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)
“This is something that I cannot get over—that a whole line could be written by half a man, that a work could be built on the quicksand of a character.”
—Karl Kraus (1874–1936)
“How oft when men are at the point of death
Have they been merry! which their keepers call
A lightning before death: O, how may I
Call this a lightning? O my love! my wife!
Death, that hath sucked the honey of thy breath,
Hath had no power yet upon thy beauty:
Thou art not conquered; beauty’s ensign yet
Is crimson in thy lips and in thy cheeks,
And death’s pale flag is not advanced there.”
—William Shakespeare (1564–1616)