Homogeneous Coordinate System
A point in the plane may be represented in homogeneous coordinates by a triple (x, y, z) where x/z and y/z are the Cartesian coordinates of the point. This introduces an "extra" coordinate since only two are needed to specify a point on the plane, but this system is useful in that it represents any point on the projective plane without the use of infinity. In general, a homogeneous coordinate system is one where only the ratios of the coordinates are significant and not the actual values.
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Famous quotes containing the words homogeneous and/or system:
“If we Americans are to survive it will have to be because we choose and elect and defend to be first of all Americans; to present to the world one homogeneous and unbroken front, whether of white Americans or black ones or purple or blue or green.... If we in America have reached that point in our desperate culture when we must murder children, no matter for what reason or what color, we don’t deserve to survive, and probably won’t.”
—William Faulkner (1897–1962)
“Such is the remorseless progression of human society, shedding lives and souls as it goes on its way. It is an ocean into which men sink who have been cast out by the law and consigned, with help most cruelly withheld, to moral death. The sea is the pitiless social darkness into which the penal system casts those it has condemned, an unfathomable waste of misery. The human soul, lost in those depths, may become a corpse. Who shall revive it?”
—Victor Hugo (1802–1885)