Class inertialsim::geometry::Vector¶
ClassList > inertialsim > geometry > Vector
3-dimensional vectors. More...
#include <vector.h>
Inherits the following classes: inertialsim::geometry::VectorBase
Public Types inherited from inertialsim::geometry::VectorBase¶
See inertialsim::geometry::VectorBase
| Type | Name |
|---|---|
| typedef MatrixLieGroup< Derived, 4, 3 > | Base |
Public Types inherited from inertialsim::geometry::MatrixLieGroup¶
See inertialsim::geometry::MatrixLieGroup
| Type | Name |
|---|---|
| typedef Eigen::Matrix< Scalar, AlgebraDimension, Eigen::Dynamic > | AlgebraArray Array of algebra elements. |
| typedef Eigen::Matrix< Scalar, AlgebraDimension, 1 > | AlgebraElement Algebra element type (vector). |
| typedef std::vector< GroupElement > | GroupArray Array of group elements. |
| typedef Eigen::Matrix< Scalar, GroupDimension, GroupDimension > | GroupElement Group element type (square matrix). |
| typedef Eigen::Matrix< Scalar, AlgebraDimension, AlgebraDimension > | JacobianMatrix Jacobian matrix (algebra to algebra). |
| typedef std::vector< JacobianMatrix > | JacobianMatrixArray Array of Jacobian matrices. |
Public Functions inherited from inertialsim::geometry::VectorBase¶
See inertialsim::geometry::VectorBase
| Type | Name |
|---|---|
| Array3D | AsSpherical () const Return spherical coordinates (radius, polar, azimuth). |
| Vector3D | AsXyz () const Return Cartesian coordinates. |
| Vector3D | Error (const Derived & reference) const Calculate error compared to a reference vector. |
| Vector3D | Error (const Vector3D & reference) const Calculate error compared to a reference array. |
| int | num_vectors () const Number of vectors stored. |
| Derived | operator* (double scalar) const Multiply by a scalar. |
| Derived | operator+ (const Derived & rhs) const Add two vectors. |
| Derived | operator- (const Derived & rhs) const Subtract two vectors. |
| Derived | operator/ (double scalar) const Divide by a scalar. |
Public Functions inherited from inertialsim::geometry::MatrixLieGroup¶
See inertialsim::geometry::MatrixLieGroup
| Type | Name |
|---|---|
| Vector3D | Apply (const Vector3D & vectors) const Apply the group action to an array of vectors. |
| Derived | Interpolate (const Timestamps & interp_time, Interpolator method=Interpolator::LINEAR) const Interpolate at given times. |
| Derived | Inverse () const Invert an instance. |
| Derived | Slice (int start, int end) const Get a slice of elements. |
| AlgebraArray | TimeDerivative (int order=1, int accuracy=4, const std::string & side="right") const Compute time derivative using finite differences. |
| int | num_elements () const Number of elements stored in the instance. |
| Derived | operator* (const Derived & rhs) const Compose elements of the group. |
| Derived | operator[] (int index) const Get a single element by index. |
| const std::optional< Timestamps > & | time () const Time array corresponding to each element. |
| virtual | ~MatrixLieGroup () = default |
Public Static Functions inherited from inertialsim::geometry::VectorBase¶
See inertialsim::geometry::VectorBase
| Type | Name |
|---|---|
| Derived | FromSpherical (const Array3D & rpa, const std::optional< Timestamps > & time=std::nullopt) Construct from spherical coordinates (radius, polar, azimuth). |
| Derived | FromXyz (const Vector3D & xyz, const std::optional< Timestamps > & time=std::nullopt) Construct from Cartesian coordinates. |
Public Static Functions inherited from inertialsim::geometry::MatrixLieGroup¶
See inertialsim::geometry::MatrixLieGroup
| Type | Name |
|---|---|
| Derived | Compose (const std::vector< Derived > & instances) Compose a sequence of instances (first to last). |
| Derived | FromIdentity (int num_elements=1) Create identity elements. |
| Derived | FromRandom (int num_elements=1, std::optional< Eigen::numext::uint64_t > seed=std::nullopt) Create random elements. |
Protected Functions inherited from inertialsim::geometry::VectorBase¶
See inertialsim::geometry::VectorBase
| Type | Name |
|---|---|
| VectorBase () Default constructor. |
|
| VectorBase (const Vector3D & xyz, const std::optional< Timestamps > & time=std::nullopt) Construct from Cartesian coordinates. |
Protected Functions inherited from inertialsim::geometry::MatrixLieGroup¶
See inertialsim::geometry::MatrixLieGroup
| Type | Name |
|---|---|
| AlgebraArray | AsAlgebra () const Get the algebra elements. |
| GroupArray | AsGroup () const Get the group elements. |
| MatrixLieGroup (const std::optional< Timestamps > & time=std::nullopt) Constructor. |
|
| int | num_times () const |
Protected Static Functions inherited from inertialsim::geometry::MatrixLieGroup¶
See inertialsim::geometry::MatrixLieGroup
| Type | Name |
|---|---|
| GroupElement | Exp (const AlgebraElement & vector) Exponential map from algebra to group. |
| Derived | FromAlgebra (const AlgebraArray & elements, const std::optional< Timestamps > & time) Create instance from algebra elements. |
| Derived | FromGroup (const GroupArray & elements, const std::optional< Timestamps > & time) Create instance from group elements. |
| JacobianMatrixArray | Jacobian (const AlgebraArray & algebra, const std::string & side="left", bool inverse=false) Calculate the Jacobian of the exponential map. |
| AlgebraElement | Log (const GroupElement & element) Logarithm map from group to algebra. |
Detailed Description¶
Vectors can represent physical points, translations, accelerations, velocities or other arbitrary tuples in \(\mathbb{R}^3\).
Vectors can be constructed from Cartesian coordinates (x, y, z) or spherical coordinates (radius, polar angle, azimuth). Use the From* methods to construct an instance.
Internally vectors are stored in Cartesian form.
Spherical coordinate conventions
Spherical coordinates follow the physics convention:
- radius: \(r \geq 0\)
- polar_angle: \(0 \leq \theta \leq \pi\)
- azimuth: \(-\pi < \phi \leq \pi\)
The Lie group for 3-dimensional vectors (under matrix multiplication) is the SE(3) sub-group whose elements are 4x4 homogeneous transform matrices with identity rotation [[I, vector],[0, 1]].
See also: Translation for translation-specific operations.
See also: geodesy::Coordinates for Earth-referenced coordinates.
The documentation for this class was generated from the following file cpp/include/inertialsim/geometry/vector.h