Transforms

Convention

Major

We always assume column-major matrix. This is equivalent to the following:

1. We use a column vector to represent a single 3D point during transformation.

2. We perform right/post multiplication with a column vector to transform the point, i.e. p = M @ p.

Reference

Pose vs Extrinsic

• Camera pose is the camera-to-world transformation while extrinsic is the world-to-camera transformation.

3D Coordinate

    z                    y
   /                     |
  /                      |
 o ---------- x (u)      |
 |                       o ---------- x
 |                      /
 |                     /
 y (v)                z

OpenCV               OpenGL

2D Coordinate

OpenCV              Matrix
o ---------- u      o ----------- y (j)
|                   |
|                   |
|                   |
v                   x (i)