rotationMatrixToVector

(Not recommended) Convert 3-D rotation matrix to rotation vector

rotationMatrixToVector is not recommended. Use the rotmat2vec3d function instead. For more information, see Version History.

Syntax

rotationVector = rotationMatrixToVector(rotationMatrix)

Description

rotationVector = rotationMatrixToVector(rotationMatrix) returns an axis-angle rotation vector that corresponds to the input 3-D rotation matrix. The function uses the Rodrigues formula for the conversion.

Examples

Convert Rotation Matrix to Rotation Vector

Create a matrix representing a 90-degree rotation about the Z-axis.

rotationMatrix = [0 1 0; -1 0 0; 0 0 1];

Find the equivalent rotation vector.

rotationVector = rotationMatrixToVector(rotationMatrix)

rotationVector = 1×3

         0         0    1.5708

Input Arguments

rotationMatrix — Rotation of camera

3-by-3 matrix

Rotation of camera, specified as a 3-by-3 matrix. You can obtain this matrix by using the estimateExtrinsics function.

Output Arguments

rotationVector — Rotation vector

three-element vector

Rotation vector, returned as a three-element vector. The vector represents the axis of rotation in 3-D, where the magnitude corresponds to the rotation angle in radians.

Data Types: single | double

References

[1] Trucco, Emanuele, and Alessandro Verri. Introductory Techniques for 3-D Computer Vision. Upper Saddle River, NJ: Prentice Hall, 1998.

Extended Capabilities

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

Version History

Introduced in R2016a

R2022b: Not recommended

Starting in R2022b, most Computer Vision Toolbox™ functions create and perform geometric transformations using the premultiply convention. However, the rotationMatrixToVector function uses the postmultiply convention. Although there are no plans to remove rotationMatrixToVector at this time, you can streamline your geometric transformation workflows by switching to the rotmat2vec3d function, which supports the premultiply convention. For more information, see Migrate Geometric Transformations to Premultiply Convention.

To update your code:

• Change instances of the function name rotationMatrixToVector to rotmat2vec3d.

• Specify the rotation matrix as the transpose of the rotationMatrix argument of the rotationMatrixToVector function. Alternatively, you can get a rotation matrix in the correct premultiply format by using the estimateExtrinsics function and querying the R property of the returned rigidtform3d object.

The table shows examples of how to update your code.

Discouraged Usage	Recommended Replacement
This example converts a 3-D rotation matrix in the postmultiply convention to a rotation vector using the rotationMatrixToVector function. rotVectorOld = rotationMatrixToVector(rotMatrixOld)	This example converts a 3-D rotation matrix in the premultiply convention to a rotation vector using the rotmat2vec2d function. The 3-D rotation matrix is the transpose of rotMatrixOld. rotMatrixNew = rotMatrixOld'; rotVectorNew = rotmat2vec2d(rotMatrixNew);
This example obtains a 3-D rotation matrix in the postmultiply convention using the extrinsics function, then converts the matrix to a rotation vector using the rotationMatrixToVector function. [rotMatrixOld,transVector] = extrinsics( ... imagePoints,worldPoints,intrinsics); rotVectorOld = rotationMatrixToVector(rotMatrixOld);	This example obtains a 3-D rotation matrix in the premultiply convention using the estimateExtrinsics function, then converts the matrix to a rotation vector using the rotmat2vec2d function. camExtrinsics = estimateExtrinsics( ... imagePoints,worldPoints,intrinsics); rotMatrixNew = camExtrinsics.R; rotVectorNew = rotmat2vec2d(rotMatrixNew);