# Obj file vertex coordinates to new coordinate space

I am trying to convert the vertex positions in my obj file to a new coordinate system. I understand I need to multiply each vertex with the transformation matrix, however I am trying to figure out the transformation matrix. The basis vector for my new coordinate system is

$$\begin{bmatrix}1\\0\\0\end{bmatrix} \begin{bmatrix}0\\1\\0\end{bmatrix} \begin{bmatrix}0\\0\\1\end{bmatrix}$$

However, I am having trouble figuring out what the basis vectors are of the obj vertices. Any ideas or insight would be helpful. Could I select a random vertex with 2 edges (connecting to other nodes) and define those as the basis vectors? The tough part is I’m pretty sure the values for the vertices are pixel values. So, I am trying to go from model space -> world space.

Use case I have a bunch of drones that I want manipulate and move so it generates the shape of the obj. For example, each vertex represents a drone. However, I’m confused on how each drone knows it’s in position of a vertex. If I could define an origin in the current drone configuration, I can then determine the position of the rest of the drones and if I determine the origin of the obj file I can map that to the drone at 0, 0, 0 and then know each position of every other vertex

• The basis vectors you've shown are the basis vectors of EVERY coordinate system, expressed within that coordinate system itself. To be useful for meaningful conversion, you need to express those basis vectors of the destination coordinate system in terms of the source coordinate system (or vice versa). Try explaining to us the geometric change you want to apply. What's wrong about the position/orientation/scaling of your model when you import it with the identity transformation? Once we clearly understand that, we can help you form a matrix to correct it Aug 15 '21 at 11:50
• That makes sense, but wouldn’t one of the points need to be at 0, 0, 0? Or are they jus translated from that point? I think if I explain an example it will make sense. I updated my question. Aug 15 '21 at 16:04
• Stop thinking in terms of converting a basis to another, and start thinking in terms of applying transformations. Aug 16 '21 at 19:05