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+///////////////////////////////////////////////////////////////////////////////////
+/// OpenGL Mathematics (glm.g-truc.net)
+///
+/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
+/// Permission is hereby granted, free of charge, to any person obtaining a copy
+/// of this software and associated documentation files (the "Software"), to deal
+/// in the Software without restriction, including without limitation the rights
+/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+/// copies of the Software, and to permit persons to whom the Software is
+/// furnished to do so, subject to the following conditions:
+///
+/// The above copyright notice and this permission notice shall be included in
+/// all copies or substantial portions of the Software.
+///
+/// Restrictions:
+/// By making use of the Software for military purposes, you choose to make
+/// a Bunny unhappy.
+///
+/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+/// THE SOFTWARE.
+///
+/// @ref gtx_matrix_decompose
+/// @file glm/gtx/matrix_decompose.inl
+/// @date 2014-08-29 / 2014-08-29
+/// @author Christophe Riccio
+///////////////////////////////////////////////////////////////////////////////////
+
+namespace glm
+{
+ /// 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 void v3Scale(tvec3<T, P> & v, T desiredLength)
+ {
+ T len = glm::length(v);
+ if(len != 0)
+ {
+ T l = desiredLength / len;
+ v[0] *= l;
+ v[1] *= l;
+ v[2] *= l;
+ }
+ }
+
+ /**
+ * 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] = 0;
+ PerspectiveMatrix[3][3] = 1;
+
+ /// TODO: Fixme!
+ if(determinant(PerspectiveMatrix) == static_cast<T>(0))
+ return false;
+
+ // First, isolate perspective. This is the messiest.
+ if(LocalMatrix[0][3] != 0 || LocalMatrix[1][3] != 0 || LocalMatrix[2][3] != 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] = 0;
+ LocalMatrix[3][3] = 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]);
+
+ v3Scale(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] = combine(Row[1], Row[0], static_cast<T>(1), -Skew.z);
+
+ // Now, compute Y scale and normalize 2nd row.
+ Scale.y = length(Row[1]);
+ v3Scale(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] = combine(Row[2], Row[0], static_cast<T>(1), -Skew.y);
+ Skew.x = glm::dot(Row[1], Row[2]);
+ Row[2] = combine(Row[2], Row[1], static_cast<T>(1), -Skew.x);
+
+ // Next, get Z scale and normalize 3rd row.
+ Scale.z = length(Row[2]);
+ v3Scale(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] + 1.0;
+
+ if(t > 1e-4)
+ {
+ s = 0.5 / sqrt(t);
+ w = 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 (1.0 + Row[0][0] - Row[1][1] - Row[2][2]) * 2.0; // S=4*qx
+ x = 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 (1.0 + Row[1][1] - Row[0][0] - Row[2][2]) * 2.0; // S=4*qy
+ x = (Row[0][1] + Row[1][0]) / s;
+ y = 0.25 * s;
+ z = (Row[1][2] + Row[2][1]) / s;
+ w = (Row[0][2] - Row[2][0]) / s;
+ }
+ else
+ {
+ s = sqrt(1.0 + Row[2][2] - Row[0][0] - Row[1][1]) * 2.0; // S=4*qz
+ x = (Row[0][2] + Row[2][0]) / s;
+ y = (Row[1][2] + Row[2][1]) / s;
+ z = 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