assimp.assimp/include/assimp/quaternion.inl

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/** @file  quaternion.inl
 *  @brief Inline implementation of aiQuaterniont<TReal> operators
 */
#pragma once
#ifndef AI_QUATERNION_INL_INC
#define AI_QUATERNION_INL_INC

#ifdef __GNUC__
#   pragma GCC system_header
#endif

#ifdef __cplusplus
#include <assimp/quaternion.h>

#include <cmath>

// ------------------------------------------------------------------------------------------------
/** Transformation of a quaternion by a 4x4 matrix */
template <typename TReal>
AI_FORCE_INLINE
aiQuaterniont<TReal> operator * (const aiMatrix4x4t<TReal>& pMatrix, const aiQuaterniont<TReal>& pQuaternion) {
    aiQuaterniont<TReal> res;
    res.x = pMatrix.a1 * pQuaternion.x + pMatrix.a2 * pQuaternion.y + pMatrix.a3 * pQuaternion.z + pMatrix.a4 * pQuaternion.w;
    res.y = pMatrix.b1 * pQuaternion.x + pMatrix.b2 * pQuaternion.y + pMatrix.b3 * pQuaternion.z + pMatrix.b4 * pQuaternion.w;
    res.z = pMatrix.c1 * pQuaternion.x + pMatrix.c2 * pQuaternion.y + pMatrix.c3 * pQuaternion.z + pMatrix.c4 * pQuaternion.w;
    res.w = pMatrix.d1 * pQuaternion.x + pMatrix.d2 * pQuaternion.y + pMatrix.d3 * pQuaternion.z + pMatrix.d4 * pQuaternion.w;
    return res;
}
// ---------------------------------------------------------------------------
template<typename TReal>
bool aiQuaterniont<TReal>::operator== (const aiQuaterniont& o) const
{
    return x == o.x && y == o.y && z == o.z && w == o.w;
}

// ---------------------------------------------------------------------------
template<typename TReal>
bool aiQuaterniont<TReal>::operator!= (const aiQuaterniont& o) const
{
    return !(*this == o);
}

// ------------------------------------------------------------------------------------------------
template <typename TReal>
AI_FORCE_INLINE
aiQuaterniont<TReal>& aiQuaterniont<TReal>::operator *= (const aiMatrix4x4t<TReal>& mat){
    return (*this = mat * (*this));
}
// ------------------------------------------------------------------------------------------------

// ---------------------------------------------------------------------------
template<typename TReal>
inline bool aiQuaterniont<TReal>::Equal(const aiQuaterniont& o, TReal epsilon) const {
    return
        std::abs(x - o.x) <= epsilon &&
        std::abs(y - o.y) <= epsilon &&
        std::abs(z - o.z) <= epsilon &&
        std::abs(w - o.w) <= epsilon;
}

// ---------------------------------------------------------------------------
// Constructs a quaternion from a rotation matrix
template<typename TReal>
inline aiQuaterniont<TReal>::aiQuaterniont( const aiMatrix3x3t<TReal> &pRotMatrix)
{
    TReal t = pRotMatrix.a1 + pRotMatrix.b2 + pRotMatrix.c3;

    // large enough
    if( t > static_cast<TReal>(0))
    {
        TReal s = std::sqrt(1 + t) * static_cast<TReal>(2.0);
        x = (pRotMatrix.c2 - pRotMatrix.b3) / s;
        y = (pRotMatrix.a3 - pRotMatrix.c1) / s;
        z = (pRotMatrix.b1 - pRotMatrix.a2) / s;
        w = static_cast<TReal>(0.25) * s;
    } // else we have to check several cases
    else if( pRotMatrix.a1 > pRotMatrix.b2 && pRotMatrix.a1 > pRotMatrix.c3 )
    {
        // Column 0:
        TReal s = std::sqrt( static_cast<TReal>(1.0) + pRotMatrix.a1 - pRotMatrix.b2 - pRotMatrix.c3) * static_cast<TReal>(2.0);
        x = static_cast<TReal>(0.25) * s;
        y = (pRotMatrix.b1 + pRotMatrix.a2) / s;
        z = (pRotMatrix.a3 + pRotMatrix.c1) / s;
        w = (pRotMatrix.c2 - pRotMatrix.b3) / s;
    }
    else if( pRotMatrix.b2 > pRotMatrix.c3)
    {
        // Column 1:
        TReal s = std::sqrt( static_cast<TReal>(1.0) + pRotMatrix.b2 - pRotMatrix.a1 - pRotMatrix.c3) * static_cast<TReal>(2.0);
        x = (pRotMatrix.b1 + pRotMatrix.a2) / s;
        y = static_cast<TReal>(0.25) * s;
        z = (pRotMatrix.c2 + pRotMatrix.b3) / s;
        w = (pRotMatrix.a3 - pRotMatrix.c1) / s;
    } else
    {
        // Column 2:
        TReal s = std::sqrt( static_cast<TReal>(1.0) + pRotMatrix.c3 - pRotMatrix.a1 - pRotMatrix.b2) * static_cast<TReal>(2.0);
        x = (pRotMatrix.a3 + pRotMatrix.c1) / s;
        y = (pRotMatrix.c2 + pRotMatrix.b3) / s;
        z = static_cast<TReal>(0.25) * s;
        w = (pRotMatrix.b1 - pRotMatrix.a2) / s;
    }
}

// ---------------------------------------------------------------------------
// Construction from euler angles
template<typename TReal>
inline aiQuaterniont<TReal>::aiQuaterniont( TReal fPitch, TReal fYaw, TReal fRoll )
{
    const TReal fSinPitch(std::sin(fPitch*static_cast<TReal>(0.5)));
    const TReal fCosPitch(std::cos(fPitch*static_cast<TReal>(0.5)));
    const TReal fSinYaw(std::sin(fYaw*static_cast<TReal>(0.5)));
    const TReal fCosYaw(std::cos(fYaw*static_cast<TReal>(0.5)));
    const TReal fSinRoll(std::sin(fRoll*static_cast<TReal>(0.5)));
    const TReal fCosRoll(std::cos(fRoll*static_cast<TReal>(0.5)));
    const TReal fCosPitchCosYaw(fCosPitch*fCosYaw);
    const TReal fSinPitchSinYaw(fSinPitch*fSinYaw);
    x = fSinRoll * fCosPitchCosYaw     - fCosRoll * fSinPitchSinYaw;
    y = fCosRoll * fSinPitch * fCosYaw + fSinRoll * fCosPitch * fSinYaw;
    z = fCosRoll * fCosPitch * fSinYaw - fSinRoll * fSinPitch * fCosYaw;
    w = fCosRoll * fCosPitchCosYaw     + fSinRoll * fSinPitchSinYaw;
}

// ---------------------------------------------------------------------------
// Returns a matrix representation of the quaternion
template<typename TReal>
inline aiMatrix3x3t<TReal> aiQuaterniont<TReal>::GetMatrix() const
{
    aiMatrix3x3t<TReal> resMatrix;
    resMatrix.a1 = static_cast<TReal>(1.0) - static_cast<TReal>(2.0) * (y * y + z * z);
    resMatrix.a2 = static_cast<TReal>(2.0) * (x * y - z * w);
    resMatrix.a3 = static_cast<TReal>(2.0) * (x * z + y * w);
    resMatrix.b1 = static_cast<TReal>(2.0) * (x * y + z * w);
    resMatrix.b2 = static_cast<TReal>(1.0) - static_cast<TReal>(2.0) * (x * x + z * z);
    resMatrix.b3 = static_cast<TReal>(2.0) * (y * z - x * w);
    resMatrix.c1 = static_cast<TReal>(2.0) * (x * z - y * w);
    resMatrix.c2 = static_cast<TReal>(2.0) * (y * z + x * w);
    resMatrix.c3 = static_cast<TReal>(1.0) - static_cast<TReal>(2.0) * (x * x + y * y);

    return resMatrix;
}

// ---------------------------------------------------------------------------
// Construction from an axis-angle pair
template<typename TReal>
inline aiQuaterniont<TReal>::aiQuaterniont( aiVector3t<TReal> axis, TReal angle)
{
    axis.Normalize();

    const TReal sin_a = std::sin( angle / 2 );
    const TReal cos_a = std::cos( angle / 2 );
    x    = axis.x * sin_a;
    y    = axis.y * sin_a;
    z    = axis.z * sin_a;
    w    = cos_a;
}
// ---------------------------------------------------------------------------
// Construction from am existing, normalized quaternion
template<typename TReal>
inline aiQuaterniont<TReal>::aiQuaterniont( aiVector3t<TReal> normalized)
{
    x = normalized.x;
    y = normalized.y;
    z = normalized.z;

    const TReal t = static_cast<TReal>(1.0) - (x*x) - (y*y) - (z*z);

    if (t < static_cast<TReal>(0.0)) {
        w = static_cast<TReal>(0.0);
    }
    else w = std::sqrt (t);
}

// ---------------------------------------------------------------------------
// Performs a spherical interpolation between two quaternions
// Implementation adopted from the gmtl project. All others I found on the net fail in some cases.
// Congrats, gmtl!
template<typename TReal>
inline void aiQuaterniont<TReal>::Interpolate( aiQuaterniont& pOut, const aiQuaterniont& pStart, const aiQuaterniont& pEnd, TReal pFactor)
{
    // calc cosine theta
    TReal cosom = pStart.x * pEnd.x + pStart.y * pEnd.y + pStart.z * pEnd.z + pStart.w * pEnd.w;

    // adjust signs (if necessary)
    aiQuaterniont end = pEnd;
    if( cosom < static_cast<TReal>(0.0))
    {
        cosom = -cosom;
        end.x = -end.x;   // Reverse all signs
        end.y = -end.y;
        end.z = -end.z;
        end.w = -end.w;
    }

    // Calculate coefficients
    TReal sclp, sclq;

    if ((static_cast<TReal>(1.0) - cosom) > ai_epsilon) // 0.0001 -> some epsillon
    {
        // Standard case (slerp)
        TReal omega, sinom;
        omega = std::acos( cosom); // extract theta from dot product's cos theta
        sinom = std::sin( omega);
        sclp  = std::sin( (static_cast<TReal>(1.0) - pFactor) * omega) / sinom;
        sclq  = std::sin( pFactor * omega) / sinom;
    } else
    {
        // Very close, do linear interp (because it's faster)
        sclp = static_cast<TReal>(1.0) - pFactor;
        sclq = pFactor;
    }

    pOut.x = sclp * pStart.x + sclq * end.x;
    pOut.y = sclp * pStart.y + sclq * end.y;
    pOut.z = sclp * pStart.z + sclq * end.z;
    pOut.w = sclp * pStart.w + sclq * end.w;
}

// ---------------------------------------------------------------------------
template<typename TReal>
inline aiQuaterniont<TReal>& aiQuaterniont<TReal>::Normalize()
{
    // compute the magnitude and divide through it
    const TReal mag = std::sqrt(x*x + y*y + z*z + w*w);
    if (mag)
    {
        const TReal invMag = static_cast<TReal>(1.0)/mag;
        x *= invMag;
        y *= invMag;
        z *= invMag;
        w *= invMag;
    }
    return *this;
}

// ---------------------------------------------------------------------------
template<typename TReal>
inline aiQuaterniont<TReal> aiQuaterniont<TReal>::operator* (const aiQuaterniont& t) const
{
    return aiQuaterniont(w*t.w - x*t.x - y*t.y - z*t.z,
        w*t.x + x*t.w + y*t.z - z*t.y,
        w*t.y + y*t.w + z*t.x - x*t.z,
        w*t.z + z*t.w + x*t.y - y*t.x);
}

// ---------------------------------------------------------------------------
template<typename TReal>
inline aiQuaterniont<TReal>& aiQuaterniont<TReal>::Conjugate ()
{
    x = -x;
    y = -y;
    z = -z;
    return *this;
}

// ---------------------------------------------------------------------------
template<typename TReal>
inline aiVector3t<TReal> aiQuaterniont<TReal>::Rotate (const aiVector3t<TReal>& v) const
{
    aiQuaterniont q2(0.f,v.x,v.y,v.z), q = *this, qinv = q;
    qinv.Conjugate();

    q = q*q2*qinv;
    return aiVector3t<TReal>(q.x,q.y,q.z);
}

#endif
#endif // AI_QUATERNION_INL_INC