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

[Reference](https://www.scratchapixel.com/lessons/mathematics-physics-for-computer-graphics/geometry/row-major-vs-column-major-vector)

### 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)
```