Checking For Incidence of A Line On A Point
Given line L and point P in a projective plane, and both expressed in homogeneous coordinates, then P⊂L if and only if the dual of the line is perpendicular to the point (so that their dot product is zero); that is, if
where g is the duality mapping.
An equivalent way of checking for this same incidence is to see whether
is true.
Read more about this topic: Incidence (geometry)
Famous quotes containing the words incidence, line and/or point:
“Hermann Goering, Joachim von Ribbentrop, Albert Speer, Walther Frank, Julius Streicher and Robert Ley did pass under my inspection and interrogation in 1945 but they only proved that National Socialism was a gangster interlude at a rather low order of mental capacity and with a surprisingly high incidence of alcoholism.”
—John Kenneth Galbraith (b. 1908)
“We have not passed that subtle line between childhood and adulthood until we move from the passive voice to the active voice—that is, until we have stopped saying “It got lost,” and say, “I lost it.””
—Sydney J. Harris (b. 1917)
“From a purely external point of view there is no will; and to find will in any phenomenon requires a certain empathy; we observe a man’s actions and place ourselves partly but not wholly in his position; or we act, and place ourselves partly in the position of an outsider.”
—T.S. (Thomas Stearns)