se3

SE(3) homogeneous transformation

Description

The se3 represents an SE(3) transformation as a homogeneous transformation matrix consisting of a translation and rotation in 3-D.

This object acts like a numerical matrix enabling you to compose poses using multiplication and division.

Creation

Syntax

transformation = se3

transformation = se3(rotation)

transformation = se3(rotation,translation)

transformation = se3(transformation)

Description

transformation = se3 creates an SE(3) transformation representing an identity rotation with no translation.

transformation = se3(rotation) creates an SE(3) transformation representing a pure rotation defined by the orthonormal rotation rotation with no translation. The rotation matrix is represented by the elements in the top left of the matrix.

transformation = se3(rotation,translation) creates an SE(3) transformation representing a rotation defined by the orthonormal rotation rotation, and the translation translation. The function applies the rotation matrix first and the translation vector second.

transformation = se3(transformation) creates an SE(3) transformation representing a translation and rotation as defined by the homogeneous transformation transformation.

Input Arguments

rotation — Orthonormal rotation

3-by-3 matrix | 3-by-3-by-M matrix | so3 object | M-element array of so3 objects

Orthonormal rotation, specified as a 3-by-3 matrix, a 3-by-3-byM array, a scalar so3 object, or an M-element array of so3 objects. M is the total number of rotations.

If rotation contains more than one rotation and you also specify translation at construction, the number of translations in translation must be one or equal to the number of rotations in rotation. The resulting number of transformation objects is equal to the larger argument between translation and rotation.

Example: eye(3)

Data Types: single | double

translation — Translation

three-element row vector | N-by-3 array

Translation, specified as a N-by-3 array. N is the total number of translations and each translation is of the form [X Y Z].

If translation contains more than one translation, the number of rotations in rotation must be one or equal to the number of translations in translation. The resulting number of created transformation objects is equal to the larger argument between translation and rotation.

Example: [1 4 3]

Data Types: single | double

transformation — Homogeneous transformation

4-by-4 matrix | 4-by-4-T array | se3 object | T-element array of se3 objects

Homogeneous transformation, specified as a 4-by-4 matrix, a 4-by-4-T or an se3 object. T is the total number of transformations specified.

If transformation is an array, the resulting number of created transformations objects is equal to T.

Example: eye(4)

Data Types: single | double

Object Functions

dist	Calculate distance between transformations
interp	Interpolate between transformations
mrdivide, ./	Transformation right division
mtimes, *	Transformation multiplication
normalize	Normalize transformation matrix
rdivide, ./	Element-wise transformation right division
rotm	Extract rotation matrix
tform	Extract homogeneous transformation
times, .*	Transformation element-wise multiplication
transform	Apply rigid body transformation to points
trvec	Extract translation vector

Examples

Create SO(2), SO(3), SE(2), and SE(3) Transformations

Define a 3-by-3 rotation matrix and a three-element translation vector.

rot = eye(3);
tr = [3 5 2];

Create the SO(2) and SO(3) rotations using the rotation matrix rot.

R2d = SO2(rot(1:2,1:2))

R2d = SO2
     1     0
     0     1

R3d = SO3(rot)

R3d = SO3
     1     0     0
     0     1     0
     0     0     1

Create the SE(2) and SE(3) rotations using the rotation matrix rot, and the translation vector tr.

T2d = SE2(rot(1:2,1:2),tr(1:2))

T2d = SE2
     1     0     3
     0     1     5
     0     0     1

T3d = SE3(rot,tr)

T3d = SE3
     1     0     0     3
     0     1     0     5
     0     0     1     2
     0     0     0     1

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2022b