 containing the result of the addition.</returns>
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public static Vector4 Add(Vector2 left, Vector4 right)
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{
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return new Vector4(left).Add(right);
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}
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/// <summary>
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/// Adds the given Vector2 to the current Vector3.
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/// </summary>
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/// <param name="right">The right operand of the addition.</param>
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/// <returns>A new Vector3 containing the result of the addition.</returns>
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public static Vector3 Add(Vector3 left, Vector2 right)
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{
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return new Vector3(left).Add(right);
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}
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/// <summary>
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/// Adds the given Vector3 to the current Vector3.
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/// </summary>
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/// <param name="right">The right operand of the addition.</param>
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/// <returns>A new Vector3 containing the result of the addition.</returns>
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public static Vector3 Add(Vector3 left, Vector3 right)
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{
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return new Vector3(left).Add(right);
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}
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/// <summary>
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/// Adds the given Vector4 to the current Vector3. W-coordinate remains unaffected.
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/// </summary>
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/// <param name="right">The right operand of the addition.</param>
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/// <returns>A new Vector4 containing the result of the addition.</returns>
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public static Vector4 Add(Vector3 left, Vector4 right)
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{
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return new Vector4(left).Add(right);
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}
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/// <summary>
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/// Adds the given Vector2 to the current Vector3.
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/// </summary>
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/// <param name="right">The right operand of the addition.</param>
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/// <returns>A new Vector3 containing the result of the addition.</returns>
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public static Vector4 Add(Vector4 left, Vector2 right)
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{
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return new Vector4(left).Add(right);
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}
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/// <summary>
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/// Adds the given Vector3 to the current Vector3.
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/// </summary>
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/// <param name="right">The right operand of the addition.</param>
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/// <returns>A new Vector3 containing the result of the addition.</returns>
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public static Vector4 Add(Vector4 left, Vector3 right)
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{
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return new Vector4(left).Add(right);
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}
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/// <summary>
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/// Adds the given Vector4 to the current Vector3. W-coordinate remains unaffected.
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/// </summary>
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/// <param name="right">The right operand of the addition.</param>
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/// <returns>A new Vector4 containing the result of the addition.</returns>
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public static Vector4 Add(Vector4 left, Vector4 right)
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{
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return new Vector4(left).Add(right);
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}
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#endregion
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#region --- Subtraction ---
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#endregion
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#region --- Cross ---
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/// <summary>
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/// Computes the cross product between the current and the given Vector3. The current Vector3 is set to the result of the computation.
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/// </summary>
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/// <param name="right">The right operand of the cross product</param>
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/// <returns>The current </returns>
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public static Vector3 Cross(Vector3 left, Vector3 right)
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{
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return new Vector3(left).Cross(right);
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}
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#endregion
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#endregion
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}
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#endif
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}
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