dcm2quat

Convert direction cosine matrix to quaternion

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Syntax

q = dcm2quat(dcm)
q = dcm2quat(dcm,action)
q = dcm2quat(dcm,action,tolerance)

Description

q = dcm2quat(dcm) calculates the quaternion q for a given direction cosine matrix, dcm.

q = dcm2quat(dcm,action) performs an action, action, if the direction cosine matrix is invalid, that is not orthogonal. The direction cosine matrix input and resulting quaternion represent a right-hand passive transformation from frame A to frame B.

q = dcm2quat(dcm,action,tolerance) uses a tolerance level, tolerance, to evaluate if the direction cosine matrix dcm is within tolerance.

example

Examples

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Open Live Script

Determine the quaternion from a direction cosine matrix.

dcm = [0 1 0; 1 0 0; 0 0 -1];
q = dcm2quat(dcm)
q = 1×4

         0    0.7071    0.7071         0
Open Live Script

This example shows how to determine the quaternions from multiple direction cosine matrices.

dcm        = [ 0 1 0; 1 0 0; 0 0 -1]; 
dcm(:,:,2) = [ 0.4330    0.2500   -0.8660; ...
               0.1768    0.9186    0.3536; ...
               0.8839   -0.3062    0.3536];
q = dcm2quat(dcm)
q = 2×4

         0    0.7071    0.7071         0
    0.8224    0.2006    0.5320    0.0223
Open Live Script

Determine the quaternion from direction cosine matrix dcm within tolerance.

dcm = [0 1 0; 1 0 0; 0 0 -1];
q = dcm2quat(dcm, 'Warning', 0.01)
q = 1×4

         0    0.7071    0.7071         0

Input Arguments

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Direction cosine matrix, specified as a 3-by-3-by-M matrix.

Data Types: double

Function behavior when direction cosine matrix is invalid, that is, not orthogonal.

  • 'Warning' — Displays warning and indicates that the direction cosine matrix is invalid.

  • 'Error' — Displays error and indicates that the direction cosine matrix is invalid.

  • 'None' — Does not display warning or error.

Data Types: char | string

Tolerance of direction cosine matrix validity, specified as a scalar. The function considers the direction cosine matrix valid if these conditions are true:

  • The transpose of the direction cosine matrix times itself equals 1 within the specified tolerance (transpose(dcm)*dcm == 1±tolerance).

  • The determinant of the direction cosine matrix equals 1 within the specified tolerance (det(dcm) == 1±tolerance).

Data Types: double

Output Arguments

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Quaternion, returned in an m-by-4 matrix. q has a scalar number as the first column.

Version History

Introduced in R2006b

See Also

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