fbxmath.h

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/****************************************************************************************
 
   Copyright (C) 2015 Autodesk, Inc.
   All rights reserved.
 
   Use of this software is subject to the terms of the Autodesk license agreement
   provided at the time of installation or download, or which otherwise accompanies
   this software in either electronic or hard copy form.
 
****************************************************************************************/

#ifndef _FBXSDK_CORE_MATH_H_
#define _FBXSDK_CORE_MATH_H_

#include <fbxsdk/fbxsdk_def.h>

#include <fbxsdk/core/math/fbxvector2.h>
#include <fbxsdk/core/math/fbxvector4.h>
#include <fbxsdk/core/math/fbxmatrix.h>
#include <fbxsdk/core/math/fbxaffinematrix.h>

//On Mac OS, cmath will include math.h and undef "isnan"
#if defined(FBXSDK_ENV_MAC)
    #include <cmath>
    extern "C" int isnan (double);
#endif

#include <fbxsdk/fbxsdk_nsbegin.h>

#if defined(FBXSDK_ENV_WIN)
    #ifndef isnan
        #define isnan   _isnan
    #endif
    #ifndef finite
        #define finite  _finite
    #endif
#endif

//---------------------------------------------------------------------------------------
//Common Constants
#define FBXSDK_PI               3.1415926535897932384626433832795028841971693993751     
#define FBXSDK_PI_DIV_2         1.5707963267948966192313216916397514420985846996875     
#define FBXSDK_PI_DIV_180       0.017453292519943295769236907684886127134428718885417   
#define FBXSDK_180_DIV_PI       57.295779513082320876798154814105170332405472466565     
#define FBXSDK_1_DIV_LN2        1.4426950408889634073599246810018921374266459541530     

//---------------------------------------------------------------------------------------
//Unit Convertion Ratio
#define FBXSDK_DEG_TO_RAD       FBXSDK_PI_DIV_180   
#define FBXSDK_RAD_TO_DEG       FBXSDK_180_DIV_PI   
#define FBXSDK_IN_TO_CM         2.54                
#define FBXSDK_MM_TO_CM         0.1                 
#define FBXSDK_CM_TO_IN         0.393700787         
#define FBXSDK_IN_TO_MM         25.4                
#define FBXSDK_MM_TO_IN         0.0393700787        
#define FBXSDK_FT_TO_M          0.3048              
#define FBXSDK_M_TO_FT          3.2808399           
#define FBXSDK_YD_TO_FT         3                   
#define FBXSDK_FT_TO_YD         0.333333333         
#define FBXSDK_KM_TO_MILE       0.621371192         
#define FBXSDK_MILE_TO_KM       1.609344            
#define FBXSDK_YD_TO_M          0.9144              
#define FBXSDK_M_TO_YD          1.0936133           

//---------------------------------------------------------------------------------------
//Euler Definition
#define FBXSDK_EULER_DEGENERATE  FbxEuler::DegenerateThreshold() 

class FBXSDK_DLL FbxEuler
{
public:
    enum EAxis {eAxisX=0, eAxisY=1, eAxisZ=2};

    enum EOrder
    {
        eOrderXYZ,
        eOrderXZY,
        eOrderYZX,
        eOrderYXZ,
        eOrderZXY,
        eOrderZYX,
        eOrderSphericXYZ
    };

    static bool IsParityOdd(EOrder pOrder);
    static bool IsRepeat(EOrder pOrder);

    static const int AxisTableSize;
    static const int AxisTable[][3];

    // Used to detect Euler gimbal locks when extracting the rotation vector from 
    // the FbxAMatrix. This value should only be changed when the user system stores
    // single floating point values into the FbxAMatrix with a very low precision.
    // In this case, the default threshold value would be too small for a proper detection
    // and the extracted values can quickly become off target by a huge amount.
    static void SetDegenerateThreshold(double pThreshold=16.0*FBXSDK_FLOAT_EPSILON);
    static inline double DegenerateThreshold() { return FbxEuler::mDegenerateThreshold; }

private:
    static double mDegenerateThreshold;
};

#define EFbxRotationOrder   FbxEuler::EOrder
#define eEulerXYZ           FbxEuler::eOrderXYZ
#define eEulerXZY           FbxEuler::eOrderXZY
#define eEulerYZX           FbxEuler::eOrderYZX
#define eEulerYXZ           FbxEuler::eOrderYXZ
#define eEulerZXY           FbxEuler::eOrderZXY
#define eEulerZYX           FbxEuler::eOrderZYX
#define eSphericXYZ         FbxEuler::eOrderSphericXYZ



enum EFbxQuatInterpMode
{
    eQuatInterpOff,                 
    eQuatInterpClassic,             
    eQuatInterpSlerp,               
    eQuatInterpCubic,               
    eQuatInterpTangentDependent,    
    eQuatInterpCount                
};

extern FBXSDK_DLL const FbxDouble FbxIdentityMatrix[4][4];
extern FBXSDK_DLL const FbxVector4 FbxZeroVector4;

inline float FbxFloor(const float x)
{
    return float(floor(x));
}

inline double FbxFloor(const double x)
{
    return floor(x);
}

inline float FbxCeil(const float x)
{
    return float(ceil(x));
}

inline double FbxCeil(const double x)
{
    return ceil(x);
}

template<class T> inline T FbxSign(const T x)
{
    return (x < 0) ? T(-1) : T(1);
}

template<class T> inline T FbxRound(const T x)
{
    T y = FbxFloor(x);
    return (x - y < T(0.5)) ? y : y + T(1);
}

inline FbxUChar FbxAbs(const FbxUChar x)
{
    return x;
}

inline FbxUShort FbxAbs(const FbxUShort x)
{
    return x;
}

inline FbxUInt FbxAbs(const FbxUInt x)
{
    return x;
}

#ifndef FBXSDK_SYSTEM_IS_LP64
    inline FbxULong FbxAbs(const FbxULong x)
    {
        return x;
    }
#endif

inline FbxULongLong FbxAbs(const FbxULongLong x)
{
    return x;
}

inline FbxFloat FbxAbs(const FbxFloat x)
{
    return (FbxFloat)fabs(x);
}

inline FbxDouble FbxAbs(const FbxDouble x)
{
    return fabs(x);
}

template<class T> inline T FbxAbs(const T x)
{
    return (x >= 0) ? x : ((x > FbxMin(x)) ? -x : FbxMax(x));
}

template<class T> inline T FbxClamp(const T value, const T min, const T max)
{
    return (value < min) ? min : ((value > max) ? max : value);
}

template<class T> inline bool FbxEqual(const T x, const T y, const T e=(T)FBXSDK_TOLERANCE)
{
    return FbxAbs(x - y) <= e;
}

inline bool FbxEqual(const FbxDouble2& x, const FbxDouble2& y, const double e=FBXSDK_TOLERANCE)
{
    return ( FbxEqual(x.mData[0], y.mData[0], e) && FbxEqual(x.mData[1], y.mData[1], e) );
}

inline bool FbxEqual(const FbxDouble3& x, const FbxDouble3& y, const double e=FBXSDK_TOLERANCE)
{
    return ( FbxEqual(x.mData[0], y.mData[0], e) && FbxEqual(x.mData[1], y.mData[1], e) && FbxEqual(x.mData[2], y.mData[2], e) );
}

inline bool FbxEqual(const FbxDouble4& x, const FbxDouble4& y, const double e=FBXSDK_TOLERANCE)
{
    return ( FbxEqual(x.mData[0], y.mData[0], e) && FbxEqual(x.mData[1], y.mData[1], e) && FbxEqual(x.mData[2], y.mData[2], e) && FbxEqual(x.mData[3], y.mData[3], e) );
}

inline bool FbxEqual(const FbxDouble4x4& x, const FbxDouble4x4& y, const double e=FBXSDK_TOLERANCE)
{
    return ( FbxEqual(x[0], y[0], e) && FbxEqual(x[1], y[1], e) && FbxEqual(x[2], y[2], e) && FbxEqual(x[3], y[3], e) );
}

inline bool FbxEqual(const FbxVector2& x, const FbxVector2& y, const double e=FBXSDK_TOLERANCE)
{
    return ( FbxEqual(x.mData[0], y.mData[0], e) && FbxEqual(x.mData[1], y.mData[1], e) );
}

inline bool FbxEqual(const FbxVector4& x, const FbxVector4& y, const double e=FBXSDK_TOLERANCE)
{
    return ( FbxEqual(x.mData[0], y.mData[0], e) && FbxEqual(x.mData[1], y.mData[1], e) && FbxEqual(x.mData[2], y.mData[2], e) && FbxEqual(x.mData[3], y.mData[3], e) );
}

inline bool FbxEqual(const FbxMatrix& x, const FbxMatrix& y, const double e=FBXSDK_TOLERANCE)
{
    return ( FbxEqual(x[0], y[0], e) && FbxEqual(x[1], y[1], e) && FbxEqual(x[2], y[2], e) && FbxEqual(x[3], y[3], e) );
}

inline bool FbxEqual(const FbxAMatrix& x, const FbxAMatrix& y, const double e=FBXSDK_TOLERANCE)
{
    return ( FbxEqual(x[0], y[0], e) && FbxEqual(x[1], y[1], e) && FbxEqual(x[2], y[2], e) && FbxEqual(x[3], y[3], e) );
}

inline FbxDouble FbxMod(const FbxFloat x, FbxFloat& i)
{
    return modff(x, &i);
}

inline FbxDouble FbxMod(const FbxDouble x, FbxDouble& i)
{
    return modf(x, &i);
}

inline FbxDouble FbxMod(const FbxFloat x)
{
    FbxFloat i;
    return modff(x, &i);
}

inline FbxDouble FbxMod(const FbxDouble x)
{
    FbxDouble i;
    return modf(x, &i);
}

template<class T> inline T FbxReciprocal(const T x)
{
    return T(1) / x;
}

inline double FbxSqrt(const double x)
{
    return sqrt(x);
}

inline float FbxSqrt(const float x)
{
    return sqrtf(x);
}

template<class T> inline T FbxSqrt(const T x)
{
    if( x > 1 )
    {
        T z, y = x >> 1; 
        do 
        { 
            z = y; 
            y = (y + (x / y)) >> 1; 
        }
        while(y < z); 

        return z;
    }
    else
    {
        return x;
    }
}

inline float FbxExp(const float x)
{
    return expf(x);
}

inline double FbxExp(const double x)
{
    return exp(x);
}

inline float FbxLog(const float x)
{
    return float(log(x));
}

inline double FbxLog(const double x)
{
    return log(x);
}

template<class T> inline T FbxPow(const T x, const T y)
{
    return (T)FbxExp(y * FbxLog((double)x));
}

template<class T> inline T FbxLog2(const T x)
{
    return (T)(FbxLog(x) * FBXSDK_1_DIV_LN2);
}

inline float FbxSin(const float x)
{
    return sinf(x);
}

inline double FbxSin(const double x)
{
    return sin(x);
}

inline float FbxCos(const float x)
{
    return cosf(x);
}

inline double FbxCos(const double x)
{
    return cos(x);
}

inline float FbxTan(const float x)
{
    return tanf(x);
}

inline double FbxTan(const double x)
{
    return tan(x);
}

// *y = cos(x), sin(x)
template<class T> inline T FbxSinCos(const T x, T* y)
{
    return *y = FbxCos(x), FbxSin(x);
}

// *y = cos(x * pi/180), sin(x * pi/180)
template<class T> inline T FbxSinCosd(const T x, T* y)
{
    return FbxSinCos(T(x * FBXSDK_PI_DIV_180), y);
}

inline float FbxASin(const float x)
{
    return asinf(x);
}

inline double FbxASin(const double x)
{
    return asin(x);
}

template<class T> inline T FbxASind(const T x)
{
    return (T)(FbxASin((double)x) * FBXSDK_180_DIV_PI);
}

inline float FbxACos(const float x)
{
    return acosf(x);
}

inline double FbxACos(const double x)
{
    return acos(x);
}

template<class T> inline T FbxACosd(const T x)
{
    return (T)(FbxACos(x) * FBXSDK_180_DIV_PI);
}

inline float FbxATan(const float x)
{
    return atanf(x);
}

inline double FbxATan(const double x)
{
    return atan(x);
}

template<class T> inline T FbxATand(const T x)
{
    return (T)(FbxATan(x) * FBXSDK_180_DIV_PI);
}

inline float FbxATan(const float y, const float x)
{
    return atan2f(y, x);
}

inline double FbxATan(const double y, const double x)
{
    return atan2(y, x);
}

template<class T> inline T FbxATand(const T y, const T x)
{
    return (T)(FbxATan(y, x) * FBXSDK_180_DIV_PI);
}

template<class T> inline T FbxNorm(const T x, const T y)
{
    return FbxSqrt(x * x + y * y);
}

template<class T> inline T FbxNorm(const T x, const T y, const T z)
{
    return FbxSqrt(x * x + y * y + z * z);
}

template<class T> inline T FbxNorm(const T w, const T x, const T y, const T z)
{
    return FbxSqrt(w * w + x * x + y * y + z * z);
}

template<class T> inline T FbxHypot(const T x, const T y)
{
    return FbxSqrt(x * x + y * y);
}

template<class T> inline T FbxHypot(const T x, const T y, const T z)
{
    return FbxSqrt(x * x + y * y + z * z);
}

template<class T> inline T FbxHypot(const T w, const T x, const T y, const T z)
{
    return FbxSqrt(w * w + x * x + y * y + z * z);
}

inline FbxVector4 FbxRejection(const FbxVector4& a, const FbxVector4& b)
{
    return a - b * (a.DotProduct(b) / b.DotProduct(b));
}

template<class T> inline int FbxBitCount(const T x)
{
    int n = 0;
    T c = x;
    while( c )
    {
        n += int(c & 1);
        c = (c >> 1);
    }
    return n;
}

template<class T> inline void FbxFixInfinite(T& x)
{
    if( x != x || x > FbxMax(x) || x < -FbxMax(x) )
    {
        x = T(0);
    }
}

template<class T> inline T FbxExp(const T x);
template<class T> inline T FbxLog(const T x);
template<class T> inline T FbxSin(const T x);
template<class T> inline T FbxCos(const T x);
template<class T> inline T FbxASin(const T x);
template<class T> inline T FbxACos(const T x);
template<class T> inline T FbxATan(const T x);
template<class T> inline T FbxATan(const T y, const T x);

#include <fbxsdk/fbxsdk_nsend.h>

#endif /* _FBXSDK_CORE_MATH_H_ */