Previous | Next --- Slide 70 of 112
Back to Lecture Thumbnails
nssampat

Where did the final equation on this slide come from? It seems like we substituted x'R = x-t, but the formula we are given (rigid motion) is the reverse: x' = R(x-t).

motoole2

The rotation matrix $R$ is unitary, meaning $R^T R = R R^T = I$. So we can re-write the left equation as

$R^T x' = R^T R (x - t) = (x-t)$

Transposing this result gives us

$x'^T R = (x-t)^T$

Finally, we simply have to plug in this result into the equation on the right hand side to get our desired result.