Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/Eigen/src/Geometry/EulerAngles.h b/Eigen/src/Geometry/EulerAngles.h
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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_EULERANGLES_H
+#define EIGEN_EULERANGLES_H
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ *
+ * \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
+ *
+ * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
+ * For instance, in:
+ * \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
+ * "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
+ * we have the following equality:
+ * \code
+ * mat == AngleAxisf(ea[0], Vector3f::UnitZ())
+ * * AngleAxisf(ea[1], Vector3f::UnitX())
+ * * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
+ * This corresponds to the right-multiply conventions (with right hand side frames).
+ *
+ * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
+ *
+ * \sa class AngleAxis
+ */
+template<typename Derived>
+inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
+MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
+{
+ using std::atan2;
+ using std::sin;
+ using std::cos;
+ /* Implemented from Graphics Gems IV */
+ EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
+
+ Matrix<Scalar,3,1> res;
+ typedef Matrix<typename Derived::Scalar,2,1> Vector2;
+
+ const Index odd = ((a0+1)%3 == a1) ? 0 : 1;
+ const Index i = a0;
+ const Index j = (a0 + 1 + odd)%3;
+ const Index k = (a0 + 2 - odd)%3;
+
+ if (a0==a2)
+ {
+ res[0] = atan2(coeff(j,i), coeff(k,i));
+ if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0)))
+ {
+ res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
+ Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
+ res[1] = -atan2(s2, coeff(i,i));
+ }
+ else
+ {
+ Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
+ res[1] = atan2(s2, coeff(i,i));
+ }
+
+ // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
+ // we can compute their respective rotation, and apply its inverse to M. Since the result must
+ // be a rotation around x, we have:
+ //
+ // c2 s1.s2 c1.s2 1 0 0
+ // 0 c1 -s1 * M = 0 c3 s3
+ // -s2 s1.c2 c1.c2 0 -s3 c3
+ //
+ // Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
+
+ Scalar s1 = sin(res[0]);
+ Scalar c1 = cos(res[0]);
+ res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
+ }
+ else
+ {
+ res[0] = atan2(coeff(j,k), coeff(k,k));
+ Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
+ if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) {
+ res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
+ res[1] = atan2(-coeff(i,k), -c2);
+ }
+ else
+ res[1] = atan2(-coeff(i,k), c2);
+ Scalar s1 = sin(res[0]);
+ Scalar c1 = cos(res[0]);
+ res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
+ }
+ if (!odd)
+ res = -res;
+
+ return res;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_EULERANGLES_H