1090 lines
40 KiB
C#
1090 lines
40 KiB
C#
// Copyright (c) 2012-2023 Wojciech Figat. All rights reserved.
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using System;
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using System.ComponentModel;
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namespace FlaxEngine
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{
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/// <summary>
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/// A collection of common math functions on double floating-points.
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/// </summary>
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[HideInEditor]
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public static class Mathd
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{
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/// <summary>
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/// The value for which all absolute numbers smaller than are considered equal to zero.
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/// </summary>
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public const double Epsilon = 1e-16;
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/// <summary>
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/// A value specifying the approximation of π which is 180 degrees.
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/// </summary>
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public const double Pi = Math.PI;
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/// <summary>
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/// A value specifying the approximation of 2π which is 360 degrees.
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/// </summary>
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public const double TwoPi = 2.0 * Math.PI;
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/// <summary>
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/// A value specifying the approximation of π/2 which is 90 degrees.
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/// </summary>
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public const double PiOverTwo = Math.PI / 2.0;
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/// <summary>
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/// A value specifying the approximation of π/4 which is 45 degrees.
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/// </summary>
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public const double PiOverFour = Math.PI / 4.0;
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/// <summary>
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/// A value specifying the golden mean
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/// </summary>
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public const double GoldenRatio = 1.6180339887;
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/// <summary>
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/// Returns the absolute value of f.
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/// </summary>
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/// <param name="f"></param>
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public static double Abs(double f)
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{
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return Math.Abs(f);
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}
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/// <summary>
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/// Returns the arc-cosine of f - the angle in radians whose cosine is f.
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/// </summary>
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/// <param name="f"></param>
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public static double Acos(double f)
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{
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return Math.Acos(f);
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}
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/// <summary>
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/// Compares two floating point values if they are similar.
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/// </summary>
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/// <param name="a"></param>
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/// <param name="b"></param>
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public static bool Approximately(double a, double b)
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{
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return Abs(b - a) < Max(Epsilon * Max(Abs(a), Abs(b)), Epsilon * 8f);
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}
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/// <summary>
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/// Returns the arc-sine of f - the angle in radians whose sine is f.
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/// </summary>
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/// <param name="f"></param>
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public static double Asin(double f)
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{
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return Math.Asin(f);
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}
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/// <summary>
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/// Returns the arc-tangent of f - the angle in radians whose tangent is f.
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/// </summary>
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/// <param name="f"></param>
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public static double Atan(double f)
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{
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return Math.Atan(f);
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}
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/// <summary>
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/// Returns the angle in radians whose Tan is y/x.
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/// </summary>
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/// <param name="y"></param>
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/// <param name="x"></param>
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public static double Atan2(double y, double x)
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{
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return Math.Atan2(y, x);
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}
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/// <summary>
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/// Returns the smallest integer greater to or equal to f.
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/// </summary>
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/// <param name="f"></param>
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public static double Ceil(double f)
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{
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return Math.Ceiling(f);
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}
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/// <summary>
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/// Returns the smallest integer greater to or equal to f.
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/// </summary>
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/// <param name="f"></param>
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public static long CeilToInt(double f)
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{
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return (long)Math.Ceiling(f);
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}
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/// <summary>
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/// Clamps value between 0 and 1 and returns value.
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/// </summary>
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/// <param name="value">Value to clamp</param>
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/// <returns>Result value</returns>
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public static double Saturate(double value)
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{
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if (value < 0d)
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return 0d;
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return value > 1d ? 1d : value;
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}
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/// <summary>
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/// Returns the cosine of angle f in radians.
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/// </summary>
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/// <param name="f"></param>
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public static double Cos(double f)
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{
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return Math.Cos(f);
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}
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/// <summary>
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/// Calculates the shortest difference between two given angles given in degrees.
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/// </summary>
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/// <param name="current"></param>
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/// <param name="target"></param>
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public static double DeltaAngle(double current, double target)
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{
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double t = Repeat(target - current, 360f);
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if (t > 180d)
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t -= 360d;
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return t;
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}
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/// <summary>
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/// Returns e raised to the specified power.
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/// </summary>
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/// <param name="power"></param>
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public static double Exp(double power)
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{
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return Math.Exp(power);
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}
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/// <summary>
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/// Returns the largest integer smaller to or equal to f.
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/// </summary>
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/// <param name="f"></param>
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public static double Floor(double f)
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{
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return Math.Floor(f);
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}
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/// <summary>
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/// Returns the largest integer smaller to or equal to f.
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/// </summary>
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/// <param name="f"></param>
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public static long FloorToInt(double f)
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{
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return (long)Math.Floor(f);
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}
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/// <summary>
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/// Remaps the specified value from the specified range to another.
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/// </summary>
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/// <param name="value">The value to remap.</param>
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/// <param name="fromMin">The source range minimum.</param>
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/// <param name="fromMax">The source range maximum.</param>
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/// <param name="toMin">The destination range minimum.</param>
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/// <param name="toMax">The destination range maximum.</param>
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/// <returns>The remapped value.</returns>
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public static double Remap(double value, double fromMin, double fromMax, double toMin, double toMax)
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{
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return (value - fromMin) / (fromMax - fromMin) * (toMax - toMin) + toMin;
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}
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/// <summary>
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/// Calculates the linear parameter t that produces the interpolation value within the range [a, b].
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/// </summary>
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/// <param name="a"></param>
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/// <param name="b"></param>
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/// <param name="value"></param>
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public static double InverseLerp(double a, double b, double value)
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{
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if (a == b)
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return 0d;
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return Saturate((value - a) / (b - a));
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}
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/// <summary>
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/// Same as Lerp but makes sure the values interpolate correctly when they wrap around 360 degrees.
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/// </summary>
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/// <param name="a"></param>
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/// <param name="b"></param>
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/// <param name="t"></param>
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public static double LerpAngle(double a, double b, double t)
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{
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double c = Repeat(b - a, 360d);
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if (c > 180d)
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c -= 360d;
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return a + c * Saturate(t);
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}
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/// <summary>
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/// Returns the logarithm of a specified number in a specified base.
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/// </summary>
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/// <param name="f"></param>
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/// <param name="p"></param>
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public static double Log(double f, double p)
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{
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return Math.Log(f, p);
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}
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/// <summary>
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/// Returns the natural (base e) logarithm of a specified number.
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/// </summary>
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/// <param name="f"></param>
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public static double Log(double f)
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{
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return Math.Log(f);
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}
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/// <summary>
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/// Returns the base 10 logarithm of a specified number.
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/// </summary>
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/// <param name="f"></param>
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public static double Log10(double f)
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{
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return Math.Log10(f);
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}
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/// <summary>
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/// Returns largest of two or more values.
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/// </summary>
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/// <param name="a"></param>
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/// <param name="b"></param>
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public static double Max(double a, double b)
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{
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return a <= b ? b : a;
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}
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/// <summary>
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/// Returns largest of two or more values.
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/// </summary>
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/// <param name="values"></param>
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public static double Max(params double[] values)
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{
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int length = values.Length;
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if (length == 0)
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return 0d;
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double t = values[0];
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for (var i = 1; i < length; i++)
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if (values[i] > t)
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t = values[i];
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return t;
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}
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/// <summary>
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/// Returns the smallest of two or more values.
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/// </summary>
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/// <param name="a"></param>
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/// <param name="b"></param>
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public static double Min(double a, double b)
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{
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return a >= b ? b : a;
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}
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/// <summary>
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/// Returns the smallest of two or more values.
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/// </summary>
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/// <param name="values"></param>
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public static double Min(params double[] values)
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{
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int length = values.Length;
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if (length == 0)
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return 0d;
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double t = values[0];
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for (var i = 1; i < length; i++)
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if (values[i] < t)
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t = values[i];
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return t;
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}
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/// <summary>
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/// Moves a value current towards target.
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/// </summary>
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/// <param name="current">The current value.</param>
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/// <param name="target">The value to move towards.</param>
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/// <param name="maxDelta">The maximum change that should be applied to the value.</param>
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public static double MoveTowards(double current, double target, double maxDelta)
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{
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if (Abs(target - current) <= maxDelta)
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return target;
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return current + Sign(target - current) * maxDelta;
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}
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/// <summary>
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/// Same as MoveTowards but makes sure the values interpolate correctly when they wrap around 360 degrees.
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/// </summary>
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/// <param name="current"></param>
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/// <param name="target"></param>
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/// <param name="maxDelta"></param>
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public static double MoveTowardsAngle(double current, double target, double maxDelta)
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{
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double delta = DeltaAngle(current, target);
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if ((-maxDelta < delta) && (delta < maxDelta))
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return target;
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target = current + delta;
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return MoveTowards(current, target, maxDelta);
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}
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/// <summary>
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/// PingPongs the value t, so that it is never larger than length and never smaller than 0.
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/// </summary>
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/// <param name="t"></param>
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/// <param name="length"></param>
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public static double PingPong(double t, double length)
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{
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t = Repeat(t, length * 2f);
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return length - Abs(t - length);
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}
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/// <summary>
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/// Returns f raised to power p.
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/// </summary>
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/// <param name="f"></param>
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/// <param name="p"></param>
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public static double Pow(double f, double p)
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{
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return Math.Pow(f, p);
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}
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/// <summary>
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/// Loops the value t, so that it is never larger than length and never smaller than 0.
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/// </summary>
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/// <param name="t"></param>
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/// <param name="length"></param>
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public static double Repeat(double t, double length)
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{
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return t - Floor(t / length) * length;
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}
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/// <summary>
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/// Returns f rounded to the nearest integer.
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/// </summary>
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/// <param name="f"></param>
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public static double Round(double f)
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{
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return Math.Round(f);
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}
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/// <summary>
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/// Returns f rounded to the nearest integer.
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/// </summary>
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/// <param name="f"></param>
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public static int RoundToInt(double f)
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{
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return (int)Math.Round(f);
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}
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/// <summary>
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/// Returns f rounded to the nearest integer.
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/// </summary>
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/// <param name="f"></param>
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public static long RoundToLong(double f)
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{
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return (long)Math.Round(f);
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}
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/// <summary>
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/// Returns the sign of f.
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/// </summary>
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/// <param name="f"></param>
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public static double Sign(double f)
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{
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return f < 0d ? -1d : 1d;
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}
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/// <summary>
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/// Returns the sine of angle f in radians.
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/// </summary>
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/// <param name="f"></param>
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public static double Sin(double f)
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{
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return Math.Sin(f);
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}
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/// <summary>
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/// Gradually changes a value towards a desired goal over time with smoothing.
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/// </summary>
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/// <param name="current">The current value.</param>
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/// <param name="target">The target value.</param>
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/// <param name="currentVelocity">The current velocity.</param>
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/// <param name="smoothTime">The smoothing time. Smaller values increase blending time.</param>
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/// <param name="maxSpeed">The maximum speed.</param>
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/// <returns>The smoothed value.</returns>
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public static double SmoothDamp(double current, double target, ref double currentVelocity, double smoothTime, double maxSpeed)
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{
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return SmoothDamp(current, target, ref currentVelocity, smoothTime, maxSpeed, Time.DeltaTime);
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}
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/// <summary>
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/// Gradually changes a value towards a desired goal over time with smoothing.
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/// </summary>
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/// <param name="current">The current value.</param>
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/// <param name="target">The target value.</param>
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/// <param name="currentVelocity">The current velocity.</param>
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/// <param name="smoothTime">The smoothing time. Smaller values increase blending time.</param>
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/// <returns>The smoothed value.</returns>
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public static double SmoothDamp(double current, double target, ref double currentVelocity, double smoothTime)
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{
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return SmoothDamp(current, target, ref currentVelocity, smoothTime, double.PositiveInfinity, Time.DeltaTime);
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}
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/// <summary>
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/// Gradually changes a value towards a desired goal over time with smoothing.
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/// </summary>
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/// <param name="current">The current value.</param>
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/// <param name="target">The target value.</param>
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/// <param name="currentVelocity">The current velocity.</param>
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/// <param name="smoothTime">The smoothing time. Smaller values increase blending time.</param>
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/// <param name="maxSpeed">The maximum speed.</param>
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/// <param name="deltaTime">The delta time (in seconds) since last update.</param>
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/// <returns>The smoothed value.</returns>
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public static double SmoothDamp(double current, double target, ref double currentVelocity, double smoothTime, [DefaultValue("double.PositiveInfinity")] double maxSpeed, [DefaultValue("Time.DeltaTime")] double deltaTime)
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{
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smoothTime = Max(0.0001d, smoothTime);
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double a = 2d / smoothTime;
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double b = a * deltaTime;
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double c = 1d / (1d + b + 0.48d * b * b + 0.235d * b * b * b);
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double d = current - target;
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double e = target;
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double f = maxSpeed * smoothTime;
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d = Clamp(d, -f, f);
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target = current - d;
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double g = (currentVelocity + a * d) * deltaTime;
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currentVelocity = (currentVelocity - a * g) * c;
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double h = target + (d + g) * c;
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if (e - current > 0d == h > e)
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{
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h = e;
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currentVelocity = (h - e) / deltaTime;
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}
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return h;
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}
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/// <summary>
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/// Gradually changes an angle towards a desired goal over time with smoothing.
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/// </summary>
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/// <param name="current">The current angle.</param>
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/// <param name="target">The target angle.</param>
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/// <param name="currentVelocity">The current velocity.</param>
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/// <param name="smoothTime">The smoothing time. Smaller values increase blending time.</param>
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/// <param name="maxSpeed">The maximum speed.</param>
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/// <returns>The smoothed value.</returns>
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public static double SmoothDampAngle(double current, double target, ref double currentVelocity, double smoothTime, double maxSpeed)
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{
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return SmoothDampAngle(current, target, ref currentVelocity, smoothTime, maxSpeed, Time.DeltaTime);
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}
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/// <summary>
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/// Gradually changes an angle towards a desired goal over time with smoothing.
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/// </summary>
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/// <param name="current">The current angle.</param>
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/// <param name="target">The target angle.</param>
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/// <param name="currentVelocity">The current velocity.</param>
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/// <param name="smoothTime">The smoothing time. Smaller values increase blending time.</param>
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/// <returns>The smoothed value.</returns>
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public static double SmoothDampAngle(double current, double target, ref double currentVelocity, double smoothTime)
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{
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return SmoothDampAngle(current, target, ref currentVelocity, smoothTime, double.PositiveInfinity, Time.DeltaTime);
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}
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/// <summary>
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/// Gradually changes an angle towards a desired goal over time with smoothing.
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/// </summary>
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/// <param name="current">The current angle.</param>
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/// <param name="target">The target angle.</param>
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/// <param name="currentVelocity">The current velocity.</param>
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/// <param name="smoothTime">The smoothing time. Smaller values increase blending time.</param>
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/// <param name="maxSpeed">The maximum speed.</param>
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/// <param name="deltaTime">The delta time (in seconds) since last update.</param>
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/// <returns>The smoothed value.</returns>
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public static double SmoothDampAngle(double current, double target, ref double currentVelocity, double smoothTime, [DefaultValue("double.PositiveInfinity")] double maxSpeed, [DefaultValue("Time.DeltaTime")] double deltaTime)
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{
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target = current + DeltaAngle(current, target);
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return SmoothDamp(current, target, ref currentVelocity, smoothTime, maxSpeed, deltaTime);
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}
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/// <summary>
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/// Interpolates between min and max with smoothing at the limits.
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/// </summary>
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/// <param name="from"></param>
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/// <param name="to"></param>
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/// <param name="t"></param>
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public static double SmoothStep(double from, double to, double t)
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{
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t = Saturate(t);
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t = -2d * t * t * t + 3d * t * t;
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return to * t + from * (1d - t);
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}
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/// <summary>
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/// Performs a cubic interpolation.
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/// </summary>
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/// <param name="p0">The first point.</param>
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/// <param name="t0">The tangent direction at first point.</param>
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/// <param name="p1">The second point.</param>
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/// <param name="t1">The tangent direction at second point.</param>
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/// <param name="alpha">The distance along the spline.</param>
|
|
/// <returns>The interpolated value.</returns>
|
|
public static double CubicInterp(double p0, double t0, double p1, double t1, double alpha)
|
|
{
|
|
double alpha2 = alpha * alpha;
|
|
double alpha3 = alpha2 * alpha;
|
|
return (((2d * alpha3) - (3d * alpha2) + 1d) * p0) + ((alpha3 - (2d * alpha2) + alpha) * t0) + ((alpha3 - alpha2) * t1) + (((-2d * alpha3) + (3d * alpha2)) * p1);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Interpolate between A and B, applying an ease in function. Exponent controls the degree of the curve.
|
|
/// </summary>
|
|
public static double InterpEaseIn(double a, double b, double alpha, double exponent)
|
|
{
|
|
double modifiedAlpha = Pow(alpha, exponent);
|
|
return Lerp(a, b, modifiedAlpha);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Interpolate between A and B, applying an ease out function. Exponent controls the degree of the curve.
|
|
/// </summary>
|
|
public static double InterpEaseOut(double a, double b, double alpha, double exponent)
|
|
{
|
|
double modifiedAlpha = 1d - Pow(1d - alpha, exponent);
|
|
return Lerp(a, b, modifiedAlpha);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Interpolate between A and B, applying an ease in/out function. Exponent controls the degree of the curve.
|
|
/// </summary>
|
|
public static double InterpEaseInOut(double a, double b, double alpha, double exponent)
|
|
{
|
|
return Lerp(a, b, (alpha < 0.5d) ? InterpEaseIn(0d, 1d, alpha * 2d, exponent) * 0.5d : InterpEaseOut(0d, 1d, alpha * 2d - 1d, exponent) * 0.5d + 0.5d);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Interpolation between A and B, applying a sinusoidal in function.
|
|
/// </summary>
|
|
public static double InterpSinIn(double a, double b, double alpha)
|
|
{
|
|
double modifiedAlpha = -1d * Cos(alpha * PiOverTwo) + 1d;
|
|
return Lerp(a, b, modifiedAlpha);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Interpolation between A and B, applying a sinusoidal out function.
|
|
/// </summary>
|
|
public static double InterpSinOut(double a, double b, double alpha)
|
|
{
|
|
double modifiedAlpha = Sin(alpha * PiOverTwo);
|
|
return Lerp(a, b, modifiedAlpha);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Interpolation between A and B, applying a sinusoidal in/out function.
|
|
/// </summary>
|
|
public static double InterpSinInOut(double a, double b, double alpha)
|
|
{
|
|
return Lerp(a, b, (alpha < 0.5d) ? InterpSinIn(0d, 1d, alpha * 2d) * 0.5d : InterpSinOut(0d, 1d, alpha * 2d - 1d) * 0.5d + 0.5d);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Interpolation between A and B, applying an exponential in function.
|
|
/// </summary>
|
|
public static double InterpExpoIn(double a, double b, double alpha)
|
|
{
|
|
double modifiedAlpha = (alpha == 0d) ? 0d : Pow(2d, 10d * (alpha - 1d));
|
|
return Lerp(a, b, modifiedAlpha);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Interpolation between A and B, applying an exponential out function.
|
|
/// </summary>
|
|
public static double InterpExpoOut(double a, double b, double alpha)
|
|
{
|
|
double modifiedAlpha = (alpha == 1d) ? 1d : -Pow(2d, -10d * alpha) + 1d;
|
|
return Lerp(a, b, modifiedAlpha);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Interpolation between A and B, applying an exponential in/out function.
|
|
/// </summary>
|
|
public static double InterpExpoInOut(double a, double b, double alpha)
|
|
{
|
|
return Lerp(a, b, (alpha < 0.5d) ? InterpExpoIn(0d, 1d, alpha * 2d) * 0.5d : InterpExpoOut(0d, 1d, alpha * 2d - 1d) * 0.5d + 0.5d);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Interpolation between A and B, applying a circular in function.
|
|
/// </summary>
|
|
public static double InterpCircularIn(double a, double b, double alpha)
|
|
{
|
|
double modifiedAlpha = -1d * (Sqrt(1d - alpha * alpha) - 1d);
|
|
return Lerp(a, b, modifiedAlpha);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Interpolation between A and B, applying a circular out function.
|
|
/// </summary>
|
|
public static double InterpCircularOut(double a, double b, double alpha)
|
|
{
|
|
alpha -= 1d;
|
|
double modifiedAlpha = Sqrt(1d - alpha * alpha);
|
|
return Lerp(a, b, modifiedAlpha);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Interpolation between A and B, applying a circular in/out function.
|
|
/// </summary>
|
|
public static double InterpCircularInOut(double a, double b, double alpha)
|
|
{
|
|
return Lerp(a, b, (alpha < 0.5d) ? InterpCircularIn(0d, 1d, alpha * 2d) * 0.5d : InterpCircularOut(0d, 1d, alpha * 2d - 1d) * 0.5d + 0.5d);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Maps the specified value from the given range into another.
|
|
/// </summary>
|
|
/// <param name="value">The value to map from range [fromMin; fromMax].</param>
|
|
/// <param name="fromMin">The source range minimum value.</param>
|
|
/// <param name="fromMax">The source range maximum value.</param>
|
|
/// <param name="toMin">The destination range minimum value.</param>
|
|
/// <param name="toMax">The destination range maximum value.</param>
|
|
/// <returns>The mapped value in range [toMin; toMax].</returns>
|
|
public static double Map(double value, double fromMin, double fromMax, double toMin, double toMax)
|
|
{
|
|
double t = (value - fromMin) / (fromMax - fromMin);
|
|
return toMin + t * (toMax - toMin);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Get the next power of two for a size.
|
|
/// </summary>
|
|
/// <param name="size">The size.</param>
|
|
/// <returns>System.Int32.</returns>
|
|
public static double NextPowerOfTwo(double size)
|
|
{
|
|
return Math.Pow(2d, Math.Ceiling(Math.Log(size, 2d)));
|
|
}
|
|
|
|
/// <summary>
|
|
/// Converts a float value from sRGB to linear.
|
|
/// </summary>
|
|
/// <param name="sRgbValue">The sRGB value.</param>
|
|
/// <returns>A linear value.</returns>
|
|
public static double SRgbToLinear(double sRgbValue)
|
|
{
|
|
if (sRgbValue < 0.04045d)
|
|
return sRgbValue / 12.92d;
|
|
return Math.Pow((sRgbValue + 0.055d) / 1.055d, 2.4d);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Converts a float value from linear to sRGB.
|
|
/// </summary>
|
|
/// <param name="linearValue">The linear value.</param>
|
|
/// <returns>The encoded sRGB value.</returns>
|
|
public static double LinearToSRgb(double linearValue)
|
|
{
|
|
if (linearValue < 0.0031308d)
|
|
return linearValue * 12.92d;
|
|
return 1.055d * Math.Pow(linearValue, 1d / 2.4d) - 0.055d;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns square root of f.
|
|
/// </summary>
|
|
/// <param name="f"></param>
|
|
public static double Sqrt(double f)
|
|
{
|
|
return Math.Sqrt(f);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns square of the given value.
|
|
/// </summary>
|
|
/// <param name="f">The value.</param>
|
|
/// <returns>The value * value.</returns>
|
|
public static double Square(double f)
|
|
{
|
|
return f * f;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the tangent of angle f in radians.
|
|
/// </summary>
|
|
/// <param name="f"></param>
|
|
public static double Tan(double f)
|
|
{
|
|
return Math.Tan(f);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Checks if a and b are almost equals, taking into account the magnitude of floating point numbers (unlike <see cref="WithinEpsilon" /> method). See Remarks. See remarks.
|
|
/// </summary>
|
|
/// <param name="a">The left value to compare.</param>
|
|
/// <param name="b">The right value to compare.</param>
|
|
/// <returns><c>true</c> if a almost equal to b, <c>false</c> otherwise</returns>
|
|
/// <remarks>The code is using the technique described by Bruce Dawson in <a href="http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/">Comparing Floating point numbers 2012 edition</a>.</remarks>
|
|
public static unsafe bool NearEqual(double a, double b)
|
|
{
|
|
// Check if the numbers are really close -- needed
|
|
// when comparing numbers near zero.
|
|
if (IsZero(a - b))
|
|
return true;
|
|
|
|
// Original from Bruce Dawson: http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
|
|
long aInt = *(long*)&a;
|
|
long bInt = *(long*)&b;
|
|
|
|
// Different signs means they do not match.
|
|
if (aInt < 0 != bInt < 0)
|
|
return false;
|
|
|
|
// Find the difference in ULPs.
|
|
long ulp = Math.Abs(aInt - bInt);
|
|
|
|
// Choose of maxUlp = 4
|
|
// according to http://code.google.com/p/googletest/source/browse/trunk/include/gtest/internal/gtest-internal.h
|
|
const long maxUlp = 4;
|
|
return ulp <= maxUlp;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Determines whether the specified value is close to zero (0.0f).
|
|
/// </summary>
|
|
/// <param name="a">The floating value.</param>
|
|
/// <returns><c>true</c> if the specified value is close to zero (0.0f); otherwise, <c>false</c>.</returns>
|
|
public static bool IsZero(double a)
|
|
{
|
|
return Math.Abs(a) < Epsilon;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Determines whether the specified value is close to one (1.0f).
|
|
/// </summary>
|
|
/// <param name="a">The floating value.</param>
|
|
/// <returns><c>true</c> if the specified value is close to one (1.0f); otherwise, <c>false</c>.</returns>
|
|
public static bool IsOne(double a)
|
|
{
|
|
return IsZero(a - 1d);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Checks if a - b are almost equals within a float epsilon.
|
|
/// </summary>
|
|
/// <param name="a">The left value to compare.</param>
|
|
/// <param name="b">The right value to compare.</param>
|
|
/// <param name="epsilon">Epsilon value</param>
|
|
/// <returns><c>true</c> if a almost equal to b within a float epsilon, <c>false</c> otherwise</returns>
|
|
public static bool WithinEpsilon(double a, double b, double epsilon)
|
|
{
|
|
double num = a - b;
|
|
return (-epsilon <= num) && (num <= epsilon);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Determines whether the specified value is in a given range [min; max].
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <param name="min">The minimum.</param>
|
|
/// <param name="max">The maximum.</param>
|
|
/// <returns>
|
|
/// <c>true</c> if the specified value is in a given range; otherwise, <c>false</c>.
|
|
/// </returns>
|
|
public static bool IsInRange(double value, double min, double max)
|
|
{
|
|
return value >= min && value <= max;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Determines whether the specified value is NOT in a given range [min; max].
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <param name="min">The minimum.</param>
|
|
/// <param name="max">The maximum.</param>
|
|
/// <returns>
|
|
/// <c>true</c> if the specified value is NOT in a given range; otherwise, <c>false</c>.
|
|
/// </returns>
|
|
public static bool IsNotInRange(double value, double min, double max)
|
|
{
|
|
return value < min || value > max;
|
|
}
|
|
|
|
#region Angle units conversions
|
|
|
|
/// <summary>
|
|
/// Converts revolutions to degrees.
|
|
/// </summary>
|
|
public static double RevolutionsToDegrees = 360d;
|
|
|
|
/// <summary>
|
|
/// Converts revolutions to radians.
|
|
/// </summary>
|
|
public static double RevolutionsToRadians = TwoPi;
|
|
|
|
/// <summary>
|
|
/// Converts revolutions to gradians.
|
|
/// </summary>
|
|
public static double RevolutionsToGradians = 400d;
|
|
|
|
/// <summary>
|
|
/// Converts degrees to revolutions.
|
|
/// </summary>
|
|
public static double DegreesToRevolutions = (1d / 360d);
|
|
|
|
/// <summary>
|
|
/// Converts degrees to radians.
|
|
/// </summary>
|
|
public static double DegreesToRadians = (Pi / 180d);
|
|
|
|
/// <summary>
|
|
/// Converts radians to revolutions.
|
|
/// </summary>
|
|
public static double RadiansToRevolutions = (1d / TwoPi);
|
|
|
|
/// <summary>
|
|
/// Converts radians to gradians.
|
|
/// </summary>
|
|
public static double RadiansToGradians = (200d / Pi);
|
|
|
|
/// <summary>
|
|
/// Converts gradians to revolutions.
|
|
/// </summary>
|
|
public static double GradiansToRevolutions = (1d / 400d);
|
|
|
|
/// <summary>
|
|
/// Converts gradians to degrees.
|
|
/// </summary>
|
|
public static double GradiansToDegrees = (9.0f / 10d);
|
|
|
|
/// <summary>
|
|
/// Converts gradians to radians.
|
|
/// </summary>
|
|
public static double GradiansToRadians = (Pi / 200d);
|
|
|
|
/// <summary>
|
|
/// Converts radians to degrees.
|
|
/// </summary>
|
|
public static double RadiansToDegrees = (180d / Pi);
|
|
|
|
#endregion
|
|
|
|
/// <summary>
|
|
/// Given a heading which may be outside the +/- PI range, 'unwind' it back into that range.
|
|
/// </summary>
|
|
/// <param name="angle">Angle in radians to unwind.</param>
|
|
/// <returns>Valid angle in radians.</returns>
|
|
public static double UnwindRadians(double angle)
|
|
{
|
|
// TODO: make it faster?
|
|
while (angle > Pi)
|
|
{
|
|
angle -= TwoPi;
|
|
}
|
|
while (angle < -Pi)
|
|
{
|
|
angle += TwoPi;
|
|
}
|
|
return angle;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Utility to ensure angle is between +/- 180 degrees by unwinding
|
|
/// </summary>
|
|
/// <param name="angle">Angle in degrees to unwind.</param>
|
|
/// <returns>Valid angle in degrees.</returns>
|
|
public static double UnwindDegrees(double angle)
|
|
{
|
|
// TODO: make it faster?
|
|
while (angle > 180.0f)
|
|
{
|
|
angle -= 360.0f;
|
|
}
|
|
while (angle < -180.0f)
|
|
{
|
|
angle += 360.0f;
|
|
}
|
|
return angle;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Clamps the specified value.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <param name="min">The min.</param>
|
|
/// <param name="max">The max.</param>
|
|
/// <returns>The result of clamping a value between min and max</returns>
|
|
public static double Clamp(double value, double min, double max)
|
|
{
|
|
return value < min ? min : value > max ? max : value;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Interpolates between two values using a linear function by a given amount.
|
|
/// </summary>
|
|
/// <remarks>
|
|
/// See http://www.encyclopediaofmath.org/index.php/Linear_interpolation and
|
|
/// http://fgiesen.wordpress.com/2012/08/15/linear-interpolation-past-present-and-future/
|
|
/// </remarks>
|
|
/// <param name="from">Value to interpolate from.</param>
|
|
/// <param name="to">Value to interpolate to.</param>
|
|
/// <param name="amount">Interpolation amount.</param>
|
|
/// <returns>The result of linear interpolation of values based on the amount.</returns>
|
|
public static double Lerp(double from, double to, double amount)
|
|
{
|
|
return from + (to - from) * amount;
|
|
}
|
|
|
|
|
|
/// <summary>
|
|
/// Performs smooth (cubic Hermite) interpolation between 0 and 1.
|
|
/// </summary>
|
|
/// <remarks>
|
|
/// See https://en.wikipedia.org/wiki/Smoothstep
|
|
/// </remarks>
|
|
/// <param name="amount">Value between 0 and 1 indicating interpolation amount.</param>
|
|
public static double SmoothStep(double amount)
|
|
{
|
|
return amount <= 0d ? 0d : amount >= 1d ? 1d : amount * amount * (3d - 2d * amount);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a smooth(er) interpolation between 0 and 1 with 1st and 2nd order derivatives of zero at endpoints.
|
|
/// </summary>
|
|
/// <remarks>
|
|
/// See https://en.wikipedia.org/wiki/Smoothstep
|
|
/// </remarks>
|
|
/// <param name="amount">Value between 0 and 1 indicating interpolation amount.</param>
|
|
public static double SmootherStep(double amount)
|
|
{
|
|
return amount <= 0d ? 0d : amount >= 1d ? 1d : amount * amount * amount * (amount * (amount * 6d - 15d) + 10d);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates the modulo of the specified value.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <param name="modulo">The modulo.</param>
|
|
/// <returns>The result of the modulo applied to value</returns>
|
|
public static double Mod(double value, double modulo)
|
|
{
|
|
if (modulo == 0d)
|
|
return value;
|
|
return value % modulo;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates the modulo 2*PI of the specified value.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the modulo applied to value</returns>
|
|
public static double Mod2PI(double value)
|
|
{
|
|
return Mod(value, TwoPi);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Wraps the specified value into a range [min, max]
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <param name="min">The min.</param>
|
|
/// <param name="max">The max.</param>
|
|
/// <returns>Result of the wrapping.</returns>
|
|
/// <exception cref="ArgumentException">Is thrown when <paramref name="min" /> is greater than <paramref name="max" />.</exception>
|
|
public static double Wrap(double value, double min, double max)
|
|
{
|
|
if (NearEqual(min, max))
|
|
return min;
|
|
|
|
double mind = min;
|
|
double maxd = max;
|
|
double valued = value;
|
|
|
|
if (mind > maxd)
|
|
throw new ArgumentException(string.Format("min {0} should be less than or equal to max {1}", min, max), nameof(min));
|
|
|
|
double rangeSize = maxd - mind;
|
|
return mind + (valued - mind) - rangeSize * Math.Floor((valued - mind) / rangeSize);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Gauss function.
|
|
/// http://en.wikipedia.org/wiki/Gaussian_function#Two-dimensional_Gaussian_function
|
|
/// </summary>
|
|
/// <param name="amplitude">Curve amplitude.</param>
|
|
/// <param name="x">Position X.</param>
|
|
/// <param name="y">Position Y</param>
|
|
/// <param name="centerX">Center X.</param>
|
|
/// <param name="centerY">Center Y.</param>
|
|
/// <param name="sigmaX">Curve sigma X.</param>
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|
/// <param name="sigmaY">Curve sigma Y.</param>
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/// <returns>The result of Gaussian function.</returns>
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|
public static double Gauss(double amplitude, double x, double y, double centerX, double centerY, double sigmaX, double sigmaY)
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|
{
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|
double cx = x - centerX;
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|
double cy = y - centerY;
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|
|
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double componentX = cx * cx / (2 * sigmaX * sigmaX);
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|
double componentY = cy * cy / (2 * sigmaY * sigmaY);
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|
|
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return amplitude * Math.Exp(-(componentX + componentY));
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|
}
|
|
|
|
/// <summary>
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|
/// Converts the input alpha value from a linear 0-1 value into the output alpha described by blend mode.
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|
/// </summary>
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|
/// <param name="alpha">The alpha (normalized to 0-1).</param>
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|
/// <param name="mode">The mode.</param>
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|
/// <returns>The output alpha (normalized to 0-1).</returns>
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|
public static double InterpolateAlphaBlend(double alpha, AlphaBlendMode mode)
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|
{
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|
switch (mode)
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|
{
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|
case AlphaBlendMode.Sinusoidal:
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|
alpha = (Sin(alpha * Pi - PiOverTwo) + 1d) / 2d;
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|
break;
|
|
case AlphaBlendMode.Cubic:
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|
alpha = CubicInterp(0d, 0d, 1d, 0d, alpha);
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|
break;
|
|
case AlphaBlendMode.QuadraticInOut:
|
|
alpha = InterpEaseInOut(0d, 1d, alpha, 2d);
|
|
break;
|
|
case AlphaBlendMode.CubicInOut:
|
|
alpha = InterpEaseInOut(0d, 1d, alpha, 3d);
|
|
break;
|
|
case AlphaBlendMode.HermiteCubic:
|
|
alpha = SmoothStep(0d, 1d, alpha);
|
|
break;
|
|
case AlphaBlendMode.QuarticInOut:
|
|
alpha = InterpEaseInOut(0d, 1d, alpha, 4d);
|
|
break;
|
|
case AlphaBlendMode.QuinticInOut:
|
|
alpha = InterpEaseInOut(0d, 1d, alpha, 5d);
|
|
break;
|
|
case AlphaBlendMode.CircularIn:
|
|
alpha = InterpCircularIn(0d, 1d, alpha);
|
|
break;
|
|
case AlphaBlendMode.CircularOut:
|
|
alpha = InterpCircularOut(0d, 1d, alpha);
|
|
break;
|
|
case AlphaBlendMode.CircularInOut:
|
|
alpha = InterpCircularInOut(0d, 1d, alpha);
|
|
break;
|
|
case AlphaBlendMode.ExpIn:
|
|
alpha = InterpExpoIn(0d, 1d, alpha);
|
|
break;
|
|
case AlphaBlendMode.ExpOut:
|
|
alpha = InterpExpoOut(0d, 1d, alpha);
|
|
break;
|
|
case AlphaBlendMode.ExpInOut:
|
|
alpha = InterpExpoInOut(0d, 1d, alpha);
|
|
break;
|
|
}
|
|
|
|
return Saturate(alpha);
|
|
}
|
|
}
|
|
}
|