Are there any improper rotations in the rotation matrix?
In some literature, the term rotation is generalized to include improper rotations, characterized by orthogonal matrices with a determinant of -1 (instead of +1). These combine proper rotations with reflections (reversing orientation). In other cases, when reflections are not considered, the label itself can be discarded.
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How to get the relative rotation matrix of two?
You can always calculate relative orientations in a similar way. Throughout the calculation, we use the convention that the transformation $J=[R|T]$ is a mapping from the scene to the camera (the opposite is therefore vice versa). The final pose transforms a point from camera $i$ to camera $j$.
How to calculate axis and angle of a rotation matrix?
There are several methods to compute the axis and angle from a rotation matrix (see also axis-angle representation). Here, we only describe the method based on the calculation of the eigenvectors and the eigenvalues of the rotation matrix. It is also possible to use the rotation matrix trace.
Is the convention of a rotation matrix the same?
The convention for these rotation matrices follows the same positive direction of rotation as the cross product in a right-hand coordinate system.
How to rotate object in global reference frame?
For rotation in the global reference frame, you must premultiply the transformation matrix, and for rotation in the local frame, postmultiply. For example, if you want a rotation by θ 1 on A for which the transformation matrix is R θ 1 and then a rotation by θ 2 on A (rotation matrix R θ 2 ), then:
What does it mean to rotate an object around a fixed axis?
A horizontal movement on the screen means rotation around a fixed Y axis, and a vertical movement means rotation around the X axis. The problem I have is that if I only allow rotation around one axis, the object rotates fine, but as soon as since I introduce a second rotation, the object does not rotate as expected.
What is the rotation matrix about the origin?
In homogeneous coordinates, a rotation matrix about the origin can be described as $R = //begin{bmatrix}//cos(/heta) & -//sin(/heta) & 0//////sin(/heta) & //cos(/heta) & 0 // // 0&0&1//end{barray}$. with the angle $/heta$ and the rotation counterclockwise.
How is the position of a point represented in a rotation matrix?
rotates points in the xy-plane counterclockwise by an angle θ relative to the origin of the Cartesian coordinate system. To perform the rotation using a rotation matrix R, the position of each point must be represented by a column vector v, which contains the coordinates of the point.
What is the only non-trivial case where the rotation matrix is commutative?
The two-dimensional case is the only non-trivial (ie not one-dimensional) case where the group of rotation matrices is commutative, so it does not matter in what order the multiple rotations are performed.