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