// MIT License - Copyright (C) The Mono.Xna Team
// This file is subject to the terms and conditions defined in
// file 'LICENSE.txt', which is part of this source code package.
using System;
namespace CommonLang.Geometry
{
/// <summary>
/// Contains commonly used precalculated values and mathematical operations.
/// </summary>
public static class MathHelper
{
/// <summary>
/// Represents the mathematical constant e(2.71828175).
/// </summary>
public const float E = (float)Math.E;
/// <summary>
/// Represents the log base ten of e(0.4342945).
/// </summary>
public const float Log10E = 0.4342945f;
/// <summary>
/// Represents the log base two of e(1.442695).
/// </summary>
public const float Log2E = 1.442695f;
/// <summary>
/// Represents the value of pi(3.14159274).
/// </summary>
public const float Pi = (float)Math.PI;
/// <summary>
/// Represents the value of pi divided by two(1.57079637).
/// </summary>
public const float PiOver2 = (float)(Math.PI / 2.0);
/// <summary>
/// Represents the value of pi divided by four(0.7853982).
/// </summary>
public const float PiOver4 = (float)(Math.PI / 4.0);
/// <summary>
/// Represents the value of pi times two(6.28318548).
/// </summary>
public const float TwoPi = (float)(Math.PI * 2.0);
/// <summary>
/// Returns the Cartesian coordinate for one axis of a point that is defined by a given triangle and two normalized barycentric (areal) coordinates.
/// </summary>
/// <param name="value1">The coordinate on one axis of vertex 1 of the defining triangle.</param>
/// <param name="value2">The coordinate on the same axis of vertex 2 of the defining triangle.</param>
/// <param name="value3">The coordinate on the same axis of vertex 3 of the defining triangle.</param>
/// <param name="amount1">The normalized barycentric (areal) coordinate b2, equal to the weighting factor for vertex 2, the coordinate of which is specified in value2.</param>
/// <param name="amount2">The normalized barycentric (areal) coordinate b3, equal to the weighting factor for vertex 3, the coordinate of which is specified in value3.</param>
/// <returns>Cartesian coordinate of the specified point with respect to the axis being used.</returns>
public static float Barycentric(float value1, float value2, float value3, float amount1, float amount2)
{
return value1 + (value2 - value1) * amount1 + (value3 - value1) * amount2;
}
/// <summary>
/// Performs a Catmull-Rom interpolation using the specified positions.
/// </summary>
/// <param name="value1">The first position in the interpolation.</param>
/// <param name="value2">The second position in the interpolation.</param>
/// <param name="value3">The third position in the interpolation.</param>
/// <param name="value4">The fourth position in the interpolation.</param>
/// <param name="amount">Weighting factor.</param>
/// <returns>A position that is the result of the Catmull-Rom interpolation.</returns>
public static float CatmullRom(float value1, float value2, float value3, float value4, float amount)
{
// Using formula from http://www.mvps.org/directx/articles/catmull/
// Internally using doubles not to lose precission
double amountSquared = amount * amount;
double amountCubed = amountSquared * amount;
return (float)(0.5 * (2.0 * value2 +
(value3 - value1) * amount +
(2.0 * value1 - 5.0 * value2 + 4.0 * value3 - value4) * amountSquared +
(3.0 * value2 - value1 - 3.0 * value3 + value4) * amountCubed));
}
/// <summary>
/// Restricts a value to be within a specified range.
/// </summary>
/// <param name="value">The value to clamp.</param>
/// <param name="min">The minimum value. If <c>value</c> is less than <c>min</c>, <c>min</c> will be returned.</param>
/// <param name="max">The maximum value. If <c>value</c> is greater than <c>max</c>, <c>max</c> will be returned.</param>
/// <returns>The clamped value.</returns>
public static float Clamp(float value, float min, float max)
{
// First we check to see if we're greater than the max
value = (value > max) ? max : value;
// Then we check to see if we're less than the min.
value = (value < min) ? min : value;
// There's no check to see if min > max.
return value;
}
/// <summary>
/// Restricts a value to be within a specified range.
/// </summary>
/// <param name="value">The value to clamp.</param>
/// <param name="min">The minimum value. If <c>value</c> is less than <c>min</c>, <c>min</c> will be returned.</param>
/// <param name="max">The maximum value. If <c>value</c> is greater than <c>max</c>, <c>max</c> will be returned.</param>
/// <returns>The clamped value.</returns>
public static int Clamp(int value, int min, int max)
{
value = (value > max) ? max : value;
value = (value < min) ? min : value;
return value;
}
/// <summary>
/// Calculates the absolute value of the difference of two values.
/// </summary>
/// <param name="value1">Source value.</param>
/// <param name="value2">Source value.</param>
/// <returns>Distance between the two values.</returns>
public static float Distance(float value1, float value2)
{
return Math.Abs(value1 - value2);
}
/// <summary>
/// Performs a Hermite spline interpolation.
/// </summary>
/// <param name="value1">Source position.</param>
/// <param name="tangent1">Source tangent.</param>
/// <param name="value2">Source position.</param>
/// <param name="tangent2">Source tangent.</param>
/// <param name="amount">Weighting factor.</param>
/// <returns>The result of the Hermite spline interpolation.</returns>
public static float Hermite(float value1, float tangent1, float value2, float tangent2, float amount)
{
// All transformed to double not to lose precission
// Otherwise, for high numbers of param:amount the result is NaN instead of Infinity
double v1 = value1, v2 = value2, t1 = tangent1, t2 = tangent2, s = amount, result;
double sCubed = s * s * s;
double sSquared = s * s;
if (amount == 0f)
result = value1;
else if (amount == 1f)
result = value2;
else
result = (2 * v1 - 2 * v2 + t2 + t1) * sCubed +
(3 * v2 - 3 * v1 - 2 * t1 - t2) * sSquared +
t1 * s +
v1;
return (float)result;
}
/// <summary>
/// Linearly interpolates between two values.
/// </summary>
/// <param name="value1">Source value.</param>
/// <param name="value2">Source value.</param>
/// <param name="amount">Value between 0 and 1 indicating the weight of value2.</param>
/// <returns>Interpolated value.</returns>
/// <remarks>This method performs the linear interpolation based on the following formula.
/// <c>value1 + (value2 - value1) * amount</c>
/// Passing amount a value of 0 will cause value1 to be returned, a value of 1 will cause value2 to be returned.
/// </remarks>
public static float Lerp(float value1, float value2, float amount)
{
return value1 + (value2 - value1) * amount;
}
/// <summary>
/// Returns the greater of two values.
/// </summary>
/// <param name="value1">Source value.</param>
/// <param name="value2">Source value.</param>
/// <returns>The greater value.</returns>
public static float Max(float value1, float value2)
{
return value1 > value2 ? value1 : value2;
}
/// <summary>
/// Returns the greater of two values.
/// </summary>
/// <param name="value1">Source value.</param>
/// <param name="value2">Source value.</param>
/// <returns>The greater value.</returns>
public static int Max(int value1, int value2)
{
return value1 > value2 ? value1 : value2;
}
/// <summary>
/// Returns the lesser of two values.
/// </summary>
/// <param name="value1">Source value.</param>
/// <param name="value2">Source value.</param>
/// <returns>The lesser value.</returns>
public static float Min(float value1, float value2)
{
return value1 < value2 ? value1 : value2;
}
/// <summary>
/// Returns the lesser of two values.
/// </summary>
/// <param name="value1">Source value.</param>
/// <param name="value2">Source value.</param>
/// <returns>The lesser value.</returns>
public static int Min(int value1, int value2)
{
return value1 < value2 ? value1 : value2;
}
/// <summary>
/// Interpolates between two values using a cubic equation.
/// </summary>
/// <param name="value1">Source value.</param>
/// <param name="value2">Source value.</param>
/// <param name="amount">Weighting value.</param>
/// <returns>Interpolated value.</returns>
public static float SmoothStep(float value1, float value2, float amount)
{
// It is expected that 0 < amount < 1
// If amount < 0, return value1
// If amount > 1, return value2
float result = MathHelper.Clamp(amount, 0f, 1f);
result = MathHelper.Hermite(value1, 0f, value2, 0f, result);
return result;
}
/// <summary>
/// Converts radians to degrees.
/// </summary>
/// <param name="radians">The angle in radians.</param>
/// <returns>The angle in degrees.</returns>
/// <remarks>
/// This method uses double precission internally,
/// though it returns single float
/// Factor = 180 / pi
/// </remarks>
public static float ToDegrees(float radians)
{
return (float)(radians * 57.295779513082320876798154814105);
}
/// <summary>
/// Converts degrees to radians.
/// </summary>
/// <param name="degrees">The angle in degrees.</param>
/// <returns>The angle in radians.</returns>
/// <remarks>
/// This method uses double precission internally,
/// though it returns single float
/// Factor = pi / 180
/// </remarks>
public static float ToRadians(float degrees)
{
return (float)(degrees * 0.017453292519943295769236907684886);
}
/// <summary>
/// Reduces a given angle to a value between π and -π.
/// </summary>
/// <param name="angle">The angle to reduce, in radians.</param>
/// <returns>The new angle, in radians.</returns>
public static float WrapAngle(float angle)
{
angle = (float)Math.IEEERemainder((double)angle, 6.2831854820251465);
if (angle <= -3.14159274f)
{
angle += 6.28318548f;
}
else
{
if (angle > 3.14159274f)
{
angle -= 6.28318548f;
}
}
return angle;
}
/// <summary>
/// Determines if value is powered by two.
/// </summary>
/// <param name="value">A value.</param>
/// <returns><c>true</c> if <c>value</c> is powered by two; otherwise <c>false</c>.</returns>
public static bool IsPowerOfTwo(int value)
{
return (value > 0) && ((value & (value - 1)) == 0);
}
}
}