src/third_party/glm/glm/gtx/matrix_decompose.inl - cobalt - Git at Google

 /// @ref gtx_matrix_decompose
 /// @file glm/gtx/matrix_decompose.inl

 namespace glm{
 namespace detail
 {
 	/// Make a linear combination of two vectors and return the result.
 	// result = (a * ascl) + (b * bscl)
 	template <typename T, precision P>
 	GLM_FUNC_QUALIFIER tvec3<T, P> combine(
 		tvec3<T, P> const & a,
 		tvec3<T, P> const & b,
 		T ascl, T bscl)
 	{
 		return (a * ascl) + (b * bscl);
 	}

 	template <typename T, precision P>
 	GLM_FUNC_QUALIFIER tvec3<T, P> scale(tvec3<T, P> 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, precision P>
 	GLM_FUNC_QUALIFIER bool decompose(tmat4x4<T, P> const & ModelMatrix, tvec3<T, P> & Scale, tquat<T, P> & Orientation, tvec3<T, P> & Translation, tvec3<T, P> & Skew, tvec4<T, P> & Perspective)
 	{
 		tmat4x4<T, P> LocalMatrix(ModelMatrix);

 		// Normalize the matrix.
 		if(LocalMatrix[3][3] == static_cast<T>(0))
 			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.
 		tmat4x4<T, P> 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(determinant(PerspectiveMatrix) == static_cast<T>(0))
 			return false;

 		// First, isolate perspective.  This is the messiest.
 		if(LocalMatrix[0][3] != static_cast<T>(0) || LocalMatrix[1][3] != static_cast<T>(0) || LocalMatrix[2][3] != static_cast<T>(0))
 		{
 			// rightHandSide is the right hand side of the equation.
 			tvec4<T, P> 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.)
 			tmat4x4<T, P> InversePerspectiveMatrix = glm::inverse(PerspectiveMatrix);//   inverse(PerspectiveMatrix, inversePerspectiveMatrix);
 			tmat4x4<T, P> TransposedInversePerspectiveMatrix = glm::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 = tvec4<T, P>(0, 0, 0, 1);
 		}

 		// Next take care of translation (easy).
 		Translation = tvec3<T, P>(LocalMatrix[3]);
 		LocalMatrix[3] = tvec4<T, P>(0, 0, 0, LocalMatrix[3].w);

 		tvec3<T, P> Row[3], Pdum3;

 		// Now get scale and shear.
 		for(length_t i = 0; i < 3; ++i)
 			for(int 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 = glm::dot(Row[0], Row[2]);
 		Row[2] = detail::combine(Row[2], Row[0], static_cast<T>(1), -Skew.y);
 		Skew.x = glm::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.x *= 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;
 		// }

 		T s, t, x, y, z, w;

 		t = Row[0][0] + Row[1][1] + Row[2][2] + static_cast<T>(1);

 		if(t > static_cast<T>(1e-4))
 		{
 			s = static_cast<T>(0.5) / sqrt(t);
 			w = static_cast<T>(0.25) / s;
 			x = (Row[2][1] - Row[1][2]) * s;
 			y = (Row[0][2] - Row[2][0]) * s;
 			z = (Row[1][0] - Row[0][1]) * s;
 		}
 		else if(Row[0][0] > Row[1][1] && Row[0][0] > Row[2][2])
 		{
 			s = sqrt (static_cast<T>(1) + Row[0][0] - Row[1][1] - Row[2][2]) * static_cast<T>(2); // S=4*qx
 			x = static_cast<T>(0.25) * s;
 			y = (Row[0][1] + Row[1][0]) / s;
 			z = (Row[0][2] + Row[2][0]) / s;
 			w = (Row[2][1] - Row[1][2]) / s;
 		}
 		else if(Row[1][1] > Row[2][2])
 		{
 			s = sqrt (static_cast<T>(1) + Row[1][1] - Row[0][0] - Row[2][2]) * static_cast<T>(2); // S=4*qy
 			x = (Row[0][1] + Row[1][0]) / s;
 			y = static_cast<T>(0.25) * s;
 			z = (Row[1][2] + Row[2][1]) / s;
 			w = (Row[0][2] - Row[2][0]) / s;
 		}
 		else
 		{
 			s = sqrt(static_cast<T>(1) + Row[2][2] - Row[0][0] - Row[1][1]) * static_cast<T>(2); // S=4*qz
 			x = (Row[0][2] + Row[2][0]) / s;
 			y = (Row[1][2] + Row[2][1]) / s;
 			z = static_cast<T>(0.25) * s;
 			w = (Row[1][0] - Row[0][1]) / s;
 		}

 		Orientation.x = x;
 		Orientation.y = y;
 		Orientation.z = z;
 		Orientation.w = w;

 		return true;
 	}
 }//namespace glm
	/// @ref gtx_matrix_decompose
	/// @file glm/gtx/matrix_decompose.inl

	namespace glm{
	namespace detail
	{
	/// Make a linear combination of two vectors and return the result.
	// result = (a * ascl) + (b * bscl)
	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> combine(
	tvec3<T, P> const & a,
	tvec3<T, P> const & b,
	T ascl, T bscl)
	{
	return (a * ascl) + (b * bscl);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> scale(tvec3<T, P> 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, precision P>
	GLM_FUNC_QUALIFIER bool decompose(tmat4x4<T, P> const & ModelMatrix, tvec3<T, P> & Scale, tquat<T, P> & Orientation, tvec3<T, P> & Translation, tvec3<T, P> & Skew, tvec4<T, P> & Perspective)
	{
	tmat4x4<T, P> LocalMatrix(ModelMatrix);

	// Normalize the matrix.
	if(LocalMatrix[3][3] == static_cast<T>(0))
	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.
	tmat4x4<T, P> 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(determinant(PerspectiveMatrix) == static_cast<T>(0))
	return false;

	// First, isolate perspective. This is the messiest.
	if(LocalMatrix[0][3] != static_cast<T>(0) \|\| LocalMatrix[1][3] != static_cast<T>(0) \|\| LocalMatrix[2][3] != static_cast<T>(0))
	{
	// rightHandSide is the right hand side of the equation.
	tvec4<T, P> 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.)
	tmat4x4<T, P> InversePerspectiveMatrix = glm::inverse(PerspectiveMatrix);// inverse(PerspectiveMatrix, inversePerspectiveMatrix);
	tmat4x4<T, P> TransposedInversePerspectiveMatrix = glm::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 = tvec4<T, P>(0, 0, 0, 1);
	}

	// Next take care of translation (easy).
	Translation = tvec3<T, P>(LocalMatrix[3]);
	LocalMatrix[3] = tvec4<T, P>(0, 0, 0, LocalMatrix[3].w);

	tvec3<T, P> Row[3], Pdum3;

	// Now get scale and shear.
	for(length_t i = 0; i < 3; ++i)
	for(int 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 = glm::dot(Row[0], Row[2]);
	Row[2] = detail::combine(Row[2], Row[0], static_cast<T>(1), -Skew.y);
	Skew.x = glm::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.x *= 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;
	// }

	T s, t, x, y, z, w;

	t = Row[0][0] + Row[1][1] + Row[2][2] + static_cast<T>(1);

	if(t > static_cast<T>(1e-4))
	{
	s = static_cast<T>(0.5) / sqrt(t);
	w = static_cast<T>(0.25) / s;
	x = (Row[2][1] - Row[1][2]) * s;
	y = (Row[0][2] - Row[2][0]) * s;
	z = (Row[1][0] - Row[0][1]) * s;
	}
	else if(Row[0][0] > Row[1][1] && Row[0][0] > Row[2][2])
	{
	s = sqrt (static_cast<T>(1) + Row[0][0] - Row[1][1] - Row[2][2]) * static_cast<T>(2); // S=4*qx
	x = static_cast<T>(0.25) * s;
	y = (Row[0][1] + Row[1][0]) / s;
	z = (Row[0][2] + Row[2][0]) / s;
	w = (Row[2][1] - Row[1][2]) / s;
	}
	else if(Row[1][1] > Row[2][2])
	{
	s = sqrt (static_cast<T>(1) + Row[1][1] - Row[0][0] - Row[2][2]) * static_cast<T>(2); // S=4*qy
	x = (Row[0][1] + Row[1][0]) / s;
	y = static_cast<T>(0.25) * s;
	z = (Row[1][2] + Row[2][1]) / s;
	w = (Row[0][2] - Row[2][0]) / s;
	}
	else
	{
	s = sqrt(static_cast<T>(1) + Row[2][2] - Row[0][0] - Row[1][1]) * static_cast<T>(2); // S=4*qz
	x = (Row[0][2] + Row[2][0]) / s;
	y = (Row[1][2] + Row[2][1]) / s;
	z = static_cast<T>(0.25) * s;
	w = (Row[1][0] - Row[0][1]) / s;
	}

	Orientation.x = x;
	Orientation.y = y;
	Orientation.z = z;
	Orientation.w = w;

	return true;
	}
	}//namespace glm