Hey stackexchange :) So when I am in a coordinate system (lets say the classic one with base vectors (1,0), (0,1)) I can just use the base vectors of the other coordinate system as a transformation matrix to change vectors from one base into another. The inverse of this matrix allows to change them back.
However this assumes that both coordinate systems are centered around the origin. If I have a coordinate system which is centered around another point can I just use a translation matrix (using homogen coordinates) to move the other coordinate system into the origin, then transform it using the transformation matrix mentioned above and then use the inverse of the above mentioned translation matrix to push it back? This would require to basically add an additional line + column to the transformation matrix to keep it in the right dimensions. Is this valid?
The whole concept of looking at coordinate systems not centered around the origin still makes me a little bit oncomfortable so I would really appreciate some help understanding it a little bit better :) Thx in advance!
