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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 __cplusplus #include "quaternion.h" #include <cmath> // --------------------------------------------------------------------------- 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> 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) > static_cast<TReal>(0.0001)) // 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) { 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