Merge branch 'math-double' of git://github.com/jb-perrier/FlaxEngine into jb-perrier-math-double

Source/Engine/Core/Math/Math.h

@@ -141,11 +141,6 @@ namespace Math
         return exp2f(value);
     }
 
-    static FORCE_INLINE double Abs(const double value)
-    {
-        return fabs(value);
-    }
-
     static FORCE_INLINE float Abs(const float value)
     {
         return fabsf(value);
@@ -161,11 +156,6 @@ namespace Math
         return value < 0 ? -value : value;
     }
 
-    static FORCE_INLINE double Mod(const double a, const double b)
-    {
-        return fmod(a, b);
-    }
-
     static FORCE_INLINE float Mod(const float a, const float b)
     {
         return fmodf(a, b);
@@ -435,14 +425,6 @@ namespace Math
         return amount <= 0 ? 0 : amount >= 1 ? 1 : amount * amount * amount * (amount * (amount * 6 - 15) + 10);
     }
 
-    // Determines whether the specified value is close to zero (0.0)
-    // @param a The floating value
-    // @returns True if the specified value is close to zero (0.0). otherwise false
-    inline bool IsZero(double a)
-    {
-        return Abs(a) < 1e-7;
-    }
-
     // Determines whether the specified value is close to zero (0.0f)
     // @param a The floating value
     // @returns True if the specified value is close to zero (0.0f). otherwise false

Source/Engine/Core/Math/Mathd.h

@@ -0,0 +1,362 @@
+// Copyright (c) 2012-2021 Wojciech Figat. All rights reserved.
+
+#pragma once
+
+#include <math.h>
+#include "Engine/Core/Types/BaseTypes.h"
+
+namespace Math
+{
+    /// <summary>
+    /// Computes the sine and cosine of a scalar double.
+    /// </summary>
+    /// <param name="angle">The input angle (in radians).</param>
+    /// <param name="sine">The output sine value.</param>
+    /// <param name="cosine">The output cosine value.</param>
+    FLAXENGINE_API void SinCos(double angle, double& sine, double& cosine);
+
+    static FORCE_INLINE double Trunc(double value)
+    {
+        return trunc(value);
+    }
+
+    static FORCE_INLINE double Round(double value)
+    {
+        return round(value);
+    }
+
+    static FORCE_INLINE double Floor(double value)
+    {
+        return floor(value);
+    }
+
+    static FORCE_INLINE double Ceil(double value)
+    {
+        return ceil(value);
+    }
+
+    static FORCE_INLINE double Sin(double value)
+    {
+        return sin(value);
+    }
+
+    static FORCE_INLINE double Asin(double value)
+    {
+        return asin(value < -1. ? -1. : value < 1. ? value : 1.);
+    }
+
+    static FORCE_INLINE double Sinh(double value)
+    {
+        return sinh(value);
+    }
+
+    static FORCE_INLINE double Cos(double value)
+    {
+        return cos(value);
+    }
+
+    static FORCE_INLINE double Acos(double value)
+    {
+        return acos(value < -1. ? -1. : value < 1. ? value : 1.);
+    }
+
+    static FORCE_INLINE double Tan(double value)
+    {
+        return tan(value);
+    }
+
+    static FORCE_INLINE double Atan(double value)
+    {
+        return atan(value);
+    }
+
+    static FORCE_INLINE double Atan2(double y, double x)
+    {
+        return atan2(y, x);
+    }
+
+    static FORCE_INLINE double InvSqrt(double value)
+    {
+        return 1.0f / sqrt(value);
+    }
+
+    static FORCE_INLINE double Log(const double value)
+    {
+        return log(value);
+    }
+
+    static FORCE_INLINE double Log2(const double value)
+    {
+        return log2(value);
+    }
+
+    static FORCE_INLINE double Log10(const double value)
+    {
+        return log10(value);
+    }
+
+    static FORCE_INLINE double Pow(const double base, const double exponent)
+    {
+        return pow(base, exponent);
+    }
+
+    static FORCE_INLINE double Sqrt(const double value)
+    {
+        return sqrt(value);
+    }
+
+    static FORCE_INLINE double Exp(const double value)
+    {
+        return exp(value);
+    }
+
+    static FORCE_INLINE double Exp2(const double value)
+    {
+        return exp2(value);
+    }
+
+    static FORCE_INLINE double Abs(const double value)
+    {
+        return fabs(value);
+    }
+
+    static FORCE_INLINE double Mod(const double a, const double b)
+    {
+        return fmod(a, b);
+    }
+
+    static FORCE_INLINE double ModF(double a, double* b)
+    {
+        return modf(a, b);
+    }
+
+    /// <summary>
+    /// Returns signed fractional part of a double.
+    /// </summary>
+    /// <param name="value">Double point value to convert.</param>
+    /// <returns>A double between [0 ; 1) for nonnegative input. A double between [-1; 0) for negative input.</returns>
+    static FORCE_INLINE double Fractional(double value)
+    {
+        return value - Trunc(value);
+    }
+
+    static int64 TruncToInt(double value)
+    {
+        return (int64)value;
+    }
+
+    static int64 FloorToInt(double value)
+    {
+        return TruncToInt(floor(value));
+    }
+
+    static FORCE_INLINE int64 RoundToInt(double value)
+    {
+        return FloorToInt(value + 0.5);
+    }
+
+    static FORCE_INLINE int64 CeilToInt(double value)
+    {
+        return TruncToInt(ceil(value));
+    }
+
+    // Performs smooth (cubic Hermite) interpolation between 0 and 1
+    // @param amount Value between 0 and 1 indicating interpolation amount
+    static double SmoothStep(double amount)
+    {
+        return amount <= 0. ? 0. : amount >= 1. ? 1. : amount * amount * (3. - 2. * amount);
+    }
+
+    // Performs a smooth(er) interpolation between 0 and 1 with 1st and 2nd order derivatives of zero at endpoints
+    // @param amount Value between 0 and 1 indicating interpolation amount
+    static double SmootherStep(double amount)
+    {
+        return amount <= 0. ? 0. : amount >= 1. ? 1. : amount * amount * amount * (amount * (amount * 6. - 15.) + 10.);
+    }
+
+    // Determines whether the specified value is close to zero (0.0)
+    // @param a The floating value
+    // @returns True if the specified value is close to zero (0.0). otherwise false
+    inline bool IsZero(double a)
+    {
+        return Abs(a) < ZeroTolerance;
+    }
+
+    // Determines whether the specified value is close to one (1.0f)
+    // @param a The floating value
+    // @returns True if the specified value is close to one (1.0f). otherwise false
+    inline bool IsOne(double a)
+    {
+        return IsZero(a - 1.);
+    }
+
+    // Returns a value indicating the sign of a number
+    // @returns A number that indicates the sign of value
+    inline double Sign(double v)
+    {
+        return v > 0. ? 1. : v < 0. ? -1. : 0.;
+    }
+
+    /// <summary>
+    /// Compares the sign of two double values.
+    /// </summary>
+    /// <param name="a">The first value.</param>
+    /// <param name="b">The second value.</param>
+    /// <returns>True if given values have the same sign (both positive or negative); otherwise false.</returns>
+    inline bool SameSign(const double a, const double b)
+    {
+        return a * b >= 0.;
+    }
+
+    /// <summary>
+    /// Compares the sign of two double values.
+    /// </summary>
+    /// <param name="a">The first value.</param>
+    /// <param name="b">The second value.</param>
+    /// <returns>True if given values don't have the same sign (first is positive and second is negative or vice versa); otherwise false.</returns>
+    inline bool NotSameSign(const double a, const double b)
+    {
+        return a * b < 0.;
+    }
+
+    /// <summary>
+    /// Checks if a and b are not even almost equal, taking into account the magnitude of double numbers
+    /// </summary>
+    /// <param name="a">The left value to compare</param>
+    /// <param name="b">The right value to compare</param>
+    /// <returns>False if a almost equal to b, otherwise true</returns>
+    static bool NotNearEqual(double a, double b)
+    {
+        // Check if the numbers are really close - needed when comparing numbers near zero
+        if (IsZero(a - b))
+            return false;
+
+        // Original from Bruce Dawson: http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
+        const int64 aInt = *(int64*)&a;
+        const int64 bInt = *(int64*)&b;
+
+        // Different signs means they do not match
+        if (aInt < 0 != bInt < 0)
+            return true;
+
+        // Find the difference in ULPs
+        const int64 ulp = Math::Abs(aInt - bInt);
+
+        // Choose of maxUlp = 4
+        // according to http://code.google.com/p/googletest/source/browse/trunk/include/gtest/internal/gtest-internal.h
+        const int maxUlp = 4;
+        return ulp > maxUlp;
+    }
+
+
+    /// <summary>
+    /// Checks if a and b are almost equals within the given epsilon value.
+    /// </summary>
+    /// <param name="a">The left value to compare.</param>
+    /// <param name="b">The right value to compare.</param>
+    /// <param name="eps">The comparision epsilon value. Should be 1e-4 or less.</param>
+    /// <returns>True if a almost equal to b, otherwise false</returns>
+    static bool NearEqual(double a, double b, double eps)
+    {
+        return Abs(a - b) < eps;
+    }
+
+    /// <summary>
+    /// Remaps the specified value from the specified range to another.
+    /// </summary>
+    /// <param name="value">The value to remap.</param>
+    /// <param name="fromMin">The source range minimum.</param>
+    /// <param name="fromMax">The source range maximum.</param>
+    /// <param name="toMin">The destination range minimum.</param>
+    /// <param name="toMax">The destination range maximum.</param>
+    /// <returns>The remapped value.</returns>
+    static double Remap(double value, double fromMin, double fromMax, double toMin, double toMax)
+    {
+        return (value - fromMin) / (fromMax - fromMin) * (toMax - toMin) + toMin;
+    }
+
+    static double ClampAxis(double angle)
+    {
+        angle = Mod(angle, 360.);
+        if (angle < 0.)
+            angle += 360.;
+        return angle;
+    }
+
+    static double NormalizeAxis(double angle)
+    {
+        angle = ClampAxis(angle);
+        if (angle > 180.)
+            angle -= 360.;
+        return angle;
+    }
+
+    // Find the smallest angle between two headings (in radians).
+    static double FindDeltaAngle(double a1, double a2)
+    {
+        double delta = a2 - a1;
+        if (delta > PI)
+            delta = delta - TWO_PI;
+        else if (delta < -PI)
+            delta = delta + TWO_PI;
+        return delta;
+    }
+
+    // Given a heading which may be outside the +/- PI range, 'unwind' it back into that range
+    static double UnwindRadians(double a)
+    {
+        while (a > PI)
+            a -= TWO_PI;
+        while (a < -PI)
+            a += TWO_PI;
+        return a;
+    }
+
+    // Utility to ensure angle is between +/- 180 degrees by unwinding
+    static double UnwindDegrees(double a)
+    {
+        while (a > 180.)
+            a -= 360.;
+        while (a < -180.)
+            a += 360.;
+        return a;
+    }
+
+    /// <summary>
+    ///  Returns value based on comparand. The main purpose of this function is to avoid branching based on floating point comparison which can be avoided via compiler intrinsics.
+    /// </summary>
+    /// <remarks>
+    /// Please note that this doesn't define what happens in the case of NaNs as there might be platform specific differences.
+    /// </remarks>
+    /// <param name="comparand">Comparand the results are based on.</param>
+    /// <param name="valueGEZero">The result value if comparand >= 0.</param>
+    /// <param name="valueLTZero">The result value if comparand < 0.</param>
+    /// <returns>the valueGEZero if comparand >= 0, valueLTZero otherwise</returns>
+    static double DoubleSelect(double comparand, double valueGEZero, double valueLTZero)
+    {
+        return comparand >= 0. ? valueGEZero : valueLTZero;
+    }
+
+    /// <summary>
+    /// Returns a smooth Hermite interpolation between 0 and 1 for the value X (where X ranges between A and B). Clamped to 0 for X <= A and 1 for X >= B.
+    /// </summary>
+    /// <param name="a">The minimum value of x.</param>
+    /// <param name="b">The maximum value of x.</param>
+    /// <param name="x">The x.</param>
+    /// <returns>The smoothed value between 0 and 1.</returns>
+    static double SmoothStep(double a, double b, double x)
+    {
+        if (x < a)
+            return 0.;
+        if (x >= b)
+            return 1.;
+        const double fraction = (x - a) / (b - a);
+        return fraction * fraction * (3. - 2. * fraction);
+    }
+
+//TODO: When double vectors are implemented
+    // Rotates position about the given axis by the given angle, in radians, and returns the offset to position
+    //Vector3 FLAXENGINE_API RotateAboutAxis(const Vector3& normalizedRotationAxis, float angle, const Vector3& positionOnAxis, const Vector3& position);
+
+    //Vector3 FLAXENGINE_API ExtractLargestComponent(const Vector3& v);
+}

Source/Engine/Core/Math/Mathf.cs

@@ -6,7 +6,7 @@ using System.ComponentModel;
 namespace FlaxEngine
 {
     /// <summary>
-    /// A collection of common math functions.
+    /// A collection of common math functions on single floating-points.
     /// </summary>
     [HideInEditor]
     public static class Mathf

Source/Engine/Core/Types/Variant.cpp

@@ -6,6 +6,7 @@
 #include "Engine/Core/Collections/Dictionary.h"
 #include "Engine/Content/Asset.h"
 #include "Engine/Core/Log.h"
+#include "Engine/Core/Math/Mathd.h"
 #include "Engine/Core/Math/BoundingBox.h"
 #include "Engine/Core/Math/BoundingSphere.h"
 #include "Engine/Core/Math/Vector2.h"

Source/Engine/Tools/ModelTool/ModelTool.OpenFBX.cpp

@@ -4,6 +4,7 @@
 
 #include "ModelTool.h"
 #include "Engine/Core/Log.h"
+#include "Engine/Core/Math/Mathd.h"
 #include "Engine/Core/Math/Matrix.h"
 #include "Engine/Core/Collections/Sorting.h"
 #include "Engine/Platform/FileSystem.h"