Merge pull request #1234 from shteren1/pose3_jacobians
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b91c43e691
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@ -489,6 +489,11 @@ boost::optional<Pose3> align(const Point3Pairs &baPointPairs) {
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}
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#endif
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/* ************************************************************************* */
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Pose3 Pose3::slerp(double t, const Pose3& other, OptionalJacobian<6, 6> Hx, OptionalJacobian<6, 6> Hy) const {
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return interpolate(*this, other, t, Hx, Hy);
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}
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/* ************************************************************************* */
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std::ostream &operator<<(std::ostream &os, const Pose3& pose) {
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// Both Rot3 and Point3 have ostream definitions so we use them.
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@ -379,6 +379,14 @@ public:
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return std::make_pair(0, 2);
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}
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/**
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* @brief Spherical Linear interpolation between *this and other
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* @param s a value between 0 and 1.5
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* @param other final point of interpolation geodesic on manifold
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*/
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Pose3 slerp(double t, const Pose3& other, OptionalJacobian<6, 6> Hx = boost::none,
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OptionalJacobian<6, 6> Hy = boost::none) const;
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/// Output stream operator
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GTSAM_EXPORT
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friend std::ostream &operator<<(std::ostream &os, const Pose3& p);
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@ -446,24 +446,43 @@ class Pose3 {
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// Group
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static gtsam::Pose3 identity();
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gtsam::Pose3 inverse() const;
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gtsam::Pose3 inverse(Eigen::Ref<Eigen::MatrixXd> H) const;
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gtsam::Pose3 compose(const gtsam::Pose3& pose) const;
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gtsam::Pose3 compose(const gtsam::Pose3& pose,
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Eigen::Ref<Eigen::MatrixXd> H1,
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Eigen::Ref<Eigen::MatrixXd> H2) const;
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gtsam::Pose3 between(const gtsam::Pose3& pose) const;
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gtsam::Pose3 between(const gtsam::Pose3& pose,
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Eigen::Ref<Eigen::MatrixXd> H1,
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Eigen::Ref<Eigen::MatrixXd> H2) const;
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gtsam::Pose3 slerp(double t, const gtsam::Pose3& pose) const;
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gtsam::Pose3 slerp(double t, const gtsam::Pose3& pose,
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Eigen::Ref<Eigen::MatrixXd> Hx,
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Eigen::Ref<Eigen::MatrixXd> Hy) const;
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// Operator Overloads
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gtsam::Pose3 operator*(const gtsam::Pose3& pose) const;
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// Manifold
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gtsam::Pose3 retract(Vector v) const;
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gtsam::Pose3 retract(Vector v, Eigen::Ref<Eigen::MatrixXd> Hxi) const;
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Vector localCoordinates(const gtsam::Pose3& pose) const;
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Vector localCoordinates(const gtsam::Pose3& pose, Eigen::Ref<Eigen::MatrixXd> Hxi) const;
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// Lie Group
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static gtsam::Pose3 Expmap(Vector v);
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static gtsam::Pose3 Expmap(Vector v, Eigen::Ref<Eigen::MatrixXd> Hxi);
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static Vector Logmap(const gtsam::Pose3& pose);
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static Vector Logmap(const gtsam::Pose3& pose, Eigen::Ref<Eigen::MatrixXd> Hpose);
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gtsam::Pose3 expmap(Vector v);
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Vector logmap(const gtsam::Pose3& pose);
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Matrix AdjointMap() const;
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Vector Adjoint(Vector xi) const;
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Vector Adjoint(Vector xi, Eigen::Ref<Eigen::MatrixXd> H_this,
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Eigen::Ref<Eigen::MatrixXd> H_xib) const;
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Vector AdjointTranspose(Vector xi) const;
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Vector AdjointTranspose(Vector xi, Eigen::Ref<Eigen::MatrixXd> H_this,
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Eigen::Ref<Eigen::MatrixXd> H_x) const;
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static Matrix adjointMap(Vector xi);
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static Vector adjoint(Vector xi, Vector y);
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static Matrix adjointMap_(Vector xi);
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@ -476,7 +495,11 @@ class Pose3 {
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// Group Action on Point3
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gtsam::Point3 transformFrom(const gtsam::Point3& point) const;
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gtsam::Point3 transformFrom(const gtsam::Point3& point, Eigen::Ref<Eigen::MatrixXd> Hself,
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Eigen::Ref<Eigen::MatrixXd> Hpoint) const;
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gtsam::Point3 transformTo(const gtsam::Point3& point) const;
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gtsam::Point3 transformTo(const gtsam::Point3& point, Eigen::Ref<Eigen::MatrixXd> Hself,
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Eigen::Ref<Eigen::MatrixXd> Hpoint) const;
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// Matrix versions
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Matrix transformFrom(const Matrix& points) const;
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@ -484,15 +507,25 @@ class Pose3 {
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// Standard Interface
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gtsam::Rot3 rotation() const;
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gtsam::Rot3 rotation(Eigen::Ref<Eigen::MatrixXd> Hself) const;
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gtsam::Point3 translation() const;
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gtsam::Point3 translation(Eigen::Ref<Eigen::MatrixXd> Hself) const;
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double x() const;
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double y() const;
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double z() const;
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Matrix matrix() const;
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gtsam::Pose3 transformPoseFrom(const gtsam::Pose3& pose) const;
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gtsam::Pose3 transformPoseFrom(const gtsam::Pose3& pose, Eigen::Ref<Eigen::MatrixXd> Hself,
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Eigen::Ref<Eigen::MatrixXd> HaTb) const;
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gtsam::Pose3 transformPoseTo(const gtsam::Pose3& pose) const;
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gtsam::Pose3 transformPoseTo(const gtsam::Pose3& pose, Eigen::Ref<Eigen::MatrixXd> Hself,
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Eigen::Ref<Eigen::MatrixXd> HwTb) const;
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double range(const gtsam::Point3& point);
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double range(const gtsam::Point3& point, Eigen::Ref<Eigen::MatrixXd> Hself,
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Eigen::Ref<Eigen::MatrixXd> Hpoint);
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double range(const gtsam::Pose3& pose);
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double range(const gtsam::Pose3& pose, Eigen::Ref<Eigen::MatrixXd> Hself,
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Eigen::Ref<Eigen::MatrixXd> Hpose);
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// enabling serialization functionality
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void serialize() const;
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@ -19,6 +19,62 @@ from gtsam import Point3, Pose3, Rot3, Point3Pairs
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from gtsam.utils.test_case import GtsamTestCase
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def numerical_derivative_pose(pose, method, delta=1e-5):
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jacobian = np.zeros((6, 6))
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for idx in range(6):
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xplus = np.zeros(6)
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xplus[idx] = delta
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xminus = np.zeros(6)
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xminus[idx] = -delta
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pose_plus = pose.retract(xplus).__getattribute__(method)()
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pose_minus = pose.retract(xminus).__getattribute__(method)()
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jacobian[:, idx] = pose_minus.localCoordinates(pose_plus) / (2 * delta)
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return jacobian
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def numerical_derivative_2_poses(pose, other_pose, method, delta=1e-5, inputs=()):
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jacobian = np.zeros((6, 6))
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other_jacobian = np.zeros((6, 6))
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for idx in range(6):
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xplus = np.zeros(6)
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xplus[idx] = delta
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xminus = np.zeros(6)
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xminus[idx] = -delta
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pose_plus = pose.retract(xplus).__getattribute__(method)(*inputs, other_pose)
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pose_minus = pose.retract(xminus).__getattribute__(method)(*inputs, other_pose)
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jacobian[:, idx] = pose_minus.localCoordinates(pose_plus) / (2 * delta)
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other_pose_plus = pose.__getattribute__(method)(*inputs, other_pose.retract(xplus))
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other_pose_minus = pose.__getattribute__(method)(*inputs, other_pose.retract(xminus))
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other_jacobian[:, idx] = other_pose_minus.localCoordinates(other_pose_plus) / (2 * delta)
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return jacobian, other_jacobian
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def numerical_derivative_pose_point(pose, point, method, delta=1e-5):
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jacobian = np.zeros((3, 6))
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point_jacobian = np.zeros((3, 3))
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for idx in range(6):
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xplus = np.zeros(6)
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xplus[idx] = delta
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xminus = np.zeros(6)
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xminus[idx] = -delta
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point_plus = pose.retract(xplus).__getattribute__(method)(point)
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point_minus = pose.retract(xminus).__getattribute__(method)(point)
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jacobian[:, idx] = (point_plus - point_minus) / (2 * delta)
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if idx < 3:
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xplus = np.zeros(3)
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xplus[idx] = delta
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xminus = np.zeros(3)
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xminus[idx] = -delta
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point_plus = pose.__getattribute__(method)(point + xplus)
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point_minus = pose.__getattribute__(method)(point + xminus)
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point_jacobian[:, idx] = (point_plus - point_minus) / (2 * delta)
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return jacobian, point_jacobian
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class TestPose3(GtsamTestCase):
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"""Test selected Pose3 methods."""
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@ -30,6 +86,47 @@ class TestPose3(GtsamTestCase):
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actual = T2.between(T3)
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self.gtsamAssertEquals(actual, expected, 1e-6)
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#test jacobians
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jacobian = np.zeros((6, 6), order='F')
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jacobian_other = np.zeros((6, 6), order='F')
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T2.between(T3, jacobian, jacobian_other)
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jacobian_numerical, jacobian_numerical_other = numerical_derivative_2_poses(T2, T3, 'between')
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self.gtsamAssertEquals(jacobian, jacobian_numerical)
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self.gtsamAssertEquals(jacobian_other, jacobian_numerical_other)
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def test_inverse(self):
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"""Test between method."""
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pose = Pose3(Rot3.Rodrigues(0, 0, -math.pi/2), Point3(2, 4, 0))
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expected = Pose3(Rot3.Rodrigues(0, 0, math.pi/2), Point3(4, -2, 0))
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actual = pose.inverse()
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self.gtsamAssertEquals(actual, expected, 1e-6)
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#test jacobians
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jacobian = np.zeros((6, 6), order='F')
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pose.inverse(jacobian)
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jacobian_numerical = numerical_derivative_pose(pose, 'inverse')
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self.gtsamAssertEquals(jacobian, jacobian_numerical)
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def test_slerp(self):
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"""Test slerp method."""
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pose0 = gtsam.Pose3()
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pose1 = Pose3(Rot3.Rodrigues(0, 0, -math.pi/2), Point3(2, 4, 0))
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actual_alpha_0 = pose0.slerp(0, pose1)
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self.gtsamAssertEquals(actual_alpha_0, pose0)
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actual_alpha_1 = pose0.slerp(1, pose1)
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self.gtsamAssertEquals(actual_alpha_1, pose1)
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actual_alpha_half = pose0.slerp(0.5, pose1)
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expected_alpha_half = Pose3(Rot3.Rodrigues(0, 0, -math.pi/4), Point3(0.17157288, 2.41421356, 0))
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self.gtsamAssertEquals(actual_alpha_half, expected_alpha_half, tol=1e-6)
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# test jacobians
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jacobian = np.zeros((6, 6), order='F')
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jacobian_other = np.zeros((6, 6), order='F')
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pose0.slerp(0.5, pose1, jacobian, jacobian_other)
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jacobian_numerical, jacobian_numerical_other = numerical_derivative_2_poses(pose0, pose1, 'slerp', inputs=[0.5])
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self.gtsamAssertEquals(jacobian, jacobian_numerical)
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self.gtsamAssertEquals(jacobian_other, jacobian_numerical_other)
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def test_transformTo(self):
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"""Test transformTo method."""
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pose = Pose3(Rot3.Rodrigues(0, 0, -math.pi/2), Point3(2, 4, 0))
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@ -37,6 +134,15 @@ class TestPose3(GtsamTestCase):
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expected = Point3(2, 1, 10)
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self.gtsamAssertEquals(actual, expected, 1e-6)
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#test jacobians
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point = Point3(3, 2, 10)
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jacobian_pose = np.zeros((3, 6), order='F')
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jacobian_point = np.zeros((3, 3), order='F')
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pose.transformTo(point, jacobian_pose, jacobian_point)
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jacobian_numerical_pose, jacobian_numerical_point = numerical_derivative_pose_point(pose, point, 'transformTo')
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self.gtsamAssertEquals(jacobian_pose, jacobian_numerical_pose)
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self.gtsamAssertEquals(jacobian_point, jacobian_numerical_point)
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# multi-point version
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points = np.stack([Point3(3, 2, 10), Point3(3, 2, 10)]).T
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actual_array = pose.transformTo(points)
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@ -51,6 +157,15 @@ class TestPose3(GtsamTestCase):
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expected = Point3(3, 2, 10)
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self.gtsamAssertEquals(actual, expected, 1e-6)
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#test jacobians
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point = Point3(3, 2, 10)
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jacobian_pose = np.zeros((3, 6), order='F')
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jacobian_point = np.zeros((3, 3), order='F')
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pose.transformFrom(point, jacobian_pose, jacobian_point)
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jacobian_numerical_pose, jacobian_numerical_point = numerical_derivative_pose_point(pose, point, 'transformFrom')
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self.gtsamAssertEquals(jacobian_pose, jacobian_numerical_pose)
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self.gtsamAssertEquals(jacobian_point, jacobian_numerical_point)
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# multi-point version
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points = np.stack([Point3(2, 1, 10), Point3(2, 1, 10)]).T
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actual_array = pose.transformFrom(points)
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@ -122,4 +237,4 @@ class TestPose3(GtsamTestCase):
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if __name__ == "__main__":
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unittest.main()
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unittest.main()
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