[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #ifndef EIGEN_EULERANGLES_H
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| 11 | #define EIGEN_EULERANGLES_H
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| 12 |
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| 13 | namespace Eigen {
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| 14 |
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| 15 | /** \geometry_module \ingroup Geometry_Module
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| 16 | *
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| 17 | *
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| 18 | * \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
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| 19 | *
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| 20 | * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
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| 21 | * For instance, in:
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| 22 | * \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
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| 23 | * "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
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| 24 | * we have the following equality:
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| 25 | * \code
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| 26 | * mat == AngleAxisf(ea[0], Vector3f::UnitZ())
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| 27 | * * AngleAxisf(ea[1], Vector3f::UnitX())
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| 28 | * * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
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| 29 | * This corresponds to the right-multiply conventions (with right hand side frames).
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| 30 | *
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| 31 | * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
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| 32 | *
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| 33 | * \sa class AngleAxis
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| 34 | */
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| 35 | template<typename Derived>
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| 36 | inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
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| 37 | MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
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| 38 | {
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| 39 | using std::atan2;
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| 40 | using std::sin;
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| 41 | using std::cos;
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| 42 | /* Implemented from Graphics Gems IV */
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| 43 | EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
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| 44 |
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| 45 | Matrix<Scalar,3,1> res;
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| 46 | typedef Matrix<typename Derived::Scalar,2,1> Vector2;
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| 47 |
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| 48 | const Index odd = ((a0+1)%3 == a1) ? 0 : 1;
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| 49 | const Index i = a0;
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| 50 | const Index j = (a0 + 1 + odd)%3;
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| 51 | const Index k = (a0 + 2 - odd)%3;
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| 52 |
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| 53 | if (a0==a2)
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| 54 | {
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| 55 | res[0] = atan2(coeff(j,i), coeff(k,i));
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| 56 | if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0)))
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| 57 | {
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| 58 | res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
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| 59 | Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
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| 60 | res[1] = -atan2(s2, coeff(i,i));
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| 61 | }
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| 62 | else
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| 63 | {
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| 64 | Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
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| 65 | res[1] = atan2(s2, coeff(i,i));
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| 66 | }
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| 67 |
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| 68 | // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
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| 69 | // we can compute their respective rotation, and apply its inverse to M. Since the result must
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| 70 | // be a rotation around x, we have:
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| 71 | //
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| 72 | // c2 s1.s2 c1.s2 1 0 0
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| 73 | // 0 c1 -s1 * M = 0 c3 s3
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| 74 | // -s2 s1.c2 c1.c2 0 -s3 c3
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| 75 | //
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| 76 | // Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
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| 77 |
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| 78 | Scalar s1 = sin(res[0]);
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| 79 | Scalar c1 = cos(res[0]);
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| 80 | res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
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| 81 | }
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| 82 | else
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| 83 | {
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| 84 | res[0] = atan2(coeff(j,k), coeff(k,k));
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| 85 | Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
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| 86 | if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) {
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| 87 | res[0] = (res[0] > Scalar(0)) ? res[0] - Scalar(M_PI) : res[0] + Scalar(M_PI);
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| 88 | res[1] = atan2(-coeff(i,k), -c2);
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| 89 | }
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| 90 | else
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| 91 | res[1] = atan2(-coeff(i,k), c2);
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| 92 | Scalar s1 = sin(res[0]);
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| 93 | Scalar c1 = cos(res[0]);
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| 94 | res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
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| 95 | }
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| 96 | if (!odd)
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| 97 | res = -res;
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| 98 |
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| 99 | return res;
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| 100 | }
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| 101 |
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| 102 | } // end namespace Eigen
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| 103 |
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| 104 | #endif // EIGEN_EULERANGLES_H
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