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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 aiMatrix3x3.inl * @brief Inline implementation of the 3x3 matrix operators */ #ifndef AI_MATRIX3x3_INL_INC #define AI_MATRIX3x3_INL_INC #ifdef __cplusplus #include "aiMatrix3x3.h" #include "aiMatrix4x4.h" #include #include // ------------------------------------------------------------------------------------------------ // Construction from a 4x4 matrix. The remaining parts of the matrix are ignored. template inline aiMatrix3x3t::aiMatrix3x3t( const aiMatrix4x4t& pMatrix) { a1 = pMatrix.a1; a2 = pMatrix.a2; a3 = pMatrix.a3; b1 = pMatrix.b1; b2 = pMatrix.b2; b3 = pMatrix.b3; c1 = pMatrix.c1; c2 = pMatrix.c2; c3 = pMatrix.c3; } // ------------------------------------------------------------------------------------------------ template inline aiMatrix3x3t& aiMatrix3x3t::operator *= (const aiMatrix3x3t& m) { *this = aiMatrix3x3t(m.a1 * a1 + m.b1 * a2 + m.c1 * a3, m.a2 * a1 + m.b2 * a2 + m.c2 * a3, m.a3 * a1 + m.b3 * a2 + m.c3 * a3, m.a1 * b1 + m.b1 * b2 + m.c1 * b3, m.a2 * b1 + m.b2 * b2 + m.c2 * b3, m.a3 * b1 + m.b3 * b2 + m.c3 * b3, m.a1 * c1 + m.b1 * c2 + m.c1 * c3, m.a2 * c1 + m.b2 * c2 + m.c2 * c3, m.a3 * c1 + m.b3 * c2 + m.c3 * c3); return *this; } // ------------------------------------------------------------------------------------------------ template template aiMatrix3x3t::operator aiMatrix3x3t () const { return aiMatrix3x3t(static_cast(a1),static_cast(a2),static_cast(a3), static_cast(b1),static_cast(b2),static_cast(b3), static_cast(c1),static_cast(c2),static_cast(c3)); } // ------------------------------------------------------------------------------------------------ template inline aiMatrix3x3t aiMatrix3x3t::operator* (const aiMatrix3x3t& m) const { aiMatrix3x3t temp( *this); temp *= m; return temp; } // ------------------------------------------------------------------------------------------------ template inline TReal* aiMatrix3x3t::operator[] (unsigned int p_iIndex) { return &this->a1 + p_iIndex * 3; } // ------------------------------------------------------------------------------------------------ template inline const TReal* aiMatrix3x3t::operator[] (unsigned int p_iIndex) const { return &this->a1 + p_iIndex * 3; } // ------------------------------------------------------------------------------------------------ template inline bool aiMatrix3x3t::operator== (const aiMatrix4x4t m) const { return a1 == m.a1 && a2 == m.a2 && a3 == m.a3 && b1 == m.b1 && b2 == m.b2 && b3 == m.b3 && c1 == m.c1 && c2 == m.c2 && c3 == m.c3; } // ------------------------------------------------------------------------------------------------ template inline bool aiMatrix3x3t::operator!= (const aiMatrix4x4t m) const { return !(*this == m); } // ------------------------------------------------------------------------------------------------ template inline aiMatrix3x3t& aiMatrix3x3t::Transpose() { // (TReal&) don't remove, GCC complains cause of packed fields std::swap( (TReal&)a2, (TReal&)b1); std::swap( (TReal&)a3, (TReal&)c1); std::swap( (TReal&)b3, (TReal&)c2); return *this; } // ---------------------------------------------------------------------------------------- template inline TReal aiMatrix3x3t::Determinant() const { return a1*b2*c3 - a1*b3*c2 + a2*b3*c1 - a2*b1*c3 + a3*b1*c2 - a3*b2*c1; } // ---------------------------------------------------------------------------------------- template inline aiMatrix3x3t& aiMatrix3x3t::Inverse() { // Compute the reciprocal determinant TReal det = Determinant(); if(det == static_cast(0.0)) { // Matrix not invertible. Setting all elements to nan is not really // correct in a mathematical sense; but at least qnans are easy to // spot. XXX we might throw an exception instead, which would // be even much better to spot :/. const TReal nan = std::numeric_limits::quiet_NaN(); *this = aiMatrix3x3t( nan,nan,nan,nan,nan,nan,nan,nan,nan); return *this; } TReal invdet = static_cast(1.0) / det; aiMatrix3x3t res; res.a1 = invdet * (b2 * c3 - b3 * c2); res.a2 = -invdet * (a2 * c3 - a3 * c2); res.a3 = invdet * (a2 * b3 - a3 * b2); res.b1 = -invdet * (b1 * c3 - b3 * c1); res.b2 = invdet * (a1 * c3 - a3 * c1); res.b3 = -invdet * (a1 * b3 - a3 * b1); res.c1 = invdet * (b1 * c2 - b2 * c1); res.c2 = -invdet * (a1 * c2 - a2 * c1); res.c3 = invdet * (a1 * b2 - a2 * b1); *this = res; return *this; } // ------------------------------------------------------------------------------------------------ template inline aiMatrix3x3t& aiMatrix3x3t::RotationZ(TReal a, aiMatrix3x3t& out) { out.a1 = out.b2 = ::cos(a); out.b1 = ::sin(a); out.a2 = - out.b1; out.a3 = out.b3 = out.c1 = out.c2 = 0.f; out.c3 = 1.f; return out; } // ------------------------------------------------------------------------------------------------ // Returns a rotation matrix for a rotation around an arbitrary axis. template inline aiMatrix3x3t& aiMatrix3x3t::Rotation( TReal a, const aiVector3t& axis, aiMatrix3x3t& out) { TReal c = cos( a), s = sin( a), t = 1 - c; TReal x = axis.x, y = axis.y, z = axis.z; // Many thanks to MathWorld and Wikipedia out.a1 = t*x*x + c; out.a2 = t*x*y - s*z; out.a3 = t*x*z + s*y; out.b1 = t*x*y + s*z; out.b2 = t*y*y + c; out.b3 = t*y*z - s*x; out.c1 = t*x*z - s*y; out.c2 = t*y*z + s*x; out.c3 = t*z*z + c; return out; } // ------------------------------------------------------------------------------------------------ template inline aiMatrix3x3t& aiMatrix3x3t::Translation( const aiVector2t& v, aiMatrix3x3t& out) { out = aiMatrix3x3t(); out.a3 = v.x; out.b3 = v.y; return out; } // ---------------------------------------------------------------------------------------- /** A function for creating a rotation matrix that rotates a vector called * "from" into another vector called "to". * Input : from[3], to[3] which both must be *normalized* non-zero vectors * Output: mtx[3][3] -- a 3x3 matrix in colum-major form * Authors: Tomas Möller, John Hughes * "Efficiently Building a Matrix to Rotate One Vector to Another" * Journal of Graphics Tools, 4(4):1-4, 1999 */ // ---------------------------------------------------------------------------------------- template inline aiMatrix3x3t& aiMatrix3x3t::FromToMatrix(const aiVector3t& from, const aiVector3t& to, aiMatrix3x3t& mtx) { const TReal e = from * to; const TReal f = (e < 0)? -e:e; if (f > static_cast(1.0) - static_cast(0.00001)) /* "from" and "to"-vector almost parallel */ { aiVector3D u,v; /* temporary storage vectors */ aiVector3D x; /* vector most nearly orthogonal to "from" */ x.x = (from.x > 0.0)? from.x : -from.x; x.y = (from.y > 0.0)? from.y : -from.y; x.z = (from.z > 0.0)? from.z : -from.z; if (x.x < x.y) { if (x.x < x.z) { x.x = static_cast(1.0); x.y = x.z = static_cast(0.0); } else { x.z = static_cast(1.0); x.y = x.z = static_cast(0.0); } } else { if (x.y < x.z) { x.y = static_cast(1.0); x.x = x.z = static_cast(0.0); } else { x.z = static_cast(1.0); x.x = x.y = static_cast(0.0); } } u.x = x.x - from.x; u.y = x.y - from.y; u.z = x.z - from.z; v.x = x.x - to.x; v.y = x.y - to.y; v.z = x.z - to.z; const TReal c1 = static_cast(2.0) / (u * u); const TReal c2 = static_cast(2.0) / (v * v); const TReal c3 = c1 * c2 * (u * v); for (unsigned int i = 0; i < 3; i++) { for (unsigned int j = 0; j < 3; j++) { mtx[i][j] = - c1 * u[i] * u[j] - c2 * v[i] * v[j] + c3 * v[i] * u[j]; } mtx[i][i] += static_cast(1.0); } } else /* the most common case, unless "from"="to", or "from"=-"to" */ { const aiVector3D v = from ^ to; /* ... use this hand optimized version (9 mults less) */ const TReal h = static_cast(1.0)/(static_cast(1.0) + e); /* optimization by Gottfried Chen */ const TReal hvx = h * v.x; const TReal hvz = h * v.z; const TReal hvxy = hvx * v.y; const TReal hvxz = hvx * v.z; const TReal hvyz = hvz * v.y; mtx[0][0] = e + hvx * v.x; mtx[0][1] = hvxy - v.z; mtx[0][2] = hvxz + v.y; mtx[1][0] = hvxy + v.z; mtx[1][1] = e + h * v.y * v.y; mtx[1][2] = hvyz - v.x; mtx[2][0] = hvxz - v.y; mtx[2][1] = hvyz + v.x; mtx[2][2] = e + hvz * v.z; } return mtx; } #endif // __cplusplus #endif // AI_MATRIX3x3_INL_INC