3-D rigid geometric transformation


A rigid3d object encapsulates a 3-D rigid transformation.




tform = rigid3d creates a default rigid3d object that corresponds to an identity transformation.

tform = rigid3d(t) creates a rigid3d object based on a specified forward rigid transformation matrix, t. The t input sets the T property.

tform = rigid3d(rot,trans) creates a rigid3d object based on the rotation, rot, and translation, trans, components of the transformation. rot sets the Rotation property. trans sets the Translation property.


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Forward rigid transformation, specified as a 4-by-4 floating point matrix. This matrix must be a homogeneous transformation matrix that satisfies the post-multiply convention given by:


T has the form


This property is read-only.

Dimensionality of the geometric transformation, specified as a positive integer.

Rotation component of the transformation, specified as a 3-by-3 floating-point matrix. This rotation matrix satisfies the post-multiply convention given by


Translation component of the transformation, specified as a three-element row vector of floating-point values. This translation vector satisfies the convention given by


Object Functions

invertInvert geometric transformation
outputLimitsFind output spatial limits given input spatial limits
transformPointsForwardApply forward geometric transformation
transformPointsInverseApply inverse geometric transformation


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Specify an angle in degrees. Set the rotation and translation components of the transformation.

theta = 30; % degrees
rot = [ cosd(theta) sind(theta) 0; ...
       -sind(theta) cosd(theta) 0; ...
                 0           0  1];
trans = [2 3 4];
tform = rigid3d(rot,trans)
tform = 
  rigid3d with properties:

       Rotation: [3x3 double]
    Translation: [2 3 4]

Introduced in R2020a