pydrake.common.eigen_geometry

Bindings for Eigen geometric types.

class pydrake.common.eigen_geometry.AngleAxis(*args, **kwargs)

Bindings for Eigen::AngleAxis<>.

Note

This class is templated; see AngleAxis_ for the list of instantiations.

__init__(self) → None

__init__(self, angle: float, axis: numpy.ndarray[dtype=float64, shape=(3), order='C']) → None

__init__(self, quaternion: pydrake.common.eigen_geometry.Quaternion) → None

__init__(self, rotation: numpy.ndarray[dtype=float64, shape=(3, 3), order='F']) → None

__init__(self, other: pydrake.common.eigen_geometry.AngleAxis) → None

angle(self) → float

axis(self) → numpy.ndarray[dtype=float64, shape=(3), order='C']

template cast

Instantiations: cast[float], cast[AutoDiffXd], cast[Expression]

cast[AutoDiffXd](self) → Eigen::AngleAxis<drake::ad::AutoDiff>

Cast to desired scalar type.

cast[Expression](self) → Eigen::AngleAxis<drake::symbolic::Expression>

Cast to desired scalar type.

cast[float](self) → pydrake.common.eigen_geometry.AngleAxis

Cast to desired scalar type.

static Identity() → pydrake.common.eigen_geometry.AngleAxis

inverse(self) → pydrake.common.eigen_geometry.AngleAxis

multiply(self, other: pydrake.common.eigen_geometry.AngleAxis) → pydrake.common.eigen_geometry.Quaternion

quaternion(self) → pydrake.common.eigen_geometry.Quaternion

rotation(self) → numpy.ndarray[dtype=float64, shape=(3, 3), order='F']

set_angle(self, angle: float) → None

set_axis(self, axis: numpy.ndarray[dtype=float64, shape=(3), order='C']) → None

set_quaternion(self, q: pydrake.common.eigen_geometry.Quaternion) → None

set_rotation(self, rotation: numpy.ndarray[dtype=float64, shape=(3, 3), order='F']) → None

template pydrake.common.eigen_geometry.AngleAxis_

Instantiations: AngleAxis_[float], AngleAxis_[AutoDiffXd], AngleAxis_[Expression]

class pydrake.common.eigen_geometry.AngleAxis_[AutoDiffXd](*args, **kwargs)

Bindings for Eigen::AngleAxis<>.

__init__(self) → None

__init__(self, angle: pydrake.autodiffutils.AutoDiffXd, axis: numpy.ndarray[dtype=object, shape=(3)]) → None

__init__(self, quaternion: pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]) → None

__init__(self, rotation: numpy.ndarray[dtype=object, shape=(3, 3)]) → None

__init__(self, other: pydrake.common.eigen_geometry.AngleAxis_[AutoDiffXd]) → None

angle(self) → pydrake.autodiffutils.AutoDiffXd

axis(self) → numpy.ndarray[dtype=object, shape=(3)]

template cast

Instantiations: cast[AutoDiffXd]

cast[AutoDiffXd](**kwargs)

cast[AutoDiffXd](self) -> pydrake.common.eigen_geometry.AngleAxis_[AutoDiffXd]

Cast to desired scalar type.

static Identity() → pydrake.common.eigen_geometry.AngleAxis_[AutoDiffXd]

inverse(self) → pydrake.common.eigen_geometry.AngleAxis_[AutoDiffXd]

multiply(self, other: pydrake.common.eigen_geometry.AngleAxis_[AutoDiffXd]) → pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]

quaternion(self) → pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]

rotation(self) → numpy.ndarray[dtype=object, shape=(3, 3)]

set_angle(self, angle: pydrake.autodiffutils.AutoDiffXd) → None

set_axis(self, axis: numpy.ndarray[dtype=object, shape=(3)]) → None

set_quaternion(self, q: pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]) → None

set_rotation(self, rotation: numpy.ndarray[dtype=object, shape=(3, 3)]) → None

class pydrake.common.eigen_geometry.AngleAxis_[Expression](*args, **kwargs)

Bindings for Eigen::AngleAxis<>.

__init__(self) → None

__init__(self, angle: pydrake.symbolic.Expression, axis: numpy.ndarray[dtype=object, shape=(3)]) → None

__init__(self, quaternion: pydrake.common.eigen_geometry.Quaternion_[Expression]) → None

__init__(self, rotation: numpy.ndarray[dtype=object, shape=(3, 3)]) → None

__init__(self, other: pydrake.common.eigen_geometry.AngleAxis_[Expression]) → None

angle(self) → pydrake.symbolic.Expression

axis(self) → numpy.ndarray[dtype=object, shape=(3)]

template cast

Instantiations: cast[Expression]

cast[Expression](**kwargs)

cast[Expression](self) -> pydrake.common.eigen_geometry.AngleAxis_[Expression]

Cast to desired scalar type.

static Identity() → pydrake.common.eigen_geometry.AngleAxis_[Expression]

inverse(self) → pydrake.common.eigen_geometry.AngleAxis_[Expression]

multiply(self, other: pydrake.common.eigen_geometry.AngleAxis_[Expression]) → pydrake.common.eigen_geometry.Quaternion_[Expression]

quaternion(self) → pydrake.common.eigen_geometry.Quaternion_[Expression]

rotation(self) → numpy.ndarray[dtype=object, shape=(3, 3)]

set_angle(self, angle: pydrake.symbolic.Expression) → None

set_axis(self, axis: numpy.ndarray[dtype=object, shape=(3)]) → None

set_quaternion(self, q: pydrake.common.eigen_geometry.Quaternion_[Expression]) → None

set_rotation(self, rotation: numpy.ndarray[dtype=object, shape=(3, 3)]) → None

class pydrake.common.eigen_geometry.Isometry3(*args, **kwargs)

Provides bindings of Eigen::Isometry3<> that only admit SE(3) (no reflections).

Note

This class is templated; see Isometry3_ for the list of instantiations.

__init__(self) → None

__init__(self, matrix: numpy.ndarray[dtype=float64, shape=(4, 4), order='F']) → None

__init__(self, rotation: numpy.ndarray[dtype=float64, shape=(3, 3), order='F'], translation: numpy.ndarray[dtype=float64, shape=(3), order='C']) → None

__init__(self, quaternion: pydrake.common.eigen_geometry.Quaternion, translation: numpy.ndarray[dtype=float64, shape=(3), order='C']) → None

__init__(self, other: pydrake.common.eigen_geometry.Isometry3) → None

template cast

Instantiations: cast[float], cast[AutoDiffXd], cast[Expression]

cast[AutoDiffXd](self) → Eigen::Transform<drake::ad::AutoDiff, 3, 1, 0>

Cast to desired scalar type.

cast[Expression](self) → Eigen::Transform<drake::symbolic::Expression, 3, 1, 0>

Cast to desired scalar type.

cast[float](self) → pydrake.common.eigen_geometry.Isometry3

Cast to desired scalar type.

static Identity() → pydrake.common.eigen_geometry.Isometry3

inverse(self) → pydrake.common.eigen_geometry.Isometry3

matrix(self) → numpy.ndarray[dtype=float64, shape=(4, 4), order='F']

multiply(self, other: pydrake.common.eigen_geometry.Isometry3) → pydrake.common.eigen_geometry.Isometry3

multiply(self, position: numpy.ndarray[dtype=float64, shape=(3), order='C']) → numpy.ndarray[dtype=float64, shape=(3), order='C']

multiply(self, position: numpy.ndarray[dtype=float64, shape=(3, *), order='F']) → numpy.ndarray[dtype=float64, shape=(3, *), order='F']

Overloaded function.

1. multiply(self, other: pydrake.common.eigen_geometry.Isometry3) -> pydrake.common.eigen_geometry.Isometry3

RigidTransform multiplication

2. multiply(self, position: numpy.ndarray[dtype=float64, shape=(3), order='C']) -> numpy.ndarray[dtype=float64, shape=(3), order='C']

Position vector multiplication

3. multiply(self, position: numpy.ndarray[dtype=float64, shape=(3, *), order='F']) -> numpy.ndarray[dtype=float64, shape=(3, *), order='F']

Position vector list multiplication

quaternion(self) → pydrake.common.eigen_geometry.Quaternion

rotation(self) → numpy.ndarray[dtype=float64, shape=(3, 3), order='F']

set_matrix(self, arg: numpy.ndarray[dtype=float64, shape=(4, 4), order='F'], /) → None

set_quaternion(self, arg: pydrake.common.eigen_geometry.Quaternion, /) → None

set_rotation(self, arg: numpy.ndarray[dtype=float64, shape=(3, 3), order='F'], /) → None

set_translation(self, arg: numpy.ndarray[dtype=float64, shape=(3), order='C'], /) → None

translation(self) → numpy.ndarray[dtype=float64, shape=(3), order='C']

template pydrake.common.eigen_geometry.Isometry3_

Instantiations: Isometry3_[float], Isometry3_[AutoDiffXd], Isometry3_[Expression]

class pydrake.common.eigen_geometry.Isometry3_[AutoDiffXd](*args, **kwargs)

Provides bindings of Eigen::Isometry3<> that only admit SE(3) (no reflections).

__init__(self) → None

__init__(self, matrix: numpy.ndarray[dtype=object, shape=(4, 4)]) → None

__init__(self, rotation: numpy.ndarray[dtype=object, shape=(3, 3)], translation: numpy.ndarray[dtype=object, shape=(3)]) → None

__init__(self, quaternion: pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd], translation: numpy.ndarray[dtype=object, shape=(3)]) → None

__init__(self, other: pydrake.common.eigen_geometry.Isometry3_[AutoDiffXd]) → None

template cast

Instantiations: cast[AutoDiffXd]

cast[AutoDiffXd](**kwargs)

cast[AutoDiffXd](self) -> pydrake.common.eigen_geometry.Isometry3_[AutoDiffXd]

Cast to desired scalar type.

static Identity() → pydrake.common.eigen_geometry.Isometry3_[AutoDiffXd]

inverse(self) → pydrake.common.eigen_geometry.Isometry3_[AutoDiffXd]

matrix(self) → numpy.ndarray[dtype=object, shape=(4, 4)]

multiply(self, other: pydrake.common.eigen_geometry.Isometry3_[AutoDiffXd]) → pydrake.common.eigen_geometry.Isometry3_[AutoDiffXd]

multiply(self, position: numpy.ndarray[dtype=object, shape=(3)]) → numpy.ndarray[dtype=object, shape=(3)]

multiply(self, position: numpy.ndarray[dtype=object, shape=(3, *)]) → numpy.ndarray[dtype=object, shape=(3, *)]

Overloaded function.

1. multiply(self, other: pydrake.common.eigen_geometry.Isometry3_[AutoDiffXd]) -> pydrake.common.eigen_geometry.Isometry3_[AutoDiffXd]

RigidTransform multiplication

2. multiply(self, position: numpy.ndarray[dtype=object, shape=(3)]) -> numpy.ndarray[dtype=object, shape=(3)]

Position vector multiplication

3. multiply(self, position: numpy.ndarray[dtype=object, shape=(3, *)]) -> numpy.ndarray[dtype=object, shape=(3, *)]

Position vector list multiplication

quaternion(self) → pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]

rotation(self) → numpy.ndarray[dtype=object, shape=(3, 3)]

set_matrix(self, arg: numpy.ndarray[dtype=object, shape=(4, 4)], /) → None

set_quaternion(self, arg: pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd], /) → None

set_rotation(self, arg: numpy.ndarray[dtype=object, shape=(3, 3)], /) → None

set_translation(self, arg: numpy.ndarray[dtype=object, shape=(3)], /) → None

translation(self) → numpy.ndarray[dtype=object, shape=(3)]

class pydrake.common.eigen_geometry.Isometry3_[Expression](*args, **kwargs)

Provides bindings of Eigen::Isometry3<> that only admit SE(3) (no reflections).

__init__(self) → None

__init__(self, matrix: numpy.ndarray[dtype=object, shape=(4, 4)]) → None

__init__(self, rotation: numpy.ndarray[dtype=object, shape=(3, 3)], translation: numpy.ndarray[dtype=object, shape=(3)]) → None

__init__(self, quaternion: pydrake.common.eigen_geometry.Quaternion_[Expression], translation: numpy.ndarray[dtype=object, shape=(3)]) → None

__init__(self, other: pydrake.common.eigen_geometry.Isometry3_[Expression]) → None

template cast

Instantiations: cast[Expression]

cast[Expression](**kwargs)

cast[Expression](self) -> pydrake.common.eigen_geometry.Isometry3_[Expression]

Cast to desired scalar type.

static Identity() → pydrake.common.eigen_geometry.Isometry3_[Expression]

inverse(self) → pydrake.common.eigen_geometry.Isometry3_[Expression]

matrix(self) → numpy.ndarray[dtype=object, shape=(4, 4)]

multiply(self, other: pydrake.common.eigen_geometry.Isometry3_[Expression]) → pydrake.common.eigen_geometry.Isometry3_[Expression]

multiply(self, position: numpy.ndarray[dtype=object, shape=(3)]) → numpy.ndarray[dtype=object, shape=(3)]

multiply(self, position: numpy.ndarray[dtype=object, shape=(3, *)]) → numpy.ndarray[dtype=object, shape=(3, *)]

Overloaded function.

1. multiply(self, other: pydrake.common.eigen_geometry.Isometry3_[Expression]) -> pydrake.common.eigen_geometry.Isometry3_[Expression]

RigidTransform multiplication

2. multiply(self, position: numpy.ndarray[dtype=object, shape=(3)]) -> numpy.ndarray[dtype=object, shape=(3)]

Position vector multiplication

3. multiply(self, position: numpy.ndarray[dtype=object, shape=(3, *)]) -> numpy.ndarray[dtype=object, shape=(3, *)]

Position vector list multiplication

quaternion(self) → pydrake.common.eigen_geometry.Quaternion_[Expression]

rotation(self) → numpy.ndarray[dtype=object, shape=(3, 3)]

set_matrix(self, arg: numpy.ndarray[dtype=object, shape=(4, 4)], /) → None

set_quaternion(self, arg: pydrake.common.eigen_geometry.Quaternion_[Expression], /) → None

set_rotation(self, arg: numpy.ndarray[dtype=object, shape=(3, 3)], /) → None

set_translation(self, arg: numpy.ndarray[dtype=object, shape=(3)], /) → None

translation(self) → numpy.ndarray[dtype=object, shape=(3)]

class pydrake.common.eigen_geometry.Quaternion(*args, **kwargs)

Provides a unit quaternion binding of Eigen::Quaternion<>.

Note

This class is templated; see Quaternion_ for the list of instantiations.

__init__(self) → None

__init__(self, wxyz: numpy.ndarray[dtype=float64, shape=(4), order='C']) → None

__init__(self, w: float, x: float, y: float, z: float) → None

__init__(self, rotation: numpy.ndarray[dtype=float64, shape=(3, 3), order='F']) → None

__init__(self, other: pydrake.common.eigen_geometry.Quaternion) → None

template cast

Instantiations: cast[float], cast[AutoDiffXd], cast[Expression]

cast[AutoDiffXd](self) → Eigen::Quaternion<drake::ad::AutoDiff, 0>

Cast to desired scalar type.

cast[Expression](self) → Eigen::Quaternion<drake::symbolic::Expression, 0>

Cast to desired scalar type.

cast[float](self) → pydrake.common.eigen_geometry.Quaternion

Cast to desired scalar type.

conjugate(self) → pydrake.common.eigen_geometry.Quaternion

static Identity() → pydrake.common.eigen_geometry.Quaternion

inverse(self) → pydrake.common.eigen_geometry.Quaternion

multiply(self, arg: pydrake.common.eigen_geometry.Quaternion, /) → pydrake.common.eigen_geometry.Quaternion

multiply(self, vector: numpy.ndarray[dtype=float64, shape=(3), order='C']) → numpy.ndarray[dtype=float64, shape=(3), order='C']

multiply(self, vector: numpy.ndarray[dtype=float64, shape=(3, *), order='F']) → numpy.ndarray[dtype=float64, shape=(3, *), order='F']

Overloaded function.

1. multiply(self, arg: pydrake.common.eigen_geometry.Quaternion, /) -> pydrake.common.eigen_geometry.Quaternion

Quaternion multiplication

2. multiply(self, vector: numpy.ndarray[dtype=float64, shape=(3), order='C']) -> numpy.ndarray[dtype=float64, shape=(3), order='C']

Multiplication by a vector expressed in a frame

3. multiply(self, vector: numpy.ndarray[dtype=float64, shape=(3, *), order='F']) -> numpy.ndarray[dtype=float64, shape=(3, *), order='F']

Multiplication by a list of vectors expressed in the same frame

rotation(self) → numpy.ndarray[dtype=float64, shape=(3, 3), order='F']

set_rotation(self, arg: numpy.ndarray[dtype=float64, shape=(3, 3), order='F'], /) → None

set_wxyz(self, wxyz: numpy.ndarray[dtype=float64, shape=(4), order='C']) → None

set_wxyz(self, w: float, x: float, y: float, z: float) → None

slerp(self, t: float, other: pydrake.common.eigen_geometry.Quaternion) → pydrake.common.eigen_geometry.Quaternion

The spherical linear interpolation between the two quaternions (self and other) at the parameter t in [0;1].

w(self) → float

wxyz(self) → numpy.ndarray[dtype=float64, shape=(4), order='C']

x(self) → float

xyz(self) → numpy.ndarray[dtype=float64, shape=(3), order='C']

y(self) → float

z(self) → float

template pydrake.common.eigen_geometry.Quaternion_

Instantiations: Quaternion_[float], Quaternion_[AutoDiffXd], Quaternion_[Expression]

class pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd](*args, **kwargs)

Provides a unit quaternion binding of Eigen::Quaternion<>.

__init__(self) → None

__init__(self, wxyz: numpy.ndarray[dtype=object, shape=(4)]) → None

__init__(self, w: pydrake.autodiffutils.AutoDiffXd, x: pydrake.autodiffutils.AutoDiffXd, y: pydrake.autodiffutils.AutoDiffXd, z: pydrake.autodiffutils.AutoDiffXd) → None

__init__(self, rotation: numpy.ndarray[dtype=object, shape=(3, 3)]) → None

__init__(self, other: pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]) → None

template cast

Instantiations: cast[AutoDiffXd]

cast[AutoDiffXd](**kwargs)

cast[AutoDiffXd](self) -> pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]

Cast to desired scalar type.

conjugate(self) → pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]

static Identity() → pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]

inverse(self) → pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]

multiply(self, arg: pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd], /) → pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]

multiply(self, vector: numpy.ndarray[dtype=object, shape=(3)]) → numpy.ndarray[dtype=object, shape=(3)]

multiply(self, vector: numpy.ndarray[dtype=object, shape=(3, *)]) → numpy.ndarray[dtype=object, shape=(3, *)]

Overloaded function.

1. multiply(self, arg: pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd], /) -> pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]

Quaternion multiplication

2. multiply(self, vector: numpy.ndarray[dtype=object, shape=(3)]) -> numpy.ndarray[dtype=object, shape=(3)]

Multiplication by a vector expressed in a frame

3. multiply(self, vector: numpy.ndarray[dtype=object, shape=(3, *)]) -> numpy.ndarray[dtype=object, shape=(3, *)]

Multiplication by a list of vectors expressed in the same frame

rotation(self) → numpy.ndarray[dtype=object, shape=(3, 3)]

set_rotation(self, arg: numpy.ndarray[dtype=object, shape=(3, 3)], /) → None

set_wxyz(self, wxyz: numpy.ndarray[dtype=object, shape=(4)]) → None

set_wxyz(self, w: pydrake.autodiffutils.AutoDiffXd, x: pydrake.autodiffutils.AutoDiffXd, y: pydrake.autodiffutils.AutoDiffXd, z: pydrake.autodiffutils.AutoDiffXd) → None

slerp(self, t: float, other: pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]) → pydrake.common.eigen_geometry.Quaternion_[AutoDiffXd]

The spherical linear interpolation between the two quaternions (self and other) at the parameter t in [0;1].

w(self) → pydrake.autodiffutils.AutoDiffXd

wxyz(self) → numpy.ndarray[dtype=object, shape=(4)]

x(self) → pydrake.autodiffutils.AutoDiffXd

xyz(self) → numpy.ndarray[dtype=object, shape=(3)]

y(self) → pydrake.autodiffutils.AutoDiffXd

z(self) → pydrake.autodiffutils.AutoDiffXd

class pydrake.common.eigen_geometry.Quaternion_[Expression](*args, **kwargs)

Provides a unit quaternion binding of Eigen::Quaternion<>.

__init__(self) → None

__init__(self, wxyz: numpy.ndarray[dtype=object, shape=(4)]) → None

__init__(self, w: pydrake.symbolic.Expression, x: pydrake.symbolic.Expression, y: pydrake.symbolic.Expression, z: pydrake.symbolic.Expression) → None

__init__(self, rotation: numpy.ndarray[dtype=object, shape=(3, 3)]) → None

__init__(self, other: pydrake.common.eigen_geometry.Quaternion_[Expression]) → None

template cast

Instantiations: cast[Expression]

cast[Expression](**kwargs)

cast[Expression](self) -> pydrake.common.eigen_geometry.Quaternion_[Expression]

Cast to desired scalar type.

conjugate(self) → pydrake.common.eigen_geometry.Quaternion_[Expression]

static Identity() → pydrake.common.eigen_geometry.Quaternion_[Expression]

inverse(self) → pydrake.common.eigen_geometry.Quaternion_[Expression]

multiply(self, arg: pydrake.common.eigen_geometry.Quaternion_[Expression], /) → pydrake.common.eigen_geometry.Quaternion_[Expression]

multiply(self, vector: numpy.ndarray[dtype=object, shape=(3)]) → numpy.ndarray[dtype=object, shape=(3)]

multiply(self, vector: numpy.ndarray[dtype=object, shape=(3, *)]) → numpy.ndarray[dtype=object, shape=(3, *)]

Overloaded function.

1. multiply(self, arg: pydrake.common.eigen_geometry.Quaternion_[Expression], /) -> pydrake.common.eigen_geometry.Quaternion_[Expression]

Quaternion multiplication

2. multiply(self, vector: numpy.ndarray[dtype=object, shape=(3)]) -> numpy.ndarray[dtype=object, shape=(3)]

Multiplication by a vector expressed in a frame

3. multiply(self, vector: numpy.ndarray[dtype=object, shape=(3, *)]) -> numpy.ndarray[dtype=object, shape=(3, *)]

Multiplication by a list of vectors expressed in the same frame

rotation(self) → numpy.ndarray[dtype=object, shape=(3, 3)]

set_rotation(self, arg: numpy.ndarray[dtype=object, shape=(3, 3)], /) → None

set_wxyz(self, wxyz: numpy.ndarray[dtype=object, shape=(4)]) → None

set_wxyz(self, w: pydrake.symbolic.Expression, x: pydrake.symbolic.Expression, y: pydrake.symbolic.Expression, z: pydrake.symbolic.Expression) → None

slerp(self, t: float, other: pydrake.common.eigen_geometry.Quaternion_[Expression]) → pydrake.common.eigen_geometry.Quaternion_[Expression]

The spherical linear interpolation between the two quaternions (self and other) at the parameter t in [0;1].

w(self) → pydrake.symbolic.Expression

wxyz(self) → numpy.ndarray[dtype=object, shape=(4)]

x(self) → pydrake.symbolic.Expression

xyz(self) → numpy.ndarray[dtype=object, shape=(3)]

y(self) → pydrake.symbolic.Expression

z(self) → pydrake.symbolic.Expression