three world vectors can be expressed as follows it can be shown that the above vectors can be obtained without any loss of generality since u03bc 1 u03bc 2 and u03bc 3 are orthogonal it follows that from equations 2 and 5 it follows that equ2 equation 6 implies that since the left hand side quantity in the above equation is real it follows that cos u03b1 cos u03b2 cos u03b3 should be negative also note u03b1 u03b2 u03b3 360 u00b0 table 1 summarizes the results by indicating possible and impossible values for u03b1 u03b2 and u03b3 and their cosines constraints on cosines are shown in parentheses table 1______________________________________possible and impossible values of angles and cosinesof angles in parentheses in a 2 d projection of a3 d orthogonal trihedral vertex possible not possible______________________________________2 angles acute 1 angle gt 270 u00b0 1 angle obtuse 2 angles acute 1 negative cosine all positive cosines 2 positive cosines all 3 angles obtuse 2 angles obtuse all 3 cosines negative 1 angle acute 2 negative cosines 1 positive cosine ______________________________________ in summary during fork filtering all the fork junctions which satisfy either 1 2 angles acute 1 angle obtuse or 2 where all three angles are obtuse are accepted the other fork junctions are rejected in addition to the fork junctions obtained after filtering.