What algorithm can I use to match or align (translate and scale) two vectors of different size in C#?

1. How do you combine translation and rotation?
2. How do you find the rotation between two vectors?
3. How do you apply a rotation matrix to a vector?

How do you combine translation and rotation?

A rotation matrix and a translation matrix can be combined into a single matrix as follows, where the r's in the upper-left 3-by-3 matrix form a rotation and p, q and r form a translation vector. This matrix represents rotations followed by a translation.

How do you find the rotation between two vectors?

First step, you want to find the angle between the two vectors using the dot product. Next, to find the axis of rotation, use the cross product. Knowing that the cross product will yield a vector perpendicular to both u and v , crossing them in either order will give an appropriate axis.

How do you apply a rotation matrix to a vector?

The formula for finding the rotation matrix corresponding to an angle-axis vector is called Rodrigues' formula, which is now derived. Let r be a rotation vector. If the vector is (0,0,0), then the rotation is zero, and the corresponding matrix is the identity matrix: r = 0 → R = I . such that p = r.