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I thought I knew what rotation matrices were until I read this article. Now I am confused. I used to think I needed a 3x3 matrix to rotate a point (with x,y,z c
by bawana 6y ago
I thought I knew what rotation matrices were until I read this article. Now I am confused. I used to think I needed a 3x3 matrix to rotate a point (with x,y,z coordinates) in 3 D space. But the article refers to Rx,Ry and Rz EACH of which are a 3x3 matrix.Why are there 3 matrices? To move an x coordinate to a new coordinate system, I only need to displace it among the the existing three axes. So each coordinate only needs a 3x1 vector to displace it . That a makes a single 3x3 matrix.
- leereeves 6y agoRx rotates about the x-axis (in the yz plane), Ry about the y-axis (in the xz plane), and Rz about the z-axis (in the xy plane). We need all three because none of them can be made from the other two, but any other rotation can be made from a combination of these three.
- dahart 6y agoThose 3 mats Rx Ry Rz are just 3 separate examples from Wikipedia of how to construct a rotation matrix where the rotation axis is in the x, y, or z direction. They are separate rotations that don’t have to be combined.
- diffeomorphism 6y ago> I only need to displace it among the the existing three axes. That is exactly what these three matrices do. R_x depends on a single parameter and tells you how much you rotate around the x-axis. R_y tells you how much you rotate around the y-axis and R_z for the z-axis. Any rotation can be written as a product of these three (which then is a single 3x3 matrix depending on three parameters).
- aesthesia 6y agoThose three matrices describe three different rotations. Rx is a rotation about the x axis, Ry about the y axis, Rz about the z axis. They're parameterized by an angle theta that describes how much to rotate.
- brummm 6y agoR_x, R_y and R_z are the basis to generate all rotations. Think of them as the equivalent of the basis vectors in 3d euclidian space: e_x = (1, 0, 0), e_y=(0, 1, 0) and e_z = (0, 0, 1)
- kergonath 6y agoAny number of successive rotations can be represented as a single matrix. Both are right at the same time: an arbitrary rotation (represented by a single matrix) is a combination of 3 rotations about the axes of the reference frame (represented by 3 matrices).
- bawana 6y agoThank you to all who replied. My clue should have been the use of the same theta instead of alpha, beta and gamma.