so2

SO(2) rotational transformation

Description

The so2 object represents an SO(2) rotational transformation in 2-D.

This object acts like a numerical matrix enabling you to compose poses using multiplication and division.$$\cos \left(\frac{\alpha }{2}\right)+\sin \left(\frac{\alpha }{2}\right)\left(xi+yj+zk\right)$$

Creation

Syntax

transformation = so2

transformation = so2(rotation)

Description

transformation = so2 creates an SO(2) rotational transformation representing an identity rotation with no translation.

transformation = so2(rotation) creates an SO(2) rotational transformation transformation representing a pure rotation defined by the orthonormal rotation rotation.

Input Arguments

rotation — Orthonormal rotation

2-by-2 matrix | 2-by-2-by-M matrix | so2 object | M-element array of so2 objects

Orthonormal rotation, specified as a 2-by-2 matrix, a 3-by-3-byM array, a scalar so2 object, or an M-element array of so2 objects. M is the total number of rotations.

The resulting number of transformation objects is equal to the larger argument between translation and rotation

Example: eye(3)

Data Types: single | double

Object Functions

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

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