KOKO\Mimi
64 lines
2.7 KiB
C++
64 lines
2.7 KiB
C++
#ifndef FESA_ELEMENTS_FINITE_ROTATION_H_
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#define FESA_ELEMENTS_FINITE_ROTATION_H_
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#include "fesa/core/status.h"
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#include "fesa/math/matrix.h"
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#include "fesa/math/vector3.h"
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namespace fesa {
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/// @brief Stores one finite-rotation coordinate and its derived triad state.
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struct FiniteRotationState {
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/// @brief Fixed-global principal-chart rotation coordinate in radians.
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Vector3 phi;
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/// @brief Proper orthogonal triad computed as exp(phi^) times the initial
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/// frame.
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Matrix q;
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/// @brief Current director computed from the third column of q.
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Vector3 director;
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};
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/// @brief Computes Rodrigues' exponential of the three-dimensional skew map.
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/// @param phi Fixed-global rotation coordinate in radians.
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/// @return The 3-by-3 rotation tensor exp(phi^).
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/// @pre phi is finite and lies inside the approved principal chart.
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Matrix ExpSkew(const Vector3& phi);
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/// @brief Computes the SO(3) left Jacobian for a fixed-global coordinate.
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/// @param phi Fixed-global rotation coordinate in radians.
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/// @return The 3-by-3 left Jacobian that maps coordinate variations to spatial
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/// rotations.
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/// @pre phi is finite and lies inside the approved principal chart.
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Matrix LeftJacobianSO3(const Vector3& phi);
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/// @brief Computes the inverse transpose of the SO(3) left Jacobian.
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/// @param phi Fixed-global rotation coordinate in radians.
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/// @return The 3-by-3 inverse-transpose left Jacobian.
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/// @pre phi is finite and lies inside the approved principal chart.
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Matrix InverseTransposeLeftJacobianSO3(const Vector3& phi);
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/// @brief Builds a checked finite-rotation state from its reference frame.
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/// @param phi Fixed-global principal-chart rotation coordinate in radians.
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/// @param initial_frame Valid initial right-handed 3-by-3 triad.
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/// @return A complete finite state or an `invalid-accepted-state` failure.
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/// @note The input frame is validated but never normalized or repaired.
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Result<FiniteRotationState> MakeFiniteRotationState(
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const Vector3& phi, const Matrix& initial_frame);
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/// @brief Applies a fixed-global Newton rotation increment to one state.
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/// @param committed Fully validated state that remains unchanged by this call.
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/// @param delta_phi Fixed-global additive rotation correction in radians.
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/// @param initial_frame Valid initial right-handed 3-by-3 triad.
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/// @return A rebuilt trial state or an `invalid-accepted-state` failure.
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/// @note The result is recomputed from phi plus delta_phi and initial_frame;
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/// incremental tensors are not successively composed.
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Result<FiniteRotationState> ApplyGlobalRotationIncrement(
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const FiniteRotationState& committed, const Vector3& delta_phi,
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const Matrix& initial_frame);
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} // namespace fesa
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#endif // FESA_ELEMENTS_FINITE_ROTATION_H_
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