assimp/include/assimp/quaternion.inl

/*
---------------------------------------------------------------------------
Open Asset Import Library (assimp)
---------------------------------------------------------------------------

Copyright (c) 2006-2022, assimp team



All rights reserved.

Redistribution and use of this software in source and binary forms,
with or without modification, are permitted provided that the following
conditions are met:

* Redistributions of source code must retain the above
  copyright notice, this list of conditions and the
  following disclaimer.

* Redistributions in binary form must reproduce the above
  copyright notice, this list of conditions and the
  following disclaimer in the documentation and/or other
  materials provided with the distribution.

* Neither the name of the assimp team, nor the names of its
  contributors may be used to endorse or promote products
  derived from this software without specific prior
  written permission of the assimp team.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
---------------------------------------------------------------------------
*/

/** @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