A general multivector in geometric algebra:
The structure of a multivector in conformal geometric algebra:
The outer product of two points results in a point pair.
The outer product of two points and the point at infinity results in a line.
Using the sandwich product of motors to transform a point results in another point. The operation is grade preserving.
Experiments
![](https://geometric-algebra.tobiloew.ch/optimal_control/oriented_pointmass.gif)
![](https://geometric-algebra.tobiloew.ch/optimal_control/mpc_point.gif)
![](https://geometric-algebra.tobiloew.ch/optimal_control/mpc_pointing_point.gif)
![](https://geometric-algebra.tobiloew.ch/optimal_control/mpc_line.gif)