In the book from Hartley and ZisserMan "Multiple View Geometry", plucker coordinates were presented as being some cells of the skew-symmetric matrix that is the wedge product of two homogeneous points:
with the definition for the coordinates:
I still need to read the section about using those ones on projected lines on the same book, but, for now, i felt this convention strange comparing to the convention of = { direction, momentum } that is common to see; In this Hartley/ZisserMan notation, seems that the direction vector is (-l14,l42,-l34) and momentum vector (p(2,3),-p(1,3),p(1,2)). I was wondering if this notation is some special notation for some reason.
Thanks!
At the end of the day it is only a convention. But I believe there is a minus missing in your direction vector.
The same convention is used here, so you can compare your notes: https://en.wikipedia.org/wiki/Pl%C3%BCcker_matrix
I find this order of coordinates comes naturally if you write down general join and meet operations. It is advantageous for programming, because it reflects the combinatorics involved (i.e. start with lowest-index coordinate, combine with others, go to the next etc.). But as with all conventions, it comes down to a matter of taste...