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

An oriented pointmass system.

System tracking a point target.

Pointing task, i.e. system tracking a point target using a line.

System tracking a line target. It can be seen that the system is compliant if moved along the line and stiff if moved away from the line.