Algorithm (Workflow)

This function, wofT, is designed to compute the angle from a 2D homogeneous transformation matrix. It is part of the SolidGeometry library and was introduced in version 4.5. The function is authored by Tim Lueth and is intended for analytical geometry applications.

Input Parameters

• T2: A 3x3xM matrix representing a 2D homogeneous transformation matrix. The matrix is expected to be in the form of a stack of 3x3 matrices, where M is the number of such matrices.

Output Results

• w: A list of angles derived from the input transformation matrices.

Algorithm Explanation

The function begins by checking if the second dimension of the input matrix T2 is equal to 3. This check ensures that the input is a 3x3 matrix, which is a requirement for 2D homogeneous transformation matrices.

If the input matrix meets this condition, the function proceeds to calculate the angle using the atan2 function. The atan2 function computes the arctangent of the quotient of its arguments, which in this case are the elements T2(2,1,:) and T2(1,1,:) of the matrix. These elements correspond to the sine and cosine of the rotation angle, respectively.

The squeeze function is then used to remove any singleton dimensions from the resulting array, effectively producing a list of angles.

If the input matrix does not meet the 3x3 requirement, the function throws an error message indicating that the implementation is only available for 2D matrices. It suggests using the rotm2eul function from Peter Corke's library for Euler angles in other dimensions.

Example Usage

An example provided in the comments demonstrates the use of the function:

w = wofT(TofR(rot(pi/3))) - pi/3

This example shows how to use the function to compute the angle from a rotation matrix generated by a rotation of pi/3 radians.