The separation of skew lines


This illustrates how the distance vectors of two skew lines in 3D can be constructed using an orthogonalization of spanned volumes. In geometric algebra, this is the interaction of the wedge product with geometric division.

The black vector is in fact (u ^ (q-p) ^ v)/(u ^ v).



You can drag the perpendicular support vectors p and q, as well as the direction vectors of the line. Try to find directions to drag p that maximize and minimize the change of the black vector. Also make sure you change the directions of the lines, to verify that the construction still works!

(This is a 2-D construction mimicking a 3-D situation, so hidden line removal does not work correctly.)


Created with Cinderella by Leo Dorst 20010716.