text: /// @ref gtx_matrix_decompose
  
  #include "../gtc/constants.hpp"
  #include "../gtc/epsilon.hpp"
  
  namespace args::core::math{
  namespace detail
  {
  	/// Make a linear combination of two vectors and return the result.
  	// result = (a * ascl) + (b * bscl)
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER vec<3, T, Q> combine(
  		vec<3, T, Q> const& a,
  		vec<3, T, Q> const& b,
  		T ascl, T bscl)
  	{
  		return (a * ascl) + (b * bscl);
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER vec<3, T, Q> scale(vec<3, T, Q> const& v, T desiredLength)
  	{
  		return v * desiredLength / length(v);
  	}
  }//namespace detail
  
  	// Matrix decompose
  	// http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp
  	// Decomposes the mode matrix to translations,rotation scale components
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER bool decompose(mat<4, 4, T, Q> const& ModelMatrix, vec<3, T, Q> & Scale, qua<T, Q> & Orientation, vec<3, T, Q> & Translation, vec<3, T, Q> & Skew, vec<4, T, Q> & Perspective)
  	{
  		mat<4, 4, T, Q> LocalMatrix(ModelMatrix);
  
  		// Normalize the matrix.
  		if(epsilonEqual(LocalMatrix[3][3], static_cast<T>(0), epsilon<T>()))
  			return false;
  
  		for(length_t i = 0; i < 4; ++i)
  		for(length_t j = 0; j < 4; ++j)
  			LocalMatrix[i][j] /= LocalMatrix[3][3];
  
  		// perspectiveMatrix is used to solve for perspective, but it also provides
  		// an easy way to test for singularity of the upper 3x3 component.
  		mat<4, 4, T, Q> PerspectiveMatrix(LocalMatrix);
  
  		for(length_t i = 0; i < 3; i++)
  			PerspectiveMatrix[i][3] = static_cast<T>(0);
  		PerspectiveMatrix[3][3] = static_cast<T>(1);
  
  		/// TODO: Fixme!
  		if(epsilonEqual(determinant(PerspectiveMatrix), static_cast<T>(0), epsilon<T>()))
  			return false;
  
  		// First, isolate perspective.  This is the messiest.
  		if(
  			epsilonNotEqual(LocalMatrix[0][3], static_cast<T>(0), epsilon<T>()) ||
  			epsilonNotEqual(LocalMatrix[1][3], static_cast<T>(0), epsilon<T>()) ||
  			epsilonNotEqual(LocalMatrix[2][3], static_cast<T>(0), epsilon<T>()))
  		{
  			// rightHandSide is the right hand side of the equation.
  			vec<4, T, Q> RightHandSide;
  			RightHandSide[0] = LocalMatrix[0][3];
  			RightHandSide[1] = LocalMatrix[1][3];
  			RightHandSide[2] = LocalMatrix[2][3];
  			RightHandSide[3] = LocalMatrix[3][3];
  
  			// Solve the equation by inverting PerspectiveMatrix and multiplying
  			// rightHandSide by the inverse.  (This is the easiest way, not
  			// necessarily the best.)
  			mat<4, 4, T, Q> InversePerspectiveMatrix = math::inverse(PerspectiveMatrix);//   inverse(PerspectiveMatrix, inversePerspectiveMatrix);
  			mat<4, 4, T, Q> TransposedInversePerspectiveMatrix = math::transpose(InversePerspectiveMatrix);//   transposeMatrix4(inversePerspectiveMatrix, transposedInversePerspectiveMatrix);
  
  			Perspective = TransposedInversePerspectiveMatrix * RightHandSide;
  			//  v4MulPointByMatrix(rightHandSide, transposedInversePerspectiveMatrix, perspectivePoint);
  
  			// Clear the perspective partition
  			LocalMatrix[0][3] = LocalMatrix[1][3] = LocalMatrix[2][3] = static_cast<T>(0);
  			LocalMatrix[3][3] = static_cast<T>(1);
  		}
  		else
  		{
  			// No perspective.
  			Perspective = vec<4, T, Q>(0, 0, 0, 1);
  		}
  
  		// Next take care of translation (easy).
  		Translation = vec<3, T, Q>(LocalMatrix[3]);
  		LocalMatrix[3] = vec<4, T, Q>(0, 0, 0, LocalMatrix[3].w);
  
  		vec<3, T, Q> Row[3], Pdum3;
  
  		// Now get scale and shear.
  		for(length_t i = 0; i < 3; ++i)
  		for(length_t j = 0; j < 3; ++j)
  			Row[i][j] = LocalMatrix[i][j];
  
  		// Compute X scale factor and normalize first row.
  		Scale.x = length(Row[0]);// v3Length(Row[0]);
  
  		Row[0] = detail::scale(Row[0], static_cast<T>(1));
  
  		// Compute XY shear factor and make 2nd row orthogonal to 1st.
  		Skew.z = dot(Row[0], Row[1]);
  		Row[1] = detail::combine(Row[1], Row[0], static_cast<T>(1), -Skew.z);
  
  		// Now, compute Y scale and normalize 2nd row.
  		Scale.y = length(Row[1]);
  		Row[1] = detail::scale(Row[1], static_cast<T>(1));
  		Skew.z /= Scale.y;
  
  		// Compute XZ and YZ shears, orthogonalize 3rd row.
  		Skew.y = math::dot(Row[0], Row[2]);
  		Row[2] = detail::combine(Row[2], Row[0], static_cast<T>(1), -Skew.y);
  		Skew.x = math::dot(Row[1], Row[2]);
  		Row[2] = detail::combine(Row[2], Row[1], static_cast<T>(1), -Skew.x);
  
  		// Next, get Z scale and normalize 3rd row.
  		Scale.z = length(Row[2]);
  		Row[2] = detail::scale(Row[2], static_cast<T>(1));
  		Skew.y /= Scale.z;
  		Skew.x /= Scale.z;
  
  		// At this point, the matrix (in rows[]) is orthonormal.
  		// Check for a coordinate system flip.  If the determinant
  		// is -1, then negate the matrix and the scaling factors.
  		Pdum3 = cross(Row[1], Row[2]); // v3Cross(row[1], row[2], Pdum3);
  		if(dot(Row[0], Pdum3) < 0)
  		{
  			for(length_t i = 0; i < 3; i++)
  			{
  				Scale[i] *= static_cast<T>(-1);
  				Row[i] *= static_cast<T>(-1);
  			}
  		}
  
  		// Now, get the rotations out, as described in the gem.
  
  		// FIXME - Add the ability to return either quaternions (which are
  		// easier to recompose with) or Euler angles (rx, ry, rz), which
  		// are easier for authors to deal with. The latter will only be useful
  		// when we fix https://bugs.webkit.org/show_bug.cgi?id=23799, so I
  		// will leave the Euler angle code here for now.
  
  		// ret.rotateY = asin(-Row[0][2]);
  		// if (cos(ret.rotateY) != 0) {
  		//     ret.rotateX = atan2(Row[1][2], Row[2][2]);
  		//     ret.rotateZ = atan2(Row[0][1], Row[0][0]);
  		// } else {
  		//     ret.rotateX = atan2(-Row[2][0], Row[1][1]);
  		//     ret.rotateZ = 0;
  		// }
  
  		int i, j, k = 0;
  		T root, trace = Row[0].x + Row[1].y + Row[2].z;
  		if(trace > static_cast<T>(0))
  		{
  			root = sqrt(trace + static_cast<T>(1.0));
  			Orientation.w = static_cast<T>(0.5) * root;
  			root = static_cast<T>(0.5) / root;
  			Orientation.x = root * (Row[1].z - Row[2].y);
  			Orientation.y = root * (Row[2].x - Row[0].z);
  			Orientation.z = root * (Row[0].y - Row[1].x);
  		} // End if > 0
  		else
  		{
  			static int Next[3] = {1, 2, 0};
  			i = 0;
  			if(Row[1].y > Row[0].x) i = 1;
  			if(Row[2].z > Row[i][i]) i = 2;
  			j = Next[i];
  			k = Next[j];
  
  			root = sqrt(Row[i][i] - Row[j][j] - Row[k][k] + static_cast<T>(1.0));
  
  			Orientation[i] = static_cast<T>(0.5) * root;
  			root = static_cast<T>(0.5) / root;
  			Orientation[j] = root * (Row[i][j] + Row[j][i]);
  			Orientation[k] = root * (Row[i][k] + Row[k][i]);
  			Orientation.w = root * (Row[j][k] - Row[k][j]);
  		} // End if <= 0
  
  		return true;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER void compose(mat<4, 4, T, Q>& ModelMatrix, const vec<3, T, Q>& Scale, const qua<T, Q>& Orientation, const vec<3, T, Q>& Translation)
  	{
  		ModelMatrix = translate(Translation) * toMat4(Orientation) * scale(Scale);
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER bool decompose(mat<4, 4, T, Q> const& ModelMatrix, vec<3, T, Q>& Scale, qua<T, Q>& Orientation, vec<3, T, Q>& Translation)
  	{
  		mat<4, 4, T, Q> LocalMatrix(ModelMatrix);
  
  		// Normalize the matrix.
  		if (epsilonEqual(LocalMatrix[3][3], static_cast<T>(0), epsilon<T>()))
  			return false;
  
  		for (length_t i = 0; i < 4; ++i)
  			for (length_t j = 0; j < 4; ++j)
  				LocalMatrix[i][j] /= LocalMatrix[3][3];
  
  		// perspectiveMatrix is used to solve for perspective, but it also provides
  		// an easy way to test for singularity of the upper 3x3 component.
  		mat<4, 4, T, Q> PerspectiveMatrix(LocalMatrix);
  
  		for (length_t i = 0; i < 3; i++)
  			PerspectiveMatrix[i][3] = static_cast<T>(0);
  		PerspectiveMatrix[3][3] = static_cast<T>(1);
  
  		/// TODO: Fixme!
  		if (epsilonEqual(determinant(PerspectiveMatrix), static_cast<T>(0), epsilon<T>()))
  			return false;
  
  		// Next take care of translation (easy).
  		Translation = vec<3, T, Q>(LocalMatrix[3]);
  		LocalMatrix[3] = vec<4, T, Q>(0, 0, 0, LocalMatrix[3].w);
  
  		vec<3, T, Q> Row[3], Pdum3;
  
  		// Now get scale and shear.
  		for (length_t i = 0; i < 3; ++i)
  			for (length_t j = 0; j < 3; ++j)
  				Row[i][j] = LocalMatrix[i][j];
  
  		// Compute X scale factor and normalize first row.
  		Scale.x = length(Row[0]);// v3Length(Row[0]);
  
  		Row[0] = detail::scale(Row[0], static_cast<T>(1));
  
  		// At this point, the matrix (in rows[]) is orthonormal.
  		// Check for a coordinate system flip.  If the determinant
  		// is -1, then negate the matrix and the scaling factors.
  		Pdum3 = cross(Row[1], Row[2]); // v3Cross(row[1], row[2], Pdum3);
  		if (dot(Row[0], Pdum3) < 0)
  		{
  			for (length_t i = 0; i < 3; i++)
  			{
  				Scale[i] *= static_cast<T>(-1);
  				Row[i] *= static_cast<T>(-1);
  			}
  		}
  
  		// Now, get the rotations out, as described in the gem.
  
  		// FIXME - Add the ability to return either quaternions (which are
  		// easier to recompose with) or Euler angles (rx, ry, rz), which
  		// are easier for authors to deal with. The latter will only be useful
  		// when we fix https://bugs.webkit.org/show_bug.cgi?id=23799, so I
  		// will leave the Euler angle code here for now.
  
  		// ret.rotateY = asin(-Row[0][2]);
  		// if (cos(ret.rotateY) != 0) {
  		//     ret.rotateX = atan2(Row[1][2], Row[2][2]);
  		//     ret.rotateZ = atan2(Row[0][1], Row[0][0]);
  		// } else {
  		//     ret.rotateX = atan2(-Row[2][0], Row[1][1]);
  		//     ret.rotateZ = 0;
  		// }
  
  		int i, j, k = 0;
  		T root, trace = Row[0].x + Row[1].y + Row[2].z;
  		if (trace > static_cast<T>(0))
  		{
  			root = sqrt(trace + static_cast<T>(1.0));
  			Orientation.w = static_cast<T>(0.5) * root;
  			root = static_cast<T>(0.5) / root;
  			Orientation.x = root * (Row[1].z - Row[2].y);
  			Orientation.y = root * (Row[2].x - Row[0].z);
  			Orientation.z = root * (Row[0].y - Row[1].x);
  		} // End if > 0
  		else
  		{
  			static int Next[3] = { 1, 2, 0 };
  			i = 0;
  			if (Row[1].y > Row[0].x) i = 1;
  			if (Row[2].z > Row[i][i]) i = 2;
  			j = Next[i];
  			k = Next[j];
  
  			root = sqrt(Row[i][i] - Row[j][j] - Row[k][k] + static_cast<T>(1.0));
  
  			Orientation[i] = static_cast<T>(0.5) * root;
  			root = static_cast<T>(0.5) / root;
  			Orientation[j] = root * (Row[i][j] + Row[j][i]);
  			Orientation[k] = root * (Row[i][k] + Row[k][i]);
  			Orientation.w = root * (Row[j][k] - Row[k][j]);
  		} // End if <= 0
  
  		return true;
  	}
  }//namespace args::core::math
  