691 lines
26 KiB
C#
691 lines
26 KiB
C#
#if REAL_T_IS_DOUBLE
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using real_t = System.Double;
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#else
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using real_t = System.Single;
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#endif
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using System;
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namespace Godot
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{
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public static partial class Mathf
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{
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// Define constants with Decimal precision and cast down to double or float.
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/// <summary>
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/// The circle constant, the circumference of the unit circle in radians.
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/// </summary>
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// 6.2831855f and 6.28318530717959
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public const real_t Tau = (real_t)6.2831853071795864769252867666M;
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/// <summary>
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/// Constant that represents how many times the diameter of a circle
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/// fits around its perimeter. This is equivalent to `Mathf.Tau / 2`.
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/// </summary>
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// 3.1415927f and 3.14159265358979
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public const real_t Pi = (real_t)3.1415926535897932384626433833M;
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/// <summary>
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/// Positive infinity. For negative infinity, use `-Mathf.Inf`.
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/// </summary>
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public const real_t Inf = real_t.PositiveInfinity;
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/// <summary>
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/// "Not a Number", an invalid value. `NaN` has special properties, including
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/// that it is not equal to itself. It is output by some invalid operations,
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/// such as dividing zero by zero.
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/// </summary>
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public const real_t NaN = real_t.NaN;
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// 0.0174532924f and 0.0174532925199433
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private const real_t Deg2RadConst = (real_t)0.0174532925199432957692369077M;
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// 57.29578f and 57.2957795130823
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private const real_t Rad2DegConst = (real_t)57.295779513082320876798154814M;
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/// <summary>
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/// Returns the absolute value of `s` (i.e. positive value).
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/// </summary>
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/// <param name="s">The input number.</param>
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/// <returns>The absolute value of `s`.</returns>
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public static int Abs(int s)
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{
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return Math.Abs(s);
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}
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/// <summary>
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/// Returns the absolute value of `s` (i.e. positive value).
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/// </summary>
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/// <param name="s">The input number.</param>
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/// <returns>The absolute value of `s`.</returns>
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public static real_t Abs(real_t s)
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{
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return Math.Abs(s);
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}
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/// <summary>
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/// Returns the arc cosine of `s` in radians. Use to get the angle of cosine s.
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/// </summary>
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/// <param name="s">The input cosine value. Must be on the range of -1.0 to 1.0.</param>
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/// <returns>An angle that would result in the given cosine value. On the range `0` to `Tau/2`.</returns>
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public static real_t Acos(real_t s)
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{
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return (real_t)Math.Acos(s);
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}
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/// <summary>
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/// Returns the arc sine of `s` in radians. Use to get the angle of sine s.
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/// </summary>
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/// <param name="s">The input sine value. Must be on the range of -1.0 to 1.0.</param>
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/// <returns>An angle that would result in the given sine value. On the range `-Tau/4` to `Tau/4`.</returns>
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public static real_t Asin(real_t s)
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{
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return (real_t)Math.Asin(s);
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}
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/// <summary>
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/// Returns the arc tangent of `s` in radians. Use to get the angle of tangent s.
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///
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/// The method cannot know in which quadrant the angle should fall.
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/// See <see cref="Atan2(real_t, real_t)"/> if you have both `y` and `x`.
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/// </summary>
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/// <param name="s">The input tangent value.</param>
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/// <returns>An angle that would result in the given tangent value. On the range `-Tau/4` to `Tau/4`.</returns>
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public static real_t Atan(real_t s)
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{
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return (real_t)Math.Atan(s);
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}
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/// <summary>
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/// Returns the arc tangent of `y` and `x` in radians. Use to get the angle
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/// of the tangent of `y/x`. To compute the value, the method takes into
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/// account the sign of both arguments in order to determine the quadrant.
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///
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/// Important note: The Y coordinate comes first, by convention.
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/// </summary>
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/// <param name="y">The Y coordinate of the point to find the angle to.</param>
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/// <param name="x">The X coordinate of the point to find the angle to.</param>
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/// <returns>An angle that would result in the given tangent value. On the range `-Tau/2` to `Tau/2`.</returns>
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public static real_t Atan2(real_t y, real_t x)
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{
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return (real_t)Math.Atan2(y, x);
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}
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/// <summary>
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/// Converts a 2D point expressed in the cartesian coordinate
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/// system (X and Y axis) to the polar coordinate system
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/// (a distance from the origin and an angle).
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/// </summary>
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/// <param name="x">The input X coordinate.</param>
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/// <param name="y">The input Y coordinate.</param>
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/// <returns>A <see cref="Vector2"/> with X representing the distance and Y representing the angle.</returns>
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public static Vector2 Cartesian2Polar(real_t x, real_t y)
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{
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return new Vector2(Sqrt(x * x + y * y), Atan2(y, x));
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}
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/// <summary>
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/// Rounds `s` upward (towards positive infinity).
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/// </summary>
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/// <param name="s">The number to ceil.</param>
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/// <returns>The smallest whole number that is not less than `s`.</returns>
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public static real_t Ceil(real_t s)
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{
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return (real_t)Math.Ceiling(s);
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}
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/// <summary>
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/// Clamps a `value` so that it is not less than `min` and not more than `max`.
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/// </summary>
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/// <param name="value">The value to clamp.</param>
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/// <param name="min">The minimum allowed value.</param>
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/// <param name="max">The maximum allowed value.</param>
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/// <returns>The clamped value.</returns>
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public static int Clamp(int value, int min, int max)
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{
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return value < min ? min : value > max ? max : value;
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}
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/// <summary>
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/// Clamps a `value` so that it is not less than `min` and not more than `max`.
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/// </summary>
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/// <param name="value">The value to clamp.</param>
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/// <param name="min">The minimum allowed value.</param>
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/// <param name="max">The maximum allowed value.</param>
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/// <returns>The clamped value.</returns>
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public static real_t Clamp(real_t value, real_t min, real_t max)
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{
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return value < min ? min : value > max ? max : value;
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}
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/// <summary>
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/// Returns the cosine of angle `s` in radians.
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/// </summary>
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/// <param name="s">The angle in radians.</param>
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/// <returns>The cosine of that angle.</returns>
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public static real_t Cos(real_t s)
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{
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return (real_t)Math.Cos(s);
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}
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/// <summary>
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/// Returns the hyperbolic cosine of angle `s` in radians.
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/// </summary>
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/// <param name="s">The angle in radians.</param>
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/// <returns>The hyperbolic cosine of that angle.</returns>
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public static real_t Cosh(real_t s)
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{
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return (real_t)Math.Cosh(s);
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}
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/// <summary>
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/// Converts an angle expressed in degrees to radians.
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/// </summary>
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/// <param name="deg">An angle expressed in degrees.</param>
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/// <returns>The same angle expressed in radians.</returns>
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public static real_t Deg2Rad(real_t deg)
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{
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return deg * Deg2RadConst;
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}
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/// <summary>
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/// Easing function, based on exponent. The curve values are:
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/// `0` is constant, `1` is linear, `0` to `1` is ease-in, `1` or more is ease-out.
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/// Negative values are in-out/out-in.
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/// </summary>
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/// <param name="s">The value to ease.</param>
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/// <param name="curve">`0` is constant, `1` is linear, `0` to `1` is ease-in, `1` or more is ease-out.</param>
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/// <returns>The eased value.</returns>
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public static real_t Ease(real_t s, real_t curve)
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{
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if (s < 0f)
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{
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s = 0f;
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}
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else if (s > 1.0f)
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{
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s = 1.0f;
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}
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if (curve > 0f)
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{
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if (curve < 1.0f)
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{
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return 1.0f - Pow(1.0f - s, 1.0f / curve);
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}
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return Pow(s, curve);
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}
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if (curve < 0f)
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{
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if (s < 0.5f)
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{
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return Pow(s * 2.0f, -curve) * 0.5f;
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}
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return (1.0f - Pow(1.0f - (s - 0.5f) * 2.0f, -curve)) * 0.5f + 0.5f;
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}
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return 0f;
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}
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/// <summary>
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/// The natural exponential function. It raises the mathematical
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/// constant `e` to the power of `s` and returns it.
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/// </summary>
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/// <param name="s">The exponent to raise `e` to.</param>
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/// <returns>`e` raised to the power of `s`.</returns>
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public static real_t Exp(real_t s)
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{
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return (real_t)Math.Exp(s);
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}
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/// <summary>
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/// Rounds `s` downward (towards negative infinity).
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/// </summary>
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/// <param name="s">The number to floor.</param>
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/// <returns>The largest whole number that is not more than `s`.</returns>
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public static real_t Floor(real_t s)
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{
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return (real_t)Math.Floor(s);
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}
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/// <summary>
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/// Returns a normalized value considering the given range.
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/// This is the opposite of <see cref="Lerp(real_t, real_t, real_t)"/>.
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/// </summary>
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/// <param name="from">The interpolated value.</param>
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/// <param name="to">The destination value for interpolation.</param>
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/// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
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/// <returns>The resulting value of the inverse interpolation.</returns>
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public static real_t InverseLerp(real_t from, real_t to, real_t weight)
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{
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return (weight - from) / (to - from);
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}
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/// <summary>
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/// Returns true if `a` and `b` are approximately equal to each other.
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/// The comparison is done using a tolerance calculation with <see cref="Epsilon"/>.
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/// </summary>
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/// <param name="a">One of the values.</param>
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/// <param name="b">The other value.</param>
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/// <returns>A bool for whether or not the two values are approximately equal.</returns>
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public static bool IsEqualApprox(real_t a, real_t b)
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{
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// Check for exact equality first, required to handle "infinity" values.
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if (a == b)
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{
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return true;
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}
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// Then check for approximate equality.
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real_t tolerance = Epsilon * Abs(a);
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if (tolerance < Epsilon)
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{
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tolerance = Epsilon;
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}
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return Abs(a - b) < tolerance;
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}
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/// <summary>
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/// Returns whether `s` is an infinity value (either positive infinity or negative infinity).
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/// </summary>
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/// <param name="s">The value to check.</param>
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/// <returns>A bool for whether or not the value is an infinity value.</returns>
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public static bool IsInf(real_t s)
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{
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return real_t.IsInfinity(s);
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}
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/// <summary>
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/// Returns whether `s` is a `NaN` ("Not a Number" or invalid) value.
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/// </summary>
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/// <param name="s">The value to check.</param>
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/// <returns>A bool for whether or not the value is a `NaN` value.</returns>
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public static bool IsNaN(real_t s)
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{
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return real_t.IsNaN(s);
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}
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/// <summary>
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/// Returns true if `s` is approximately zero.
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/// The comparison is done using a tolerance calculation with <see cref="Epsilon"/>.
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///
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/// This method is faster than using <see cref="IsEqualApprox(real_t, real_t)"/> with one value as zero.
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/// </summary>
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/// <param name="s">The value to check.</param>
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/// <returns>A bool for whether or not the value is nearly zero.</returns>
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public static bool IsZeroApprox(real_t s)
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{
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return Abs(s) < Epsilon;
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}
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/// <summary>
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/// Linearly interpolates between two values by a normalized value.
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/// This is the opposite <see cref="InverseLerp(real_t, real_t, real_t)"/>.
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/// </summary>
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/// <param name="from">The start value for interpolation.</param>
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/// <param name="to">The destination value for interpolation.</param>
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/// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
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/// <returns>The resulting value of the interpolation.</returns>
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public static real_t Lerp(real_t from, real_t to, real_t weight)
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{
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return from + (to - from) * weight;
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}
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/// <summary>
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/// Linearly interpolates between two angles (in radians) by a normalized value.
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///
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/// Similar to <see cref="Lerp(real_t, real_t, real_t)"/>,
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/// but interpolates correctly when the angles wrap around <see cref="Tau"/>.
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/// </summary>
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/// <param name="from">The start angle for interpolation.</param>
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/// <param name="to">The destination angle for interpolation.</param>
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/// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
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/// <returns>The resulting angle of the interpolation.</returns>
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public static real_t LerpAngle(real_t from, real_t to, real_t weight)
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{
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real_t difference = (to - from) % Mathf.Tau;
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real_t distance = ((2 * difference) % Mathf.Tau) - difference;
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return from + distance * weight;
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}
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/// <summary>
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/// Natural logarithm. The amount of time needed to reach a certain level of continuous growth.
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///
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/// Note: This is not the same as the "log" function on most calculators, which uses a base 10 logarithm.
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/// </summary>
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/// <param name="s">The input value.</param>
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/// <returns>The natural log of `s`.</returns>
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public static real_t Log(real_t s)
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{
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return (real_t)Math.Log(s);
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}
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/// <summary>
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/// Returns the maximum of two values.
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/// </summary>
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/// <param name="a">One of the values.</param>
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/// <param name="b">The other value.</param>
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/// <returns>Whichever of the two values is higher.</returns>
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public static int Max(int a, int b)
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{
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return a > b ? a : b;
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}
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/// <summary>
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/// Returns the maximum of two values.
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/// </summary>
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/// <param name="a">One of the values.</param>
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/// <param name="b">The other value.</param>
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/// <returns>Whichever of the two values is higher.</returns>
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public static real_t Max(real_t a, real_t b)
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{
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return a > b ? a : b;
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}
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/// <summary>
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/// Returns the minimum of two values.
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/// </summary>
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/// <param name="a">One of the values.</param>
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/// <param name="b">The other value.</param>
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/// <returns>Whichever of the two values is lower.</returns>
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public static int Min(int a, int b)
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{
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return a < b ? a : b;
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}
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/// <summary>
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/// Returns the minimum of two values.
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/// </summary>
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/// <param name="a">One of the values.</param>
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/// <param name="b">The other value.</param>
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/// <returns>Whichever of the two values is lower.</returns>
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public static real_t Min(real_t a, real_t b)
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{
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return a < b ? a : b;
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}
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/// <summary>
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/// Moves `from` toward `to` by the `delta` value.
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///
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/// Use a negative delta value to move away.
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/// </summary>
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/// <param name="from">The start value.</param>
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/// <param name="to">The value to move towards.</param>
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/// <param name="delta">The amount to move by.</param>
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/// <returns>The value after moving.</returns>
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public static real_t MoveToward(real_t from, real_t to, real_t delta)
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{
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return Abs(to - from) <= delta ? to : from + Sign(to - from) * delta;
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}
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/// <summary>
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/// Returns the nearest larger power of 2 for the integer `value`.
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/// </summary>
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/// <param name="value">The input value.</param>
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/// <returns>The nearest larger power of 2.</returns>
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public static int NearestPo2(int value)
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{
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value--;
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value |= value >> 1;
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value |= value >> 2;
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value |= value >> 4;
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value |= value >> 8;
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value |= value >> 16;
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value++;
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return value;
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}
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/// <summary>
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/// Converts a 2D point expressed in the polar coordinate
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/// system (a distance from the origin `r` and an angle `th`)
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/// to the cartesian coordinate system (X and Y axis).
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/// </summary>
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/// <param name="r">The distance from the origin.</param>
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/// <param name="th">The angle of the point.</param>
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/// <returns>A <see cref="Vector2"/> representing the cartesian coordinate.</returns>
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public static Vector2 Polar2Cartesian(real_t r, real_t th)
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{
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return new Vector2(r * Cos(th), r * Sin(th));
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}
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/// <summary>
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/// Performs a canonical Modulus operation, where the output is on the range `[0, b)`.
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/// </summary>
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/// <param name="a">The dividend, the primary input.</param>
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/// <param name="b">The divisor. The output is on the range `[0, b)`.</param>
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/// <returns>The resulting output.</returns>
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public static int PosMod(int a, int b)
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{
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int c = a % b;
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if ((c < 0 && b > 0) || (c > 0 && b < 0))
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{
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c += b;
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}
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return c;
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}
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/// <summary>
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/// Performs a canonical Modulus operation, where the output is on the range `[0, b)`.
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/// </summary>
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/// <param name="a">The dividend, the primary input.</param>
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/// <param name="b">The divisor. The output is on the range `[0, b)`.</param>
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/// <returns>The resulting output.</returns>
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public static real_t PosMod(real_t a, real_t b)
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{
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real_t c = a % b;
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if ((c < 0 && b > 0) || (c > 0 && b < 0))
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{
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c += b;
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}
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return c;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the result of `x` raised to the power of `y`.
|
|
/// </summary>
|
|
/// <param name="x">The base.</param>
|
|
/// <param name="y">The exponent.</param>
|
|
/// <returns>`x` raised to the power of `y`.</returns>
|
|
public static real_t Pow(real_t x, real_t y)
|
|
{
|
|
return (real_t)Math.Pow(x, y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Converts an angle expressed in radians to degrees.
|
|
/// </summary>
|
|
/// <param name="rad">An angle expressed in radians.</param>
|
|
/// <returns>The same angle expressed in degrees.</returns>
|
|
public static real_t Rad2Deg(real_t rad)
|
|
{
|
|
return rad * Rad2DegConst;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Rounds `s` to the nearest whole number,
|
|
/// with halfway cases rounded towards the nearest multiple of two.
|
|
/// </summary>
|
|
/// <param name="s">The number to round.</param>
|
|
/// <returns>The rounded number.</returns>
|
|
public static real_t Round(real_t s)
|
|
{
|
|
return (real_t)Math.Round(s);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the sign of `s`: `-1` or `1`. Returns `0` if `s` is `0`.
|
|
/// </summary>
|
|
/// <param name="s">The input number.</param>
|
|
/// <returns>One of three possible values: `1`, `-1`, or `0`.</returns>
|
|
public static int Sign(int s)
|
|
{
|
|
if (s == 0)
|
|
return 0;
|
|
return s < 0 ? -1 : 1;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the sign of `s`: `-1` or `1`. Returns `0` if `s` is `0`.
|
|
/// </summary>
|
|
/// <param name="s">The input number.</param>
|
|
/// <returns>One of three possible values: `1`, `-1`, or `0`.</returns>
|
|
public static int Sign(real_t s)
|
|
{
|
|
if (s == 0)
|
|
return 0;
|
|
return s < 0 ? -1 : 1;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the sine of angle `s` in radians.
|
|
/// </summary>
|
|
/// <param name="s">The angle in radians.</param>
|
|
/// <returns>The sine of that angle.</returns>
|
|
public static real_t Sin(real_t s)
|
|
{
|
|
return (real_t)Math.Sin(s);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the hyperbolic sine of angle `s` in radians.
|
|
/// </summary>
|
|
/// <param name="s">The angle in radians.</param>
|
|
/// <returns>The hyperbolic sine of that angle.</returns>
|
|
public static real_t Sinh(real_t s)
|
|
{
|
|
return (real_t)Math.Sinh(s);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a number smoothly interpolated between `from` and `to`,
|
|
/// based on the `weight`. Similar to <see cref="Lerp(real_t, real_t, real_t)"/>,
|
|
/// but interpolates faster at the beginning and slower at the end.
|
|
/// </summary>
|
|
/// <param name="from">The start value for interpolation.</param>
|
|
/// <param name="to">The destination value for interpolation.</param>
|
|
/// <param name="weight">A value representing the amount of interpolation.</param>
|
|
/// <returns>The resulting value of the interpolation.</returns>
|
|
public static real_t SmoothStep(real_t from, real_t to, real_t weight)
|
|
{
|
|
if (IsEqualApprox(from, to))
|
|
{
|
|
return from;
|
|
}
|
|
real_t x = Clamp((weight - from) / (to - from), (real_t)0.0, (real_t)1.0);
|
|
return x * x * (3 - 2 * x);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the square root of `s`, where `s` is a non-negative number.
|
|
///
|
|
/// If you need negative inputs, use `System.Numerics.Complex`.
|
|
/// </summary>
|
|
/// <param name="s">The input number. Must not be negative.</param>
|
|
/// <returns>The square root of `s`.</returns>
|
|
public static real_t Sqrt(real_t s)
|
|
{
|
|
return (real_t)Math.Sqrt(s);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the position of the first non-zero digit, after the
|
|
/// decimal point. Note that the maximum return value is 10,
|
|
/// which is a design decision in the implementation.
|
|
/// </summary>
|
|
/// <param name="step">The input value.</param>
|
|
/// <returns>The position of the first non-zero digit.</returns>
|
|
public static int StepDecimals(real_t step)
|
|
{
|
|
double[] sd = new double[] {
|
|
0.9999,
|
|
0.09999,
|
|
0.009999,
|
|
0.0009999,
|
|
0.00009999,
|
|
0.000009999,
|
|
0.0000009999,
|
|
0.00000009999,
|
|
0.000000009999,
|
|
};
|
|
double abs = Mathf.Abs(step);
|
|
double decs = abs - (int)abs; // Strip away integer part
|
|
for (int i = 0; i < sd.Length; i++)
|
|
{
|
|
if (decs >= sd[i])
|
|
{
|
|
return i;
|
|
}
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Snaps float value `s` to a given `step`.
|
|
/// This can also be used to round a floating point
|
|
/// number to an arbitrary number of decimals.
|
|
/// </summary>
|
|
/// <param name="s">The value to snap.</param>
|
|
/// <param name="step">The step size to snap to.</param>
|
|
/// <returns></returns>
|
|
public static real_t Snapped(real_t s, real_t step)
|
|
{
|
|
if (step != 0f)
|
|
{
|
|
return Floor(s / step + 0.5f) * step;
|
|
}
|
|
|
|
return s;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the tangent of angle `s` in radians.
|
|
/// </summary>
|
|
/// <param name="s">The angle in radians.</param>
|
|
/// <returns>The tangent of that angle.</returns>
|
|
public static real_t Tan(real_t s)
|
|
{
|
|
return (real_t)Math.Tan(s);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the hyperbolic tangent of angle `s` in radians.
|
|
/// </summary>
|
|
/// <param name="s">The angle in radians.</param>
|
|
/// <returns>The hyperbolic tangent of that angle.</returns>
|
|
public static real_t Tanh(real_t s)
|
|
{
|
|
return (real_t)Math.Tanh(s);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Wraps `value` between `min` and `max`. Usable for creating loop-alike
|
|
/// behavior or infinite surfaces. If `min` is `0`, this is equivalent
|
|
/// to <see cref="PosMod(int, int)"/>, so prefer using that instead.
|
|
/// </summary>
|
|
/// <param name="value">The value to wrap.</param>
|
|
/// <param name="min">The minimum allowed value and lower bound of the range.</param>
|
|
/// <param name="max">The maximum allowed value and upper bound of the range.</param>
|
|
/// <returns>The wrapped value.</returns>
|
|
public static int Wrap(int value, int min, int max)
|
|
{
|
|
int range = max - min;
|
|
return range == 0 ? min : min + ((value - min) % range + range) % range;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Wraps `value` between `min` and `max`. Usable for creating loop-alike
|
|
/// behavior or infinite surfaces. If `min` is `0`, this is equivalent
|
|
/// to <see cref="PosMod(real_t, real_t)"/>, so prefer using that instead.
|
|
/// </summary>
|
|
/// <param name="value">The value to wrap.</param>
|
|
/// <param name="min">The minimum allowed value and lower bound of the range.</param>
|
|
/// <param name="max">The maximum allowed value and upper bound of the range.</param>
|
|
/// <returns>The wrapped value.</returns>
|
|
public static real_t Wrap(real_t value, real_t min, real_t max)
|
|
{
|
|
real_t range = max - min;
|
|
return IsZeroApprox(range) ? min : min + ((value - min) % range + range) % range;
|
|
}
|
|
}
|
|
}
|