> We could do it in the Plane class as you above described but that would also
> require a lot of if instance statements in the plane class as well  as we
> have to check whether a point is 2D or 3D and act accordingly.

I do not see why this would be the case. Could you give an example?
Projections work only on 3d points. Promotion to 3d works only on 2d
points. These are very different operations. There is no need of
switch/case statements.

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