diff options
Diffstat (limited to 'modules')
| -rw-r--r-- | modules/mono/glue/GodotSharp/GodotSharp/Core/Mathf.cs | 1109 | ||||
| -rw-r--r-- | modules/mono/glue/GodotSharp/GodotSharp/Core/MathfEx.cs | 112 |
2 files changed, 1049 insertions, 172 deletions
diff --git a/modules/mono/glue/GodotSharp/GodotSharp/Core/Mathf.cs b/modules/mono/glue/GodotSharp/GodotSharp/Core/Mathf.cs index 137a42a6de..ca0032df73 100644 --- a/modules/mono/glue/GodotSharp/GodotSharp/Core/Mathf.cs +++ b/modules/mono/glue/GodotSharp/GodotSharp/Core/Mathf.cs @@ -1,4 +1,5 @@ using System; +using System.Runtime.CompilerServices; namespace Godot { @@ -35,15 +36,18 @@ namespace Godot public const real_t NaN = real_t.NaN; // 0.0174532924f and 0.0174532925199433 - private const real_t _degToRadConst = (real_t)0.0174532925199432957692369077M; + private const float _degToRadConstF = (float)0.0174532925199432957692369077M; + private const double _degToRadConstD = (double)0.0174532925199432957692369077M; // 57.29578f and 57.2957795130823 - private const real_t _radToDegConst = (real_t)57.295779513082320876798154814M; + private const float _radToDegConstF = (float)57.295779513082320876798154814M; + private const double _radToDegConstD = (double)57.295779513082320876798154814M; /// <summary> /// Returns the absolute value of <paramref name="s"/> (i.e. positive value). /// </summary> /// <param name="s">The input number.</param> /// <returns>The absolute value of <paramref name="s"/>.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] public static int Abs(int s) { return Math.Abs(s); @@ -54,7 +58,19 @@ namespace Godot /// </summary> /// <param name="s">The input number.</param> /// <returns>The absolute value of <paramref name="s"/>.</returns> - public static real_t Abs(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Abs(float s) + { + return Math.Abs(s); + } + + /// <summary> + /// Returns the absolute value of <paramref name="s"/> (i.e. positive value). + /// </summary> + /// <param name="s">The input number.</param> + /// <returns>The absolute value of <paramref name="s"/>.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Abs(double s) { return Math.Abs(s); } @@ -67,9 +83,38 @@ namespace Godot /// <returns> /// An angle that would result in the given cosine value. On the range <c>0</c> to <c>Tau/2</c>. /// </returns> - public static real_t Acos(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Acos(float s) { - return (real_t)Math.Acos(s); + return MathF.Acos(s); + } + + /// <summary> + /// Returns the arc cosine of <paramref name="s"/> in radians. + /// Use to get the angle of cosine <paramref name="s"/>. + /// </summary> + /// <param name="s">The input cosine value. Must be on the range of -1.0 to 1.0.</param> + /// <returns> + /// An angle that would result in the given cosine value. On the range <c>0</c> to <c>Tau/2</c>. + /// </returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Acos(double s) + { + return Math.Acos(s); + } + + /// <summary> + /// Returns the arc sine of <paramref name="s"/> in radians. + /// Use to get the angle of sine <paramref name="s"/>. + /// </summary> + /// <param name="s">The input sine value. Must be on the range of -1.0 to 1.0.</param> + /// <returns> + /// An angle that would result in the given sine value. On the range <c>-Tau/4</c> to <c>Tau/4</c>. + /// </returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Asin(float s) + { + return MathF.Asin(s); } /// <summary> @@ -80,9 +125,10 @@ namespace Godot /// <returns> /// An angle that would result in the given sine value. On the range <c>-Tau/4</c> to <c>Tau/4</c>. /// </returns> - public static real_t Asin(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Asin(double s) { - return (real_t)Math.Asin(s); + return Math.Asin(s); } /// <summary> @@ -90,15 +136,51 @@ namespace Godot /// Use to get the angle of tangent <paramref name="s"/>. /// /// The method cannot know in which quadrant the angle should fall. - /// See <see cref="Atan2(real_t, real_t)"/> if you have both <c>y</c> and <c>x</c>. + /// See <see cref="Atan2(float, float)"/> if you have both <c>y</c> and <c>x</c>. /// </summary> /// <param name="s">The input tangent value.</param> /// <returns> /// An angle that would result in the given tangent value. On the range <c>-Tau/4</c> to <c>Tau/4</c>. /// </returns> - public static real_t Atan(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Atan(float s) { - return (real_t)Math.Atan(s); + return MathF.Atan(s); + } + + /// <summary> + /// Returns the arc tangent of <paramref name="s"/> in radians. + /// Use to get the angle of tangent <paramref name="s"/>. + /// + /// The method cannot know in which quadrant the angle should fall. + /// See <see cref="Atan2(double, double)"/> if you have both <c>y</c> and <c>x</c>. + /// </summary> + /// <param name="s">The input tangent value.</param> + /// <returns> + /// An angle that would result in the given tangent value. On the range <c>-Tau/4</c> to <c>Tau/4</c>. + /// </returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Atan(double s) + { + return Math.Atan(s); + } + + /// <summary> + /// Returns the arc tangent of <paramref name="y"/> and <paramref name="x"/> in radians. + /// Use to get the angle of the tangent of <c>y/x</c>. To compute the value, the method takes into + /// account the sign of both arguments in order to determine the quadrant. + /// + /// Important note: The Y coordinate comes first, by convention. + /// </summary> + /// <param name="y">The Y coordinate of the point to find the angle to.</param> + /// <param name="x">The X coordinate of the point to find the angle to.</param> + /// <returns> + /// An angle that would result in the given tangent value. On the range <c>-Tau/2</c> to <c>Tau/2</c>. + /// </returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Atan2(float y, float x) + { + return MathF.Atan2(y, x); } /// <summary> @@ -113,9 +195,21 @@ namespace Godot /// <returns> /// An angle that would result in the given tangent value. On the range <c>-Tau/2</c> to <c>Tau/2</c>. /// </returns> - public static real_t Atan2(real_t y, real_t x) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Atan2(double y, double x) + { + return Math.Atan2(y, x); + } + + /// <summary> + /// Rounds <paramref name="s"/> upward (towards positive infinity). + /// </summary> + /// <param name="s">The number to ceil.</param> + /// <returns>The smallest whole number that is not less than <paramref name="s"/>.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Ceil(float s) { - return (real_t)Math.Atan2(y, x); + return MathF.Ceiling(s); } /// <summary> @@ -123,9 +217,10 @@ namespace Godot /// </summary> /// <param name="s">The number to ceil.</param> /// <returns>The smallest whole number that is not less than <paramref name="s"/>.</returns> - public static real_t Ceil(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Ceil(double s) { - return (real_t)Math.Ceiling(s); + return Math.Ceiling(s); } /// <summary> @@ -136,9 +231,24 @@ namespace Godot /// <param name="min">The minimum allowed value.</param> /// <param name="max">The maximum allowed value.</param> /// <returns>The clamped value.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] public static int Clamp(int value, int min, int max) { - return value < min ? min : value > max ? max : value; + return Math.Clamp(value, min, max); + } + + /// <summary> + /// Clamps a <paramref name="value"/> so that it is not less than <paramref name="min"/> + /// and not more than <paramref name="max"/>. + /// </summary> + /// <param name="value">The value to clamp.</param> + /// <param name="min">The minimum allowed value.</param> + /// <param name="max">The maximum allowed value.</param> + /// <returns>The clamped value.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Clamp(float value, float min, float max) + { + return Math.Clamp(value, min, max); } /// <summary> @@ -149,9 +259,10 @@ namespace Godot /// <param name="min">The minimum allowed value.</param> /// <param name="max">The maximum allowed value.</param> /// <returns>The clamped value.</returns> - public static real_t Clamp(real_t value, real_t min, real_t max) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Clamp(double value, double min, double max) { - return value < min ? min : value > max ? max : value; + return Math.Clamp(value, min, max); } /// <summary> @@ -159,9 +270,21 @@ namespace Godot /// </summary> /// <param name="s">The angle in radians.</param> /// <returns>The cosine of that angle.</returns> - public static real_t Cos(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Cos(float s) { - return (real_t)Math.Cos(s); + return MathF.Cos(s); + } + + /// <summary> + /// Returns the cosine of angle <paramref name="s"/> in radians. + /// </summary> + /// <param name="s">The angle in radians.</param> + /// <returns>The cosine of that angle.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Cos(double s) + { + return Math.Cos(s); } /// <summary> @@ -169,9 +292,21 @@ namespace Godot /// </summary> /// <param name="s">The angle in radians.</param> /// <returns>The hyperbolic cosine of that angle.</returns> - public static real_t Cosh(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Cosh(float s) { - return (real_t)Math.Cosh(s); + return MathF.Cosh(s); + } + + /// <summary> + /// Returns the hyperbolic cosine of angle <paramref name="s"/> in radians. + /// </summary> + /// <param name="s">The angle in radians.</param> + /// <returns>The hyperbolic cosine of that angle.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Cosh(double s) + { + return Math.Cosh(s); } /// <summary> @@ -184,7 +319,7 @@ namespace Godot /// <param name="post">The value which after "to" value for interpolation.</param> /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> /// <returns>The resulting value of the interpolation.</returns> - public static real_t CubicInterpolate(real_t from, real_t to, real_t pre, real_t post, real_t weight) + public static float CubicInterpolate(float from, float to, float pre, float post, float weight) { return 0.5f * ((from * 2.0f) + @@ -194,9 +329,28 @@ namespace Godot } /// <summary> + /// Cubic interpolates between two values by the factor defined in <paramref name="weight"/> + /// with pre and post values. + /// </summary> + /// <param name="from">The start value for interpolation.</param> + /// <param name="to">The destination value for interpolation.</param> + /// <param name="pre">The value which before "from" value for interpolation.</param> + /// <param name="post">The value which after "to" value for interpolation.</param> + /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> + /// <returns>The resulting value of the interpolation.</returns> + public static double CubicInterpolate(double from, double to, double pre, double post, double weight) + { + return 0.5 * + ((from * 2.0) + + (-pre + to) * weight + + (2.0 * pre - 5.0 * from + 4.0 * to - post) * (weight * weight) + + (-pre + 3.0 * from - 3.0 * to + post) * (weight * weight * weight)); + } + + /// <summary> /// Cubic interpolates between two rotation values with shortest path /// by the factor defined in <paramref name="weight"/> with pre and post values. - /// See also <see cref="LerpAngle"/>. + /// See also <see cref="LerpAngle(float, float, float)"/>. /// </summary> /// <param name="from">The start value for interpolation.</param> /// <param name="to">The destination value for interpolation.</param> @@ -204,18 +358,45 @@ namespace Godot /// <param name="post">The value which after "to" value for interpolation.</param> /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> /// <returns>The resulting value of the interpolation.</returns> - public static real_t CubicInterpolateAngle(real_t from, real_t to, real_t pre, real_t post, real_t weight) + public static float CubicInterpolateAngle(float from, float to, float pre, float post, float weight) { - real_t fromRot = from % Mathf.Tau; + float fromRot = from % MathF.Tau; - real_t preDiff = (pre - fromRot) % Mathf.Tau; - real_t preRot = fromRot + (2.0f * preDiff) % Mathf.Tau - preDiff; + float preDiff = (pre - fromRot) % MathF.Tau; + float preRot = fromRot + (2.0f * preDiff) % MathF.Tau - preDiff; - real_t toDiff = (to - fromRot) % Mathf.Tau; - real_t toRot = fromRot + (2.0f * toDiff) % Mathf.Tau - toDiff; + float toDiff = (to - fromRot) % MathF.Tau; + float toRot = fromRot + (2.0f * toDiff) % MathF.Tau - toDiff; - real_t postDiff = (post - toRot) % Mathf.Tau; - real_t postRot = toRot + (2.0f * postDiff) % Mathf.Tau - postDiff; + float postDiff = (post - toRot) % MathF.Tau; + float postRot = toRot + (2.0f * postDiff) % MathF.Tau - postDiff; + + return CubicInterpolate(fromRot, toRot, preRot, postRot, weight); + } + + /// <summary> + /// Cubic interpolates between two rotation values with shortest path + /// by the factor defined in <paramref name="weight"/> with pre and post values. + /// See also <see cref="LerpAngle(double, double, double)"/>. + /// </summary> + /// <param name="from">The start value for interpolation.</param> + /// <param name="to">The destination value for interpolation.</param> + /// <param name="pre">The value which before "from" value for interpolation.</param> + /// <param name="post">The value which after "to" value for interpolation.</param> + /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> + /// <returns>The resulting value of the interpolation.</returns> + public static double CubicInterpolateAngle(double from, double to, double pre, double post, double weight) + { + double fromRot = from % Math.Tau; + + double preDiff = (pre - fromRot) % Math.Tau; + double preRot = fromRot + (2.0 * preDiff) % Math.Tau - preDiff; + + double toDiff = (to - fromRot) % Math.Tau; + double toRot = fromRot + (2.0 * toDiff) % Math.Tau - toDiff; + + double postDiff = (post - toRot) % Math.Tau; + double postRot = toRot + (2.0 * postDiff) % Math.Tau - postDiff; return CubicInterpolate(fromRot, toRot, preRot, postRot, weight); } @@ -223,7 +404,8 @@ namespace Godot /// <summary> /// Cubic interpolates between two values by the factor defined in <paramref name="weight"/> /// with pre and post values. - /// It can perform smoother interpolation than <see cref="CubicInterpolate"/> + /// It can perform smoother interpolation than + /// <see cref="CubicInterpolate(float, float, float, float, float)"/> /// by the time values. /// </summary> /// <param name="from">The start value for interpolation.</param> @@ -235,23 +417,52 @@ namespace Godot /// <param name="preT"></param> /// <param name="postT"></param> /// <returns>The resulting value of the interpolation.</returns> - public static real_t CubicInterpolateInTime(real_t from, real_t to, real_t pre, real_t post, real_t weight, real_t toT, real_t preT, real_t postT) + public static float CubicInterpolateInTime(float from, float to, float pre, float post, float weight, float toT, float preT, float postT) { /* Barry-Goldman method */ - real_t t = Lerp(0.0f, toT, weight); - real_t a1 = Lerp(pre, from, preT == 0 ? 0.0f : (t - preT) / -preT); - real_t a2 = Lerp(from, to, toT == 0 ? 0.5f : t / toT); - real_t a3 = Lerp(to, post, postT - toT == 0 ? 1.0f : (t - toT) / (postT - toT)); - real_t b1 = Lerp(a1, a2, toT - preT == 0 ? 0.0f : (t - preT) / (toT - preT)); - real_t b2 = Lerp(a2, a3, postT == 0 ? 1.0f : t / postT); + float t = Lerp(0.0f, toT, weight); + float a1 = Lerp(pre, from, preT == 0 ? 0.0f : (t - preT) / -preT); + float a2 = Lerp(from, to, toT == 0 ? 0.5f : t / toT); + float a3 = Lerp(to, post, postT - toT == 0 ? 1.0f : (t - toT) / (postT - toT)); + float b1 = Lerp(a1, a2, toT - preT == 0 ? 0.0f : (t - preT) / (toT - preT)); + float b2 = Lerp(a2, a3, postT == 0 ? 1.0f : t / postT); return Lerp(b1, b2, toT == 0 ? 0.5f : t / toT); } /// <summary> + /// Cubic interpolates between two values by the factor defined in <paramref name="weight"/> + /// with pre and post values. + /// It can perform smoother interpolation than + /// <see cref="CubicInterpolate(double, double, double, double, double)"/> + /// by the time values. + /// </summary> + /// <param name="from">The start value for interpolation.</param> + /// <param name="to">The destination value for interpolation.</param> + /// <param name="pre">The value which before "from" value for interpolation.</param> + /// <param name="post">The value which after "to" value for interpolation.</param> + /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> + /// <param name="toT"></param> + /// <param name="preT"></param> + /// <param name="postT"></param> + /// <returns>The resulting value of the interpolation.</returns> + public static double CubicInterpolateInTime(double from, double to, double pre, double post, double weight, double toT, double preT, double postT) + { + /* Barry-Goldman method */ + double t = Lerp(0.0, toT, weight); + double a1 = Lerp(pre, from, preT == 0 ? 0.0 : (t - preT) / -preT); + double a2 = Lerp(from, to, toT == 0 ? 0.5 : t / toT); + double a3 = Lerp(to, post, postT - toT == 0 ? 1.0 : (t - toT) / (postT - toT)); + double b1 = Lerp(a1, a2, toT - preT == 0 ? 0.0 : (t - preT) / (toT - preT)); + double b2 = Lerp(a2, a3, postT == 0 ? 1.0 : t / postT); + return Lerp(b1, b2, toT == 0 ? 0.5 : t / toT); + } + + /// <summary> /// Cubic interpolates between two rotation values with shortest path /// by the factor defined in <paramref name="weight"/> with pre and post values. - /// See also <see cref="LerpAngle"/>. - /// It can perform smoother interpolation than <see cref="CubicInterpolateAngle"/> + /// See also <see cref="LerpAngle(float, float, float)"/>. + /// It can perform smoother interpolation than + /// <see cref="CubicInterpolateAngle(float, float, float, float, float)"/> /// by the time values. /// </summary> /// <param name="from">The start value for interpolation.</param> @@ -263,24 +474,78 @@ namespace Godot /// <param name="preT"></param> /// <param name="postT"></param> /// <returns>The resulting value of the interpolation.</returns> - public static real_t CubicInterpolateAngleInTime(real_t from, real_t to, real_t pre, real_t post, real_t weight, - real_t toT, real_t preT, real_t postT) + public static float CubicInterpolateAngleInTime(float from, float to, float pre, float post, float weight, float toT, float preT, float postT) { - real_t fromRot = from % Mathf.Tau; + float fromRot = from % MathF.Tau; - real_t preDiff = (pre - fromRot) % Mathf.Tau; - real_t preRot = fromRot + (2.0f * preDiff) % Mathf.Tau - preDiff; + float preDiff = (pre - fromRot) % MathF.Tau; + float preRot = fromRot + (2.0f * preDiff) % MathF.Tau - preDiff; - real_t toDiff = (to - fromRot) % Mathf.Tau; - real_t toRot = fromRot + (2.0f * toDiff) % Mathf.Tau - toDiff; + float toDiff = (to - fromRot) % MathF.Tau; + float toRot = fromRot + (2.0f * toDiff) % MathF.Tau - toDiff; - real_t postDiff = (post - toRot) % Mathf.Tau; - real_t postRot = toRot + (2.0f * postDiff) % Mathf.Tau - postDiff; + float postDiff = (post - toRot) % MathF.Tau; + float postRot = toRot + (2.0f * postDiff) % MathF.Tau - postDiff; return CubicInterpolateInTime(fromRot, toRot, preRot, postRot, weight, toT, preT, postT); } /// <summary> + /// Cubic interpolates between two rotation values with shortest path + /// by the factor defined in <paramref name="weight"/> with pre and post values. + /// See also <see cref="LerpAngle(double, double, double)"/>. + /// It can perform smoother interpolation than + /// <see cref="CubicInterpolateAngle(double, double, double, double, double)"/> + /// by the time values. + /// </summary> + /// <param name="from">The start value for interpolation.</param> + /// <param name="to">The destination value for interpolation.</param> + /// <param name="pre">The value which before "from" value for interpolation.</param> + /// <param name="post">The value which after "to" value for interpolation.</param> + /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> + /// <param name="toT"></param> + /// <param name="preT"></param> + /// <param name="postT"></param> + /// <returns>The resulting value of the interpolation.</returns> + public static double CubicInterpolateAngleInTime(double from, double to, double pre, double post, double weight, double toT, double preT, double postT) + { + double fromRot = from % Math.Tau; + + double preDiff = (pre - fromRot) % Math.Tau; + double preRot = fromRot + (2.0 * preDiff) % Math.Tau - preDiff; + + double toDiff = (to - fromRot) % Math.Tau; + double toRot = fromRot + (2.0 * toDiff) % Math.Tau - toDiff; + + double postDiff = (post - toRot) % Math.Tau; + double postRot = toRot + (2.0 * postDiff) % Math.Tau - postDiff; + + return CubicInterpolateInTime(fromRot, toRot, preRot, postRot, weight, toT, preT, postT); + } + + /// <summary> + /// Returns the point at the given <paramref name="t"/> on a one-dimensional Bezier curve defined by + /// the given <paramref name="control1"/>, <paramref name="control2"/>, and <paramref name="end"/> points. + /// </summary> + /// <param name="start">The start value for the interpolation.</param> + /// <param name="control1">Control point that defines the bezier curve.</param> + /// <param name="control2">Control point that defines the bezier curve.</param> + /// <param name="end">The destination value for the interpolation.</param> + /// <param name="t">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> + /// <returns>The resulting value of the interpolation.</returns> + public static float BezierInterpolate(float start, float control1, float control2, float end, float t) + { + // Formula from Wikipedia article on Bezier curves + float omt = 1.0f - t; + float omt2 = omt * omt; + float omt3 = omt2 * omt; + float t2 = t * t; + float t3 = t2 * t; + + return start * omt3 + control1 * omt2 * t * 3.0f + control2 * omt * t2 * 3.0f + end * t3; + } + + /// <summary> /// Returns the point at the given <paramref name="t"/> on a one-dimensional Bezier curve defined by /// the given <paramref name="control1"/>, <paramref name="control2"/>, and <paramref name="end"/> points. /// </summary> @@ -290,16 +555,16 @@ namespace Godot /// <param name="end">The destination value for the interpolation.</param> /// <param name="t">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> /// <returns>The resulting value of the interpolation.</returns> - public static real_t BezierInterpolate(real_t start, real_t control1, real_t control2, real_t end, real_t t) + public static double BezierInterpolate(double start, double control1, double control2, double end, double t) { // Formula from Wikipedia article on Bezier curves - real_t omt = 1 - t; - real_t omt2 = omt * omt; - real_t omt3 = omt2 * omt; - real_t t2 = t * t; - real_t t3 = t2 * t; + double omt = 1.0 - t; + double omt2 = omt * omt; + double omt3 = omt2 * omt; + double t2 = t * t; + double t3 = t2 * t; - return start * omt3 + control1 * omt2 * t * 3 + control2 * omt * t2 * 3 + end * t3; + return start * omt3 + control1 * omt2 * t * 3.0 + control2 * omt * t2 * 3.0 + end * t3; } /// <summary> @@ -312,26 +577,68 @@ namespace Godot /// <param name="end">The destination value for the interpolation.</param> /// <param name="t">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> /// <returns>The resulting value of the interpolation.</returns> - public static real_t BezierDerivative(real_t start, real_t control1, real_t control2, real_t end, real_t t) + public static float BezierDerivative(float start, float control1, float control2, float end, float t) { // Formula from Wikipedia article on Bezier curves - real_t omt = 1 - t; - real_t omt2 = omt * omt; - real_t t2 = t * t; + float omt = 1.0f - t; + float omt2 = omt * omt; + float t2 = t * t; - real_t d = (control1 - start) * 3 * omt2 + (control2 - control1) * 6 * omt * t + (end - control2) * 3 * t2; + float d = (control1 - start) * 3.0f * omt2 + (control2 - control1) * 6.0f * omt * t + (end - control2) * 3.0f * t2; return d; } /// <summary> + /// Returns the derivative at the given <paramref name="t"/> on a one dimensional Bezier curve defined by + /// the given <paramref name="control1"/>, <paramref name="control2"/>, and <paramref name="end"/> points. + /// </summary> + /// <param name="start">The start value for the interpolation.</param> + /// <param name="control1">Control point that defines the bezier curve.</param> + /// <param name="control2">Control point that defines the bezier curve.</param> + /// <param name="end">The destination value for the interpolation.</param> + /// <param name="t">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> + /// <returns>The resulting value of the interpolation.</returns> + public static double BezierDerivative(double start, double control1, double control2, double end, double t) + { + // Formula from Wikipedia article on Bezier curves + double omt = 1.0 - t; + double omt2 = omt * omt; + double t2 = t * t; + + double d = (control1 - start) * 3.0 * omt2 + (control2 - control1) * 6.0 * omt * t + (end - control2) * 3.0 * t2; + return d; + } + + /// <summary> + /// Converts from decibels to linear energy (audio). + /// </summary> + /// <seealso cref="LinearToDb(float)"/> + /// <param name="db">Decibels to convert.</param> + /// <returns>Audio volume as linear energy.</returns> + public static float DbToLinear(float db) + { + return MathF.Exp(db * 0.11512925464970228420089957273422f); + } + + /// <summary> /// Converts from decibels to linear energy (audio). /// </summary> - /// <seealso cref="LinearToDb(real_t)"/> + /// <seealso cref="LinearToDb(double)"/> /// <param name="db">Decibels to convert.</param> /// <returns>Audio volume as linear energy.</returns> - public static real_t DbToLinear(real_t db) + public static double DbToLinear(double db) + { + return Math.Exp(db * 0.11512925464970228420089957273422); + } + + /// <summary> + /// Converts an angle expressed in degrees to radians. + /// </summary> + /// <param name="deg">An angle expressed in degrees.</param> + /// <returns>The same angle expressed in radians.</returns> + public static float DegToRad(float deg) { - return (real_t)Math.Exp(db * 0.11512925464970228420089957273422); + return deg * _degToRadConstF; } /// <summary> @@ -339,9 +646,9 @@ namespace Godot /// </summary> /// <param name="deg">An angle expressed in degrees.</param> /// <returns>The same angle expressed in radians.</returns> - public static real_t DegToRad(real_t deg) + public static double DegToRad(double deg) { - return deg * _degToRadConst; + return deg * _degToRadConstD; } /// <summary> @@ -354,38 +661,94 @@ namespace Godot /// <c>0</c> is constant, <c>1</c> is linear, <c>0</c> to <c>1</c> is ease-in, <c>1</c> or more is ease-out. /// </param> /// <returns>The eased value.</returns> - public static real_t Ease(real_t s, real_t curve) + public static float Ease(float s, float curve) { - if (s < 0f) + if (s < 0.0f) { - s = 0f; + s = 0.0f; } else if (s > 1.0f) { s = 1.0f; } - if (curve > 0f) + if (curve > 0.0f) { if (curve < 1.0f) { - return 1.0f - Pow(1.0f - s, 1.0f / curve); + return 1.0f - MathF.Pow(1.0f - s, 1.0f / curve); } - return Pow(s, curve); + return MathF.Pow(s, curve); } - if (curve < 0f) + if (curve < 0.0f) { if (s < 0.5f) { - return Pow(s * 2.0f, -curve) * 0.5f; + return MathF.Pow(s * 2.0f, -curve) * 0.5f; } - return ((1.0f - Pow(1.0f - ((s - 0.5f) * 2.0f), -curve)) * 0.5f) + 0.5f; + return ((1.0f - MathF.Pow(1.0f - ((s - 0.5f) * 2.0f), -curve)) * 0.5f) + 0.5f; } - return 0f; + return 0.0f; + } + + /// <summary> + /// Easing function, based on exponent. The <paramref name="curve"/> values are: + /// <c>0</c> is constant, <c>1</c> is linear, <c>0</c> to <c>1</c> is ease-in, <c>1</c> or more is ease-out. + /// Negative values are in-out/out-in. + /// </summary> + /// <param name="s">The value to ease.</param> + /// <param name="curve"> + /// <c>0</c> is constant, <c>1</c> is linear, <c>0</c> to <c>1</c> is ease-in, <c>1</c> or more is ease-out. + /// </param> + /// <returns>The eased value.</returns> + public static double Ease(double s, double curve) + { + if (s < 0.0) + { + s = 0.0; + } + else if (s > 1.0) + { + s = 1.0; + } + + if (curve > 0) + { + if (curve < 1.0) + { + return 1.0 - Math.Pow(1.0 - s, 1.0 / curve); + } + + return Math.Pow(s, curve); + } + + if (curve < 0.0) + { + if (s < 0.5) + { + return Math.Pow(s * 2.0, -curve) * 0.5; + } + + return ((1.0 - Math.Pow(1.0 - ((s - 0.5) * 2.0), -curve)) * 0.5) + 0.5; + } + + return 0.0; + } + + /// <summary> + /// The natural exponential function. It raises the mathematical + /// constant <c>e</c> to the power of <paramref name="s"/> and returns it. + /// </summary> + /// <param name="s">The exponent to raise <c>e</c> to.</param> + /// <returns><c>e</c> raised to the power of <paramref name="s"/>.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Exp(float s) + { + return MathF.Exp(s); } /// <summary> @@ -394,9 +757,21 @@ namespace Godot /// </summary> /// <param name="s">The exponent to raise <c>e</c> to.</param> /// <returns><c>e</c> raised to the power of <paramref name="s"/>.</returns> - public static real_t Exp(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Exp(double s) + { + return Math.Exp(s); + } + + /// <summary> + /// Rounds <paramref name="s"/> downward (towards negative infinity). + /// </summary> + /// <param name="s">The number to floor.</param> + /// <returns>The largest whole number that is not more than <paramref name="s"/>.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Floor(float s) { - return (real_t)Math.Exp(s); + return MathF.Floor(s); } /// <summary> @@ -404,14 +779,32 @@ namespace Godot /// </summary> /// <param name="s">The number to floor.</param> /// <returns>The largest whole number that is not more than <paramref name="s"/>.</returns> - public static real_t Floor(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Floor(double s) + { + return Math.Floor(s); + } + + /// <summary> + /// Returns a normalized value considering the given range. + /// This is the opposite of <see cref="Lerp(float, float, float)"/>. + /// </summary> + /// <param name="from">The start value for interpolation.</param> + /// <param name="to">The destination value for interpolation.</param> + /// <param name="weight">The interpolated value.</param> + /// <returns> + /// The resulting value of the inverse interpolation. + /// The returned value will be between 0.0 and 1.0 if <paramref name="weight"/> is + /// between <paramref name="from"/> and <paramref name="to"/> (inclusive). + /// </returns> + public static float InverseLerp(float from, float to, float weight) { - return (real_t)Math.Floor(s); + return (weight - from) / (to - from); } /// <summary> /// Returns a normalized value considering the given range. - /// This is the opposite of <see cref="Lerp(real_t, real_t, real_t)"/>. + /// This is the opposite of <see cref="Lerp(double, double, double)"/>. /// </summary> /// <param name="from">The start value for interpolation.</param> /// <param name="to">The destination value for interpolation.</param> @@ -421,7 +814,7 @@ namespace Godot /// The returned value will be between 0.0 and 1.0 if <paramref name="weight"/> is /// between <paramref name="from"/> and <paramref name="to"/> (inclusive). /// </returns> - public static real_t InverseLerp(real_t from, real_t to, real_t weight) + public static double InverseLerp(double from, double to, double weight) { return (weight - from) / (to - from); } @@ -434,7 +827,7 @@ namespace Godot /// <param name="a">One of the values.</param> /// <param name="b">The other value.</param> /// <returns>A <see langword="bool"/> for whether or not the two values are approximately equal.</returns> - public static bool IsEqualApprox(real_t a, real_t b) + public static bool IsEqualApprox(float a, float b) { // Check for exact equality first, required to handle "infinity" values. if (a == b) @@ -442,12 +835,36 @@ namespace Godot return true; } // Then check for approximate equality. - real_t tolerance = Epsilon * Abs(a); - if (tolerance < Epsilon) + float tolerance = _epsilonF * Math.Abs(a); + if (tolerance < _epsilonF) { - tolerance = Epsilon; + tolerance = _epsilonF; } - return Abs(a - b) < tolerance; + return Math.Abs(a - b) < tolerance; + } + + /// <summary> + /// Returns <see langword="true"/> if <paramref name="a"/> and <paramref name="b"/> are approximately equal + /// to each other. + /// The comparison is done using a tolerance calculation with <see cref="Epsilon"/>. + /// </summary> + /// <param name="a">One of the values.</param> + /// <param name="b">The other value.</param> + /// <returns>A <see langword="bool"/> for whether or not the two values are approximately equal.</returns> + public static bool IsEqualApprox(double a, double b) + { + // Check for exact equality first, required to handle "infinity" values. + if (a == b) + { + return true; + } + // Then check for approximate equality. + double tolerance = _epsilonD * Math.Abs(a); + if (tolerance < _epsilonD) + { + tolerance = _epsilonD; + } + return Math.Abs(a - b) < tolerance; } /// <summary> @@ -456,9 +873,22 @@ namespace Godot /// </summary> /// <param name="s">The value to check.</param> /// <returns>A <see langword="bool"/> for whether or not the value is a finite value.</returns> - public static bool IsFinite(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static bool IsFinite(float s) { - return real_t.IsFinite(s); + return float.IsFinite(s); + } + + /// <summary> + /// Returns whether <paramref name="s"/> is a finite value, i.e. it is not + /// <see cref="NaN"/>, positive infinite, or negative infinity. + /// </summary> + /// <param name="s">The value to check.</param> + /// <returns>A <see langword="bool"/> for whether or not the value is a finite value.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static bool IsFinite(double s) + { + return double.IsFinite(s); } /// <summary> @@ -466,9 +896,32 @@ namespace Godot /// </summary> /// <param name="s">The value to check.</param> /// <returns>A <see langword="bool"/> for whether or not the value is an infinity value.</returns> - public static bool IsInf(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static bool IsInf(float s) { - return real_t.IsInfinity(s); + return float.IsInfinity(s); + } + + /// <summary> + /// Returns whether <paramref name="s"/> is an infinity value (either positive infinity or negative infinity). + /// </summary> + /// <param name="s">The value to check.</param> + /// <returns>A <see langword="bool"/> for whether or not the value is an infinity value.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static bool IsInf(double s) + { + return double.IsInfinity(s); + } + + /// <summary> + /// Returns whether <paramref name="s"/> is a <c>NaN</c> ("Not a Number" or invalid) value. + /// </summary> + /// <param name="s">The value to check.</param> + /// <returns>A <see langword="bool"/> for whether or not the value is a <c>NaN</c> value.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static bool IsNaN(float s) + { + return float.IsNaN(s); } /// <summary> @@ -476,34 +929,64 @@ namespace Godot /// </summary> /// <param name="s">The value to check.</param> /// <returns>A <see langword="bool"/> for whether or not the value is a <c>NaN</c> value.</returns> - public static bool IsNaN(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static bool IsNaN(double s) { - return real_t.IsNaN(s); + return double.IsNaN(s); } /// <summary> /// Returns <see langword="true"/> if <paramref name="s"/> is zero or almost zero. /// The comparison is done using a tolerance calculation with <see cref="Epsilon"/>. /// - /// This method is faster than using <see cref="IsEqualApprox(real_t, real_t)"/> with + /// This method is faster than using <see cref="IsEqualApprox(float, float)"/> with /// one value as zero. /// </summary> /// <param name="s">The value to check.</param> /// <returns>A <see langword="bool"/> for whether or not the value is nearly zero.</returns> - public static bool IsZeroApprox(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static bool IsZeroApprox(float s) { - return Abs(s) < Epsilon; + return Math.Abs(s) < _epsilonF; + } + + /// <summary> + /// Returns <see langword="true"/> if <paramref name="s"/> is zero or almost zero. + /// The comparison is done using a tolerance calculation with <see cref="Epsilon"/>. + /// + /// This method is faster than using <see cref="IsEqualApprox(double, double)"/> with + /// one value as zero. + /// </summary> + /// <param name="s">The value to check.</param> + /// <returns>A <see langword="bool"/> for whether or not the value is nearly zero.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static bool IsZeroApprox(double s) + { + return Math.Abs(s) < _epsilonD; + } + + /// <summary> + /// Linearly interpolates between two values by a normalized value. + /// This is the opposite <see cref="InverseLerp(float, float, float)"/>. + /// </summary> + /// <param name="from">The start value for interpolation.</param> + /// <param name="to">The destination value for interpolation.</param> + /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> + /// <returns>The resulting value of the interpolation.</returns> + public static float Lerp(float from, float to, float weight) + { + return from + ((to - from) * weight); } /// <summary> /// Linearly interpolates between two values by a normalized value. - /// This is the opposite <see cref="InverseLerp(real_t, real_t, real_t)"/>. + /// This is the opposite <see cref="InverseLerp(double, double, double)"/>. /// </summary> /// <param name="from">The start value for interpolation.</param> /// <param name="to">The destination value for interpolation.</param> /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> /// <returns>The resulting value of the interpolation.</returns> - public static real_t Lerp(real_t from, real_t to, real_t weight) + public static double Lerp(double from, double to, double weight) { return from + ((to - from) * weight); } @@ -511,17 +994,34 @@ namespace Godot /// <summary> /// Linearly interpolates between two angles (in radians) by a normalized value. /// - /// Similar to <see cref="Lerp(real_t, real_t, real_t)"/>, + /// Similar to <see cref="Lerp(float, float, float)"/>, + /// but interpolates correctly when the angles wrap around <see cref="Tau"/>. + /// </summary> + /// <param name="from">The start angle for interpolation.</param> + /// <param name="to">The destination angle for interpolation.</param> + /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> + /// <returns>The resulting angle of the interpolation.</returns> + public static float LerpAngle(float from, float to, float weight) + { + float difference = (to - from) % MathF.Tau; + float distance = ((2 * difference) % MathF.Tau) - difference; + return from + (distance * weight); + } + + /// <summary> + /// Linearly interpolates between two angles (in radians) by a normalized value. + /// + /// Similar to <see cref="Lerp(double, double, double)"/>, /// but interpolates correctly when the angles wrap around <see cref="Tau"/>. /// </summary> /// <param name="from">The start angle for interpolation.</param> /// <param name="to">The destination angle for interpolation.</param> /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param> /// <returns>The resulting angle of the interpolation.</returns> - public static real_t LerpAngle(real_t from, real_t to, real_t weight) + public static double LerpAngle(double from, double to, double weight) { - real_t difference = (to - from) % Mathf.Tau; - real_t distance = ((2 * difference) % Mathf.Tau) - difference; + double difference = (to - from) % Math.Tau; + double distance = ((2 * difference) % Math.Tau) - difference; return from + (distance * weight); } @@ -529,7 +1029,7 @@ namespace Godot /// Converts from linear energy to decibels (audio). /// This can be used to implement volume sliders that behave as expected (since volume isn't linear). /// </summary> - /// <seealso cref="DbToLinear(real_t)"/> + /// <seealso cref="DbToLinear(float)"/> /// <example> /// <code> /// // "slider" refers to a node that inherits Range such as HSlider or VSlider. @@ -540,9 +1040,42 @@ namespace Godot /// </example> /// <param name="linear">The linear energy to convert.</param> /// <returns>Audio as decibels.</returns> - public static real_t LinearToDb(real_t linear) + public static float LinearToDb(float linear) { - return (real_t)(Math.Log(linear) * 8.6858896380650365530225783783321); + return MathF.Log(linear) * 8.6858896380650365530225783783321f; + } + + /// <summary> + /// Converts from linear energy to decibels (audio). + /// This can be used to implement volume sliders that behave as expected (since volume isn't linear). + /// </summary> + /// <seealso cref="DbToLinear(double)"/> + /// <example> + /// <code> + /// // "slider" refers to a node that inherits Range such as HSlider or VSlider. + /// // Its range must be configured to go from 0 to 1. + /// // Change the bus name if you'd like to change the volume of a specific bus only. + /// AudioServer.SetBusVolumeDb(AudioServer.GetBusIndex("Master"), GD.LinearToDb(slider.value)); + /// </code> + /// </example> + /// <param name="linear">The linear energy to convert.</param> + /// <returns>Audio as decibels.</returns> + public static double LinearToDb(double linear) + { + return Math.Log(linear) * 8.6858896380650365530225783783321; + } + + /// <summary> + /// Natural logarithm. The amount of time needed to reach a certain level of continuous growth. + /// + /// Note: This is not the same as the "log" function on most calculators, which uses a base 10 logarithm. + /// </summary> + /// <param name="s">The input value.</param> + /// <returns>The natural log of <paramref name="s"/>.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Log(float s) + { + return MathF.Log(s); } /// <summary> @@ -552,9 +1085,10 @@ namespace Godot /// </summary> /// <param name="s">The input value.</param> /// <returns>The natural log of <paramref name="s"/>.</returns> - public static real_t Log(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Log(double s) { - return (real_t)Math.Log(s); + return Math.Log(s); } /// <summary> @@ -563,9 +1097,22 @@ namespace Godot /// <param name="a">One of the values.</param> /// <param name="b">The other value.</param> /// <returns>Whichever of the two values is higher.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] public static int Max(int a, int b) { - return a > b ? a : b; + return Math.Max(a, b); + } + + /// <summary> + /// Returns the maximum of two values. + /// </summary> + /// <param name="a">One of the values.</param> + /// <param name="b">The other value.</param> + /// <returns>Whichever of the two values is higher.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Max(float a, float b) + { + return Math.Max(a, b); } /// <summary> @@ -574,9 +1121,10 @@ namespace Godot /// <param name="a">One of the values.</param> /// <param name="b">The other value.</param> /// <returns>Whichever of the two values is higher.</returns> - public static real_t Max(real_t a, real_t b) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Max(double a, double b) { - return a > b ? a : b; + return Math.Max(a, b); } /// <summary> @@ -585,9 +1133,22 @@ namespace Godot /// <param name="a">One of the values.</param> /// <param name="b">The other value.</param> /// <returns>Whichever of the two values is lower.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] public static int Min(int a, int b) { - return a < b ? a : b; + return Math.Min(a, b); + } + + /// <summary> + /// Returns the minimum of two values. + /// </summary> + /// <param name="a">One of the values.</param> + /// <param name="b">The other value.</param> + /// <returns>Whichever of the two values is lower.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Min(float a, float b) + { + return Math.Min(a, b); } /// <summary> @@ -596,9 +1157,27 @@ namespace Godot /// <param name="a">One of the values.</param> /// <param name="b">The other value.</param> /// <returns>Whichever of the two values is lower.</returns> - public static real_t Min(real_t a, real_t b) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Min(double a, double b) + { + return Math.Min(a, b); + } + + /// <summary> + /// Moves <paramref name="from"/> toward <paramref name="to"/> by the <paramref name="delta"/> value. + /// + /// Use a negative <paramref name="delta"/> value to move away. + /// </summary> + /// <param name="from">The start value.</param> + /// <param name="to">The value to move towards.</param> + /// <param name="delta">The amount to move by.</param> + /// <returns>The value after moving.</returns> + public static float MoveToward(float from, float to, float delta) { - return a < b ? a : b; + if (Math.Abs(to - from) <= delta) + return to; + + return from + (Math.Sign(to - from) * delta); } /// <summary> @@ -610,12 +1189,12 @@ namespace Godot /// <param name="to">The value to move towards.</param> /// <param name="delta">The amount to move by.</param> /// <returns>The value after moving.</returns> - public static real_t MoveToward(real_t from, real_t to, real_t delta) + public static double MoveToward(double from, double to, double delta) { - if (Abs(to - from) <= delta) + if (Math.Abs(to - from) <= delta) return to; - return from + (Sign(to - from) * delta); + return from + (Math.Sign(to - from) * delta); } /// <summary> @@ -657,9 +1236,25 @@ namespace Godot /// <param name="a">The dividend, the primary input.</param> /// <param name="b">The divisor. The output is on the range [0, <paramref name="b"/>).</param> /// <returns>The resulting output.</returns> - public static real_t PosMod(real_t a, real_t b) + public static float PosMod(float a, float b) + { + float c = a % b; + if ((c < 0 && b > 0) || (c > 0 && b < 0)) + { + c += b; + } + return c; + } + + /// <summary> + /// Performs a canonical Modulus operation, where the output is on the range [0, <paramref name="b"/>). + /// </summary> + /// <param name="a">The dividend, the primary input.</param> + /// <param name="b">The divisor. The output is on the range [0, <paramref name="b"/>).</param> + /// <returns>The resulting output.</returns> + public static double PosMod(double a, double b) { - real_t c = a % b; + double c = a % b; if ((c < 0 && b > 0) || (c > 0 && b < 0)) { c += b; @@ -673,9 +1268,22 @@ namespace Godot /// <param name="x">The base.</param> /// <param name="y">The exponent.</param> /// <returns><paramref name="x"/> raised to the power of <paramref name="y"/>.</returns> - public static real_t Pow(real_t x, real_t y) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Pow(float x, float y) + { + return MathF.Pow(x, y); + } + + /// <summary> + /// Returns the result of <paramref name="x"/> raised to the power of <paramref name="y"/>. + /// </summary> + /// <param name="x">The base.</param> + /// <param name="y">The exponent.</param> + /// <returns><paramref name="x"/> raised to the power of <paramref name="y"/>.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Pow(double x, double y) { - return (real_t)Math.Pow(x, y); + return Math.Pow(x, y); } /// <summary> @@ -683,9 +1291,21 @@ namespace Godot /// </summary> /// <param name="rad">An angle expressed in radians.</param> /// <returns>The same angle expressed in degrees.</returns> - public static real_t RadToDeg(real_t rad) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float RadToDeg(float rad) { - return rad * _radToDegConst; + return rad * _radToDegConstF; + } + + /// <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> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double RadToDeg(double rad) + { + return rad * _radToDegConstD; } /// <summary> @@ -698,20 +1318,48 @@ namespace Godot /// <param name="outFrom">The start value for the output interpolation.</param> /// <param name="outTo">The destination value for the output interpolation.</param> /// <returns>The resulting mapped value mapped.</returns> - public static real_t Remap(real_t value, real_t inFrom, real_t inTo, real_t outFrom, real_t outTo) + public static float Remap(float value, float inFrom, float inTo, float outFrom, float outTo) { return Lerp(outFrom, outTo, InverseLerp(inFrom, inTo, value)); } /// <summary> + /// Maps a <paramref name="value"/> from [<paramref name="inFrom"/>, <paramref name="inTo"/>] + /// to [<paramref name="outFrom"/>, <paramref name="outTo"/>]. + /// </summary> + /// <param name="value">The value to map.</param> + /// <param name="inFrom">The start value for the input interpolation.</param> + /// <param name="inTo">The destination value for the input interpolation.</param> + /// <param name="outFrom">The start value for the output interpolation.</param> + /// <param name="outTo">The destination value for the output interpolation.</param> + /// <returns>The resulting mapped value mapped.</returns> + public static double Remap(double value, double inFrom, double inTo, double outFrom, double outTo) + { + return Lerp(outFrom, outTo, InverseLerp(inFrom, inTo, value)); + } + + /// <summary> + /// Rounds <paramref name="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> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Round(float s) + { + return MathF.Round(s); + } + + /// <summary> /// Rounds <paramref name="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) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Round(double s) { - return (real_t)Math.Round(s); + return Math.Round(s); } /// <summary> @@ -720,11 +1368,10 @@ namespace Godot /// </summary> /// <param name="s">The input number.</param> /// <returns>One of three possible values: <c>1</c>, <c>-1</c>, or <c>0</c>.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] public static int Sign(int s) { - if (s == 0) - return 0; - return s < 0 ? -1 : 1; + return Math.Sign(s); } /// <summary> @@ -733,11 +1380,33 @@ namespace Godot /// </summary> /// <param name="s">The input number.</param> /// <returns>One of three possible values: <c>1</c>, <c>-1</c>, or <c>0</c>.</returns> - public static int Sign(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static int Sign(float s) { - if (s == 0) - return 0; - return s < 0 ? -1 : 1; + return Math.Sign(s); + } + + /// <summary> + /// Returns the sign of <paramref name="s"/>: <c>-1</c> or <c>1</c>. + /// Returns <c>0</c> if <paramref name="s"/> is <c>0</c>. + /// </summary> + /// <param name="s">The input number.</param> + /// <returns>One of three possible values: <c>1</c>, <c>-1</c>, or <c>0</c>.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static int Sign(double s) + { + return Math.Sign(s); + } + + /// <summary> + /// Returns the sine of angle <paramref name="s"/> in radians. + /// </summary> + /// <param name="s">The angle in radians.</param> + /// <returns>The sine of that angle.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Sin(float s) + { + return MathF.Sin(s); } /// <summary> @@ -745,9 +1414,21 @@ namespace Godot /// </summary> /// <param name="s">The angle in radians.</param> /// <returns>The sine of that angle.</returns> - public static real_t Sin(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Sin(double s) + { + return Math.Sin(s); + } + + /// <summary> + /// Returns the hyperbolic sine of angle <paramref name="s"/> in radians. + /// </summary> + /// <param name="s">The angle in radians.</param> + /// <returns>The hyperbolic sine of that angle.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Sinh(float s) { - return (real_t)Math.Sin(s); + return MathF.Sinh(s); } /// <summary> @@ -755,27 +1436,47 @@ namespace Godot /// </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) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Sinh(double s) + { + return Math.Sinh(s); + } + + /// <summary> + /// Returns a number smoothly interpolated between <paramref name="from"/> and <paramref name="to"/>, + /// based on the <paramref name="weight"/>. Similar to <see cref="Lerp(float, float, float)"/>, + /// 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 float SmoothStep(float from, float to, float weight) { - return (real_t)Math.Sinh(s); + if (IsEqualApprox(from, to)) + { + return from; + } + float x = Math.Clamp((weight - from) / (to - from), 0.0f, 1.0f); + return x * x * (3 - (2 * x)); } /// <summary> /// Returns a number smoothly interpolated between <paramref name="from"/> and <paramref name="to"/>, - /// based on the <paramref name="weight"/>. Similar to <see cref="Lerp(real_t, real_t, real_t)"/>, + /// based on the <paramref name="weight"/>. Similar to <see cref="Lerp(double, double, double)"/>, /// 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) + public static double SmoothStep(double from, double to, double weight) { if (IsEqualApprox(from, to)) { return from; } - real_t x = Clamp((weight - from) / (to - from), (real_t)0.0, (real_t)1.0); + double x = Math.Clamp((weight - from) / (to - from), 0.0, 1.0); return x * x * (3 - (2 * x)); } @@ -786,9 +1487,23 @@ namespace Godot /// </summary> /// <param name="s">The input number. Must not be negative.</param> /// <returns>The square root of <paramref name="s"/>.</returns> - public static real_t Sqrt(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Sqrt(float s) { - return (real_t)Math.Sqrt(s); + return MathF.Sqrt(s); + } + + /// <summary> + /// Returns the square root of <paramref name="s"/>, where <paramref name="s"/> is a non-negative number. + /// + /// If you need negative inputs, use <see cref="System.Numerics.Complex"/>. + /// </summary> + /// <param name="s">The input number. Must not be negative.</param> + /// <returns>The square root of <paramref name="s"/>.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Sqrt(double s) + { + return Math.Sqrt(s); } /// <summary> @@ -798,7 +1513,7 @@ namespace Godot /// </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) + public static int StepDecimals(double step) { double[] sd = new double[] { @@ -812,7 +1527,7 @@ namespace Godot 0.00000009999, 0.000000009999, }; - double abs = Abs(step); + double abs = Math.Abs(step); double decs = abs - (int)abs; // Strip away integer part for (int i = 0; i < sd.Length; i++) { @@ -831,11 +1546,28 @@ namespace Godot /// <param name="s">The value to snap.</param> /// <param name="step">The step size to snap to.</param> /// <returns>The snapped value.</returns> - public static real_t Snapped(real_t s, real_t step) + public static float Snapped(float s, float step) + { + if (step != 0f) + { + return MathF.Floor((s / step) + 0.5f) * step; + } + + return s; + } + + /// <summary> + /// Snaps float value <paramref name="s"/> to a given <paramref name="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>The snapped value.</returns> + public static double Snapped(double s, double step) { if (step != 0f) { - return Floor((s / step) + 0.5f) * step; + return Math.Floor((s / step) + 0.5f) * step; } return s; @@ -846,9 +1578,32 @@ namespace Godot /// </summary> /// <param name="s">The angle in radians.</param> /// <returns>The tangent of that angle.</returns> - public static real_t Tan(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Tan(float s) + { + return MathF.Tan(s); + } + + /// <summary> + /// Returns the tangent of angle <paramref name="s"/> in radians. + /// </summary> + /// <param name="s">The angle in radians.</param> + /// <returns>The tangent of that angle.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Tan(double s) + { + return Math.Tan(s); + } + + /// <summary> + /// Returns the hyperbolic tangent of angle <paramref name="s"/> in radians. + /// </summary> + /// <param name="s">The angle in radians.</param> + /// <returns>The hyperbolic tangent of that angle.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static float Tanh(float s) { - return (real_t)Math.Tan(s); + return MathF.Tanh(s); } /// <summary> @@ -856,9 +1611,10 @@ namespace Godot /// </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) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static double Tanh(double s) { - return (real_t)Math.Tanh(s); + return Math.Tanh(s); } /// <summary> @@ -884,15 +1640,35 @@ namespace Godot /// Wraps <paramref name="value"/> between <paramref name="min"/> and <paramref name="max"/>. /// Usable for creating loop-alike behavior or infinite surfaces. /// If <paramref name="min"/> is <c>0</c>, this is equivalent - /// to <see cref="PosMod(real_t, real_t)"/>, so prefer using that instead. + /// to <see cref="PosMod(float, float)"/>, 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 float Wrap(float value, float min, float max) + { + float range = max - min; + if (IsZeroApprox(range)) + { + return min; + } + return min + ((((value - min) % range) + range) % range); + } + + /// <summary> + /// Wraps <paramref name="value"/> between <paramref name="min"/> and <paramref name="max"/>. + /// Usable for creating loop-alike behavior or infinite surfaces. + /// If <paramref name="min"/> is <c>0</c>, this is equivalent + /// to <see cref="PosMod(double, double)"/>, 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) + public static double Wrap(double value, double min, double max) { - real_t range = max - min; + double range = max - min; if (IsZeroApprox(range)) { return min; @@ -900,9 +1676,23 @@ namespace Godot return min + ((((value - min) % range) + range) % range); } - private static real_t Fract(real_t value) + /// <summary> + /// Returns the <paramref name="value"/> wrapped between <c>0</c> and the <paramref name="length"/>. + /// If the limit is reached, the next value the function returned is decreased to the <c>0</c> side + /// or increased to the <paramref name="length"/> side (like a triangle wave). + /// If <paramref name="length"/> is less than zero, it becomes positive. + /// </summary> + /// <param name="value">The value to pingpong.</param> + /// <param name="length">The maximum value of the function.</param> + /// <returns>The ping-ponged value.</returns> + public static float PingPong(float value, float length) { - return value - (real_t)Math.Floor(value); + return (length != 0.0f) ? Math.Abs(Fract((value - length) / (length * 2.0f)) * length * 2.0f - length) : 0.0f; + + static float Fract(float value) + { + return value - MathF.Floor(value); + } } /// <summary> @@ -914,9 +1704,14 @@ namespace Godot /// <param name="value">The value to pingpong.</param> /// <param name="length">The maximum value of the function.</param> /// <returns>The ping-ponged value.</returns> - public static real_t PingPong(real_t value, real_t length) + public static double PingPong(double value, double length) { - return (length != (real_t)0.0) ? Abs(Fract((value - length) / (length * (real_t)2.0)) * length * (real_t)2.0 - length) : (real_t)0.0; + return (length != 0.0) ? Math.Abs(Fract((value - length) / (length * 2.0)) * length * 2.0 - length) : 0.0; + + static double Fract(double value) + { + return value - Math.Floor(value); + } } } } diff --git a/modules/mono/glue/GodotSharp/GodotSharp/Core/MathfEx.cs b/modules/mono/glue/GodotSharp/GodotSharp/Core/MathfEx.cs index 72a1868964..cc2d61f58d 100644 --- a/modules/mono/glue/GodotSharp/GodotSharp/Core/MathfEx.cs +++ b/modules/mono/glue/GodotSharp/GodotSharp/Core/MathfEx.cs @@ -1,4 +1,8 @@ using System; +using System.Runtime.CompilerServices; + +// This file contains extra members for the Mathf class that aren't part of Godot's Core API. +// Math API that is also part of Core should go into Mathf.cs. namespace Godot { @@ -16,14 +20,18 @@ namespace Godot /// </summary> public const real_t Sqrt2 = (real_t)1.4142135623730950488016887242M; // 1.4142136f and 1.414213562373095 + // Epsilon size should depend on the precision used. + private const float _epsilonF = 1e-06f; + private const double _epsilonD = 1e-14; + /// <summary> /// A very small number used for float comparison with error tolerance. /// 1e-06 with single-precision floats, but 1e-14 if <c>REAL_T_IS_DOUBLE</c>. /// </summary> #if REAL_T_IS_DOUBLE - public const real_t Epsilon = 1e-14; // Epsilon size should depend on the precision used. + public const real_t Epsilon = _epsilonD; #else - public const real_t Epsilon = 1e-06f; + public const real_t Epsilon = _epsilonF; #endif /// <summary> @@ -31,7 +39,8 @@ namespace Godot /// </summary> /// <param name="s">The input value.</param> /// <returns>The amount of digits.</returns> - public static int DecimalCount(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static int DecimalCount(double s) { return DecimalCount((decimal)s); } @@ -41,6 +50,7 @@ namespace Godot /// </summary> /// <param name="s">The input <see langword="decimal"/> value.</param> /// <returns>The amount of digits.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] public static int DecimalCount(decimal s) { return BitConverter.GetBytes(decimal.GetBits(s)[3])[2]; @@ -49,11 +59,25 @@ namespace Godot /// <summary> /// Rounds <paramref name="s"/> upward (towards positive infinity). /// - /// This is the same as <see cref="Ceil(real_t)"/>, but returns an <see langword="int"/>. + /// This is the same as <see cref="Ceil(float)"/>, but returns an <see langword="int"/>. + /// </summary> + /// <param name="s">The number to ceil.</param> + /// <returns>The smallest whole number that is not less than <paramref name="s"/>.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static int CeilToInt(float s) + { + return (int)MathF.Ceiling(s); + } + + /// <summary> + /// Rounds <paramref name="s"/> upward (towards positive infinity). + /// + /// This is the same as <see cref="Ceil(double)"/>, but returns an <see langword="int"/>. /// </summary> /// <param name="s">The number to ceil.</param> /// <returns>The smallest whole number that is not less than <paramref name="s"/>.</returns> - public static int CeilToInt(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static int CeilToInt(double s) { return (int)Math.Ceiling(s); } @@ -61,11 +85,25 @@ namespace Godot /// <summary> /// Rounds <paramref name="s"/> downward (towards negative infinity). /// - /// This is the same as <see cref="Floor(real_t)"/>, but returns an <see langword="int"/>. + /// This is the same as <see cref="Floor(float)"/>, but returns an <see langword="int"/>. + /// </summary> + /// <param name="s">The number to floor.</param> + /// <returns>The largest whole number that is not more than <paramref name="s"/>.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static int FloorToInt(float s) + { + return (int)MathF.Floor(s); + } + + /// <summary> + /// Rounds <paramref name="s"/> downward (towards negative infinity). + /// + /// This is the same as <see cref="Floor(double)"/>, but returns an <see langword="int"/>. /// </summary> /// <param name="s">The number to floor.</param> /// <returns>The largest whole number that is not more than <paramref name="s"/>.</returns> - public static int FloorToInt(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static int FloorToInt(double s) { return (int)Math.Floor(s); } @@ -73,11 +111,25 @@ namespace Godot /// <summary> /// Rounds <paramref name="s"/> to the nearest whole number. /// - /// This is the same as <see cref="Round(real_t)"/>, but returns an <see langword="int"/>. + /// This is the same as <see cref="Round(float)"/>, but returns an <see langword="int"/>. /// </summary> /// <param name="s">The number to round.</param> /// <returns>The rounded number.</returns> - public static int RoundToInt(real_t s) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static int RoundToInt(float s) + { + return (int)MathF.Round(s); + } + + /// <summary> + /// Rounds <paramref name="s"/> to the nearest whole number. + /// + /// This is the same as <see cref="Round(double)"/>, but returns an <see langword="int"/>. + /// </summary> + /// <param name="s">The number to round.</param> + /// <returns>The rounded number.</returns> + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static int RoundToInt(double s) { return (int)Math.Round(s); } @@ -87,23 +139,53 @@ namespace Godot /// </summary> /// <param name="s">The angle in radians.</param> /// <returns>The sine and cosine of that angle.</returns> - public static (real_t Sin, real_t Cos) SinCos(real_t s) + public static (float Sin, float Cos) SinCos(float s) + { + return MathF.SinCos(s); + } + + /// <summary> + /// Returns the sine and cosine of angle <paramref name="s"/> in radians. + /// </summary> + /// <param name="s">The angle in radians.</param> + /// <returns>The sine and cosine of that angle.</returns> + public static (double Sin, double Cos) SinCos(double s) { - (double sin, double cos) = Math.SinCos(s); - return ((real_t)sin, (real_t)cos); + return Math.SinCos(s); + } + + /// <summary> + /// Returns <see langword="true"/> if <paramref name="a"/> and <paramref name="b"/> are approximately + /// equal to each other. + /// The comparison is done using the provided tolerance value. + /// If you want the tolerance to be calculated for you, use <see cref="IsEqualApprox(float, float)"/>. + /// </summary> + /// <param name="a">One of the values.</param> + /// <param name="b">The other value.</param> + /// <param name="tolerance">The pre-calculated tolerance value.</param> + /// <returns>A <see langword="bool"/> for whether or not the two values are equal.</returns> + public static bool IsEqualApprox(float a, float b, float tolerance) + { + // Check for exact equality first, required to handle "infinity" values. + if (a == b) + { + return true; + } + // Then check for approximate equality. + return Math.Abs(a - b) < tolerance; } /// <summary> /// Returns <see langword="true"/> if <paramref name="a"/> and <paramref name="b"/> are approximately /// equal to each other. /// The comparison is done using the provided tolerance value. - /// If you want the tolerance to be calculated for you, use <see cref="IsEqualApprox(real_t, real_t)"/>. + /// If you want the tolerance to be calculated for you, use <see cref="IsEqualApprox(double, double)"/>. /// </summary> /// <param name="a">One of the values.</param> /// <param name="b">The other value.</param> /// <param name="tolerance">The pre-calculated tolerance value.</param> /// <returns>A <see langword="bool"/> for whether or not the two values are equal.</returns> - public static bool IsEqualApprox(real_t a, real_t b, real_t tolerance) + public static bool IsEqualApprox(double a, double b, double tolerance) { // Check for exact equality first, required to handle "infinity" values. if (a == b) @@ -111,7 +193,7 @@ namespace Godot return true; } // Then check for approximate equality. - return Abs(a - b) < tolerance; + return Math.Abs(a - b) < tolerance; } } } |