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+///////////////////////////////////////////////////////////////////////////////////
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+/// OpenGL Mathematics (glm.g-truc.net)
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+///
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+/// Copyright (c) 2005 - 2014 G-Truc Creation (www.g-truc.net)
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+/// Permission is hereby granted, free of charge, to any person obtaining a copy
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+/// of this software and associated documentation files (the "Software"), to deal
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+/// in the Software without restriction, including without limitation the rights
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+/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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+/// copies of the Software, and to permit persons to whom the Software is
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+/// furnished to do so, subject to the following conditions:
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+///
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+/// The above copyright notice and this permission notice shall be included in
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+/// all copies or substantial portions of the Software.
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+///
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+/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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+/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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+/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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+/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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+/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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+/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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+/// THE SOFTWARE.
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+///
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+/// @ref gtx_decomposition
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+/// @file glm/gtx/decomposition.inl
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+/// @date 2014-08-29 / 2014-08-29
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+/// @author Christophe Riccio
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+///////////////////////////////////////////////////////////////////////////////////
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+
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+namespace glm
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+{
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+ /// Make a linear combination of two vectors and return the result.
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+ // result = (a * ascl) + (b * bscl)
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+ template <typename T, precision P>
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+ GLM_FUNC_QUALIFIER detail::tvec3<T, P> combine(
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+ detail::tvec3<T, P> const & a,
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+ detail::tvec3<T, P> const & b,
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+ T ascl, T bscl)
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+ {
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+ return (a * ascl) + (b * bscl);
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+ }
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+
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+ template <typename T, precision P>
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+ GLM_FUNC_QUALIFIER void v3Scale(detail::tvec3<T, P> & v, T desiredLength)
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+ {
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+ T len = glm::length(v);
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+ if(len != 0)
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+ {
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+ T l = desiredLength / len;
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+ v[0] *= l;
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+ v[1] *= l;
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+ v[2] *= l;
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+ }
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+ }
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+
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+ /**
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+ * Matrix decompose
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+ * http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp
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+ * Decomposes the mode matrix to translations,rotation scale components
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+ *
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+ */
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+
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+ template <typename T, precision P>
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+ GLM_FUNC_QUALIFIER bool decompose(detail::tmat4x4<T, P> const & ModelMatrix, detail::tvec3<T, P> & Scale, detail::tquat<T, P> & Orientation, detail::tvec3<T, P> & Translation, detail::tvec3<T, P> & Skew, detail::tvec4<T, P> & Perspective)
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+ {
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+ detail::tmat4x4<T, P> LocalMatrix(ModelMatrix);
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+
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+ // Normalize the matrix.
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+ if(LocalMatrix[3][3] == static_cast<T>(0))
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+ return false;
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+
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+ for(length_t i = 0; i < 4; i++)
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+ for(length_t j = 0; j < 4; j++)
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+ LocalMatrix[i][j] /= LocalMatrix[3][3];
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+
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+ // perspectiveMatrix is used to solve for perspective, but it also provides
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+ // an easy way to test for singularity of the upper 3x3 component.
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+ detail::tmat4x4<T, P> PerspectiveMatrix(LocalMatrix);
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+
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+ for(length_t i = 0; i < 3; i++)
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+ PerspectiveMatrix[i][3] = 0;
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+ PerspectiveMatrix[3][3] = 1;
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+
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+ /// TODO: Fixme!
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+ if(determinant(PerspectiveMatrix) == static_cast<T>(0))
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+ return false;
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+
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+ // First, isolate perspective. This is the messiest.
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+ if(LocalMatrix[0][3] != 0 || LocalMatrix[1][3] != 0 || LocalMatrix[2][3] != 0)
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+ {
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+ // rightHandSide is the right hand side of the equation.
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+ detail::tvec4<T, P> RightHandSide;
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+ RightHandSide[0] = LocalMatrix[0][3];
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+ RightHandSide[1] = LocalMatrix[1][3];
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+ RightHandSide[2] = LocalMatrix[2][3];
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+ RightHandSide[3] = LocalMatrix[3][3];
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+
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+ // Solve the equation by inverting PerspectiveMatrix and multiplying
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+ // rightHandSide by the inverse. (This is the easiest way, not
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+ // necessarily the best.)
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+ detail::tmat4x4<T, P> InversePerspectiveMatrix = glm::inverse(PerspectiveMatrix);// inverse(PerspectiveMatrix, inversePerspectiveMatrix);
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+ detail::tmat4x4<T, P> TransposedInversePerspectiveMatrix = glm::transpose(InversePerspectiveMatrix);// transposeMatrix4(inversePerspectiveMatrix, transposedInversePerspectiveMatrix);
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+
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+ Perspective = TransposedInversePerspectiveMatrix * RightHandSide;
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+ // v4MulPointByMatrix(rightHandSide, transposedInversePerspectiveMatrix, perspectivePoint);
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+
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+ // Clear the perspective partition
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+ LocalMatrix[0][3] = LocalMatrix[1][3] = LocalMatrix[2][3] = 0;
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+ LocalMatrix[3][3] = 1;
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+ }
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+ else
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+ {
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+ // No perspective.
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+ Perspective = detail::tvec4<T, P>(0, 0, 0, 1);
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+ }
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+
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+ // Next take care of translation (easy).
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+ Translation = detail::tvec3<T, P>(LocalMatrix[3]);
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+ LocalMatrix[3] = detail::tvec4<T, P>(0, 0, 0, LocalMatrix[3].w);
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+
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+ detail::tvec3<T, P> Row[3], Pdum3;
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+
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+ // Now get scale and shear.
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+ for(length_t i = 0; i < 3; ++i)
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+ Row[i] = LocalMatrix[i];
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+
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+ // Compute X scale factor and normalize first row.
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+ Scale.x = length(Row[0]);// v3Length(Row[0]);
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+
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+ v3Scale(Row[0], 1.0);
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+
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+ // Compute XY shear factor and make 2nd row orthogonal to 1st.
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+ Skew.z = dot(Row[0], Row[1]);
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+ Row[1] = combine(Row[1], Row[0], 1.0, -Skew.z);
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+
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+ // Now, compute Y scale and normalize 2nd row.
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+ Scale.y = length(Row[1]);
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+ v3Scale(Row[1], 1.0);
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+ Skew.z /= Scale.y;
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+
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+ // Compute XZ and YZ shears, orthogonalize 3rd row.
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+ Skew.y = glm::dot(Row[0], Row[2]);
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+ Row[2] = combine(Row[2], Row[0], 1.0, -Skew.y);
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+ Skew.x = glm::dot(Row[1], Row[2]);
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+ Row[2] = combine(Row[2], Row[1], 1.0, -Skew.x);
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+
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+ // Next, get Z scale and normalize 3rd row.
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+ Scale.z = length(Row[2]);
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+ v3Scale(Row[2], 1.0);
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+ Skew.y /= Scale.z;
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+ Skew.x /= Scale.z;
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+
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+ // At this point, the matrix (in rows[]) is orthonormal.
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+ // Check for a coordinate system flip. If the determinant
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+ // is -1, then negate the matrix and the scaling factors.
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+ Pdum3 = cross(Row[1], Row[2]); // v3Cross(row[1], row[2], Pdum3);
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+ if(dot(Row[0], Pdum3) < 0)
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+ {
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+ for(length_t i = 0; i < 3; i++)
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+ {
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+ Scale.x *= static_cast<T>(-1);
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+ Row[i] *= static_cast<T>(-1);
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+ }
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+ }
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+
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+ // Now, get the rotations out, as described in the gem.
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+
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+ // FIXME - Add the ability to return either quaternions (which are
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+ // easier to recompose with) or Euler angles (rx, ry, rz), which
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+ // are easier for authors to deal with. The latter will only be useful
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+ // when we fix https://bugs.webkit.org/show_bug.cgi?id=23799, so I
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+ // will leave the Euler angle code here for now.
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+
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+ // ret.rotateY = asin(-Row[0][2]);
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+ // if (cos(ret.rotateY) != 0) {
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+ // ret.rotateX = atan2(Row[1][2], Row[2][2]);
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+ // ret.rotateZ = atan2(Row[0][1], Row[0][0]);
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+ // } else {
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+ // ret.rotateX = atan2(-Row[2][0], Row[1][1]);
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+ // ret.rotateZ = 0;
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+ // }
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+
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+ T s, t, x, y, z, w;
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+
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+ t = Row[0][0] + Row[1][1] + Row[2][2] + 1.0;
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+
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+ if(t > 1e-4)
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+ {
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+ s = 0.5 / sqrt(t);
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+ w = 0.25 / s;
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+ x = (Row[2][1] - Row[1][2]) * s;
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+ y = (Row[0][2] - Row[2][0]) * s;
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+ z = (Row[1][0] - Row[0][1]) * s;
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+ }
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+ else if(Row[0][0] > Row[1][1] && Row[0][0] > Row[2][2])
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+ {
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+ s = sqrt (1.0 + Row[0][0] - Row[1][1] - Row[2][2]) * 2.0; // S=4*qx
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+ x = 0.25 * s;
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+ y = (Row[0][1] + Row[1][0]) / s;
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+ z = (Row[0][2] + Row[2][0]) / s;
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+ w = (Row[2][1] - Row[1][2]) / s;
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+ }
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+ else if(Row[1][1] > Row[2][2])
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+ {
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+ s = sqrt (1.0 + Row[1][1] - Row[0][0] - Row[2][2]) * 2.0; // S=4*qy
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+ x = (Row[0][1] + Row[1][0]) / s;
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+ y = 0.25 * s;
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+ z = (Row[1][2] + Row[2][1]) / s;
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+ w = (Row[0][2] - Row[2][0]) / s;
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+ }
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+ else
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+ {
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+ s = sqrt(1.0 + Row[2][2] - Row[0][0] - Row[1][1]) * 2.0; // S=4*qz
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+ x = (Row[0][2] + Row[2][0]) / s;
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+ y = (Row[1][2] + Row[2][1]) / s;
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+ z = 0.25 * s;
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+ w = (Row[1][0] - Row[0][1]) / s;
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+ }
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+
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+ Orientation.x = x;
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+ Orientation.y = y;
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+ Orientation.z = z;
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+ Orientation.w = w;
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+
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+ return true;
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+
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+ }
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+}//namespace glm
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Christophe Riccio