Inverting rotation in 3D, to make an object always face the camera?

Question

i have lots of sprites arranged in 3D space, and their parent container has rotations applied. How do i reverse the sprites 3D rotation, that they always face the camera (Ac

Answer 1

The easiest way to do this is "clearing" the rotational part of the transform matrix. Your typical homogenous transformation looks like this

| xx xy xz xw |
| yx yy yz yw |
| zx zy zz zw |
| wx wy wz ww | 

with wx = wy = wz = 0, ww = 1. If you take a closer look you'll see that in fact this matrix is composed of a 3x3 submatrix defining the rotation, a 3 subvector for the translation and a homogenous row 0 0 0 1

| R       T |
| (0,0,0) 1 |

For a billboard/sprite you want to keep the translation, but get rid of the rotation, i.e. R = I. In case some scaleing was applied the identity needs to be scaled as well.

This gives the following recipie:

d = sqrt( xx² + yx² + zx² )

| d 0 0 T.x |
| 0 d 0 T.y |
| 0 0 d T.z |
| 0 0 0   1 |

Loading this matrix allows you to draw camera aligned sprites.