Provide functions to write numerically stable code and avoid pitfalls

[AlexanderFabisch]

Features

• Add conversions between axis-angle representation and MRP
• Add functions to write numerically stable code and avoid pitfalls
  • matrix_requires_renormalization - check if rotation matrix needs renormalization
  • norm_euler - maps Euler angles to unique interval
  • euler_near_gimbal_lock - checks if angles are close to gimbal lock singularity
  • assert_euler_almost_equal - checks if two sets of Euler angles are similar
  • compact_axis_angle_near_pi - check if angle is close to pi
  • quaternion_double - create another quaternion that represents the same orientation (double cover)
  • quaternion_requires_renormalization - check if quaternion needs renormalization
  • mrp_near_singularity - check if angle is close to 2 * pi
  • norm_mrp_angle - normalize angle to [-pi, pi]
  • mrp_double - create another mrp that represents the same orientation (double cover)
  • assert_mrp_almost_equal - check if two mrp vectors are similar
  • transform_requires_renormalization - check if transformation matrix needs renormalization
  • assert_exponential_coordinates_almost_equal - check if exp. coordinates are similar
  • dual_quaternion_requires_renormalization - check if dual quaternion needs renormalization
  • dual_quaternion_double - create another dual quaternion that represents the same transformation (double cover)

Documentation

• Sort API documentation of rotations and transformations by representation

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Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 100.00%. Comparing base (ea69792) to head (96f5592).
Report is 170 commits behind head on develop.

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Additional details and impacted files

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  Files           31        33     +2     
  Lines         2552      2669   +117     
  Branches       294       280    -14     
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+ Hits          2552      2669   +117     

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