The opposite of a curve is mirrored image of that curve, so a half circle plus an opposite would be a full circle.
Anti grav was invented by the Germans in WW2, the amercans took it and the scientists back to the US in 1945 2 years later there was the roswell incident which was a prototype craft developed by these scientists working with the US. Anti Grav works on magnetism which is why saucers and pyramid shaped crafts are most commonly seen, they are the 2 best shapes to manipulate magnetism, by firing magnetic fields both up and out and down and out, one running with the magnetic frequencies of the planet and one working opposite you can essentially lock your self in place( imagine 2 pyramids one upside down and stacked tip to tip). Then by adding more magnetic fields behind the direction you wish to travel both up and down at an angle you can create a squeeze effect to propel you along. Well, it works with magnets.