Can I create a transformation matrix from rotation/translation vectors?

1. How do you create a transformation matrix?
2. What is the transformation matrix for translation transformation?
3. How do you combine translation and rotation matrix?

How do you create a transformation matrix?

The position vector of a point A = xi + yj, on multiplying with a matrix T = (abcd) ( a b c d ) is transformed to another vector B = x'i + y'j. Here the vector A = xi + yj is represented as a column matrix A = [xy] , and the matrix B = x'i + y'j is another column matrix B = [x′y′] .

What is the transformation matrix for translation transformation?

A type of transformation that occurs when a figure is moved from one location to another on the coordinate plane without changing its size, shape or orientation is a translation . Matrix addition can be used to find the coordinates of the translated figure.

How do you combine translation and rotation matrix?

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.