rotation.hpp

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//
// Copyright (c) 2019-2020 CNRS INRIA
//
 
#ifndef __pinocchio_math_rotation_hpp__
#define __pinocchio_math_rotation_hpp__
 
#include "pinocchio/fwd.hpp"
#include "pinocchio/math/matrix.hpp"
#include "pinocchio/math/sincos.hpp"
 
#include <Eigen/Core>
#include <Eigen/Geometry>
#include <Eigen/SVD>
 
namespace pinocchio
{
 
  template<typename Vector3, typename Scalar, typename Matrix3>
  void toRotationMatrix(
    const Eigen::MatrixBase<Vector3> & axis,
    const Scalar & cos_value,
    const Scalar & sin_value,
    const Eigen::MatrixBase<Matrix3> & res)
  {
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3, 3);
    EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3, 3, 3);
 
    assert(isUnitary(axis) && "The axis is not unitary.");
 
    Matrix3 & res_ = PINOCCHIO_EIGEN_CONST_CAST(Matrix3, res);
    Vector3 sin_axis = sin_value * axis;
    Vector3 cos1_axis = (Scalar(1) - cos_value) * axis;
 
    Scalar tmp;
    tmp = cos1_axis.x() * axis.y();
    res_.coeffRef(0, 1) = tmp - sin_axis.z();
    res_.coeffRef(1, 0) = tmp + sin_axis.z();
 
    tmp = cos1_axis.x() * axis.z();
    res_.coeffRef(0, 2) = tmp + sin_axis.y();
    res_.coeffRef(2, 0) = tmp - sin_axis.y();
 
    tmp = cos1_axis.y() * axis.z();
    res_.coeffRef(1, 2) = tmp - sin_axis.x();
    res_.coeffRef(2, 1) = tmp + sin_axis.x();
 
    res_.diagonal() = (cos1_axis.cwiseProduct(axis)).array() + cos_value;
  }
 
  template<typename Vector3, typename Scalar, typename Matrix3>
  void toRotationMatrix(
    const Eigen::MatrixBase<Vector3> & axis,
    const Scalar & angle,
    const Eigen::MatrixBase<Matrix3> & res)
  {
    Scalar sa, ca;
    SINCOS(angle, &sa, &ca);
    toRotationMatrix(axis, ca, sa, PINOCCHIO_EIGEN_CONST_CAST(Matrix3, res));
  }
 
  template<typename Matrix3>
  void normalizeRotation(const Eigen::MatrixBase<Matrix3> & rot)
  {
    EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3, 3, 3);
    Matrix3 & rot_ = PINOCCHIO_EIGEN_CONST_CAST(Matrix3, rot);
 
    typedef typename Matrix3::Scalar Scalar;
    enum
    {
      Options = PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3)::Options
    };
    typedef Eigen::Quaternion<Scalar, Options> Quaternion;
    Quaternion quat(rot);
    normalize(quat.coeffs());
    rot_ = quat.toRotationMatrix();
  }
 
  template<typename Matrix3>
  typename PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3)
    orthogonalProjection(const Eigen::MatrixBase<Matrix3> & mat)
  {
    EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3, 3, 3);
    typedef typename PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3) ReturnType;
 
    typedef Eigen::JacobiSVD<Matrix3> SVD;
    const SVD svd(mat, Eigen::ComputeFullU | Eigen::ComputeFullV);
 
    ReturnType res;
    res.template leftCols<2>().noalias() =
      svd.matrixU() * svd.matrixV().transpose().template leftCols<2>();
    res.col(2).noalias() = res.col(0).cross(res.col(1));
    return res;
  }
} // namespace pinocchio
 
#endif // #ifndef __pinocchio_math_rotation_hpp__