Hi Melissa,

in my opinion it woud be the best if we could reuse existing properties in changing their range and domain such that they include 'anatomical line'.

The main problem I see here however is that in general the orthogonal complement of a subspace like a line or a plane is always dependend on the dimension of the space one is refering to. So in 2D the orthogonal complement of a line is a line, while in 3D the orthogonal complement of a line is a plane.
That makes it dificult to define domain and range for a general purpose orthogonal_to property.

Further a general purpose orthogonal_to property should be symmetric, but then domain and range should be the same, right? So this is probably not possible without making domain and range too abstract as beeing of any use for reasoning.

So I see the following options:
1. Braoden range and domain of the orthogonal_to relation to make it general purpose: domain and range ('anatomical plane' OR 'anatomical line').
However you mentioned that the domain and range restrictions on orthogonal_to are used in some error checking on Cartesian components...
2. Define a new (symmetric) property perpendicular_to with domain and range 'anatomical line'.
3. Change domain and range of approximately_perpendicular_to to 'anatomical line'. Approximately perpendicular includes perpendicular so that would be fine for me, even though not perfect.

I think a pragmatic solution would be the second option (as you proposed as well).

Heiner