3 ms·
And in 3 dimensions it's points and planes that are dual - and finding the line between two points or the common line of two planes can now be done in a similar
by user51442 9y ago
And in 3 dimensions it's points and planes that are dual - and finding the line between two points or the common line of two planes can now be done in a similar way, but using Plücker coordinates for the lines instead.
- theoh 9y agoThose two operations are called "meet" and "join", and in principle they work with any linear subspaces (point, line, plane, etc.) So the meet of a line and a plane in 3D is a point, the join of a point and a line in 3D is a plane, etc. Wikipedia is good on this stuff if you are patient with mathematician's way of expressing things... https://en.m.wikipedia.org/wiki/Join_and_meet https://en.m.wikipedia.org/wiki/Join_and_meet https://en.m.wikipedia.org/wiki/Linear_subspace https://en.m.wikipedia.org/wiki/Linear_subspace "Lattice of subspaces The operations intersection and sum make the set of all subspaces a bounded modular lattice, where the {0} subspace, the least element, is an identity element of the sum operation, and the identical subspace V, the greatest element, is an identity element of the intersection operation."
- tel 9y agoThen you can go full geometric algebra and base your whole geometry on this latticez