fbxmath.h

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/****************************************************************************************
 
   Copyright (C) 2012 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   //!< Degree to Radian
#define FBXSDK_RAD_TO_DEG   FBXSDK_180_DIV_PI   //!< Radian to Degree
#define FBXSDK_IN_TO_CM     2.54                //!< Inch to Centimeter
#define FBXSDK_CM_TO_IN     0.393700787         //!< Centimeter to Inch
#define FBXSDK_IN_TO_MM     25.4                //!< Inch to Millimeter
#define FBXSDK_MM_TO_IN     0.0393700787        //!< Millimeter to Inch
#define FBXSDK_FT_TO_M      0.3048              //!< Feet to Meter
#define FBXSDK_M_TO_FT      3.2808399           //!< Meter to Feet
#define FBXSDK_YD_TO_FT     3                   //!< Yard to Feet
#define FBXSDK_FT_TO_YD     0.333333333         //!< Feet to Yard
#define FBXSDK_KM_TO_MILE   0.621371192         //!< Kilometer to Mile
#define FBXSDK_MILE_TO_KM   1.609344            //!< Mile to Kilometer
#define FBXSDK_YD_TO_M      0.9144              //!< Yard to Meter
#define FBXSDK_M_TO_YD      1.0936133           //!< Meter to Yard

//---------------------------------------------------------------------------------------
//Euler Definition
class FBXSDK_DLL FbxEuler
{
public:
    enum ERepeat {eRepeatNo=0, eRepeatYes=1};
    enum EParity {eParityEven=0, eParityOdd=2};
    enum EAxis {eAxisX=0, eAxisY=1, eAxisZ=2};

    #define EulerOrder(EAxis, EParity, ERepeat) (((EAxis) << 2) | (EParity) | (ERepeat))

    enum EOrder
    {
        eOrderXYZ = EulerOrder(eAxisX, eParityEven, eRepeatNo),
        eOrderXYX = EulerOrder(eAxisX, eParityEven, eRepeatYes),    //deprecated
        eOrderXZY = EulerOrder(eAxisX, eParityOdd, eRepeatNo),
        eOrderXZX = EulerOrder(eAxisX, eParityOdd, eRepeatYes),     //deprecated
        eOrderYZX = EulerOrder(eAxisY, eParityEven, eRepeatNo),
        eOrderYZY = EulerOrder(eAxisY, eParityEven, eRepeatYes),    //deprecated
        eOrderYXZ = EulerOrder(eAxisY, eParityOdd, eRepeatNo),
        eOrderYXY = EulerOrder(eAxisY, eParityOdd, eRepeatYes),     //deprecated
        eOrderZXY = EulerOrder(eAxisZ, eParityEven, eRepeatNo),
        eOrderZXZ = EulerOrder(eAxisZ, eParityEven, eRepeatYes),    //deprecated
        eOrderZYX = EulerOrder(eAxisZ, eParityOdd, eRepeatNo),
        eOrderZYZ = EulerOrder(eAxisZ, eParityOdd, eRepeatYes)      //deprecated
    };

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

enum EFbxRotationOrder
{ 
    eEulerXYZ,
    eEulerXZY,
    eEulerYZX,
    eEulerYXZ,
    eEulerZXY,
    eEulerZYX,
    eSphericXYZ
};

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

extern FBXSDK_DLL const double FbxIdentityMatrix[4][4];

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

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

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

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

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

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

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

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

template<class T> inline T FbxAbs(const T& x, const T& y)
{
    T ax, ay;
    if( x )
    {
        if( ax = FbxAbs(x), y )
        {
            return ( ax > (ay = FbxAbs(y)) ) ? ay * FbxSqrt(T(1) + kSq(x / y)) : ax * FbxSqrt(T(1) + kSq(y / x));
        }
        else
        {
            return ax;
        }
    }
    else
    {
        return FbxAbs(y);
    }
}

template<class T> inline const 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=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) );
}

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);
}

template<class T> inline T FbxPow(const T& x, const T& y)
{
    return FbxExp(y * FbxLog(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 FbxLog2(const T& x)
{
    return FbxLog(x) * T(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);
}

template<class T> inline T FbxCos(const T& 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 double FbxASin(const double& x)
{
    return asin(x);
}

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

template<class T> inline T FbxACosd(const T& x)
{
    return 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 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 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 float FbxASin(const float& x)
{
    return asinf(x);
}

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

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

template<class T> inline const 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 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_ */