ProjectiveGeometri geometryprojektif istidaklah lessbegitu restrictivemengungkung thanbila eitherdibandingkan dengan [[Euclideangeometri geometryeuklides]] oratau [[affinegeometri geometryafin]]. ItIa issecara anintrinsik intrinsicallymerupakan geometri non-[[Metricmetrik (mathematicsmatematika)|metricalmetrik]] geometry, whoseyang factsfakta-faktanya aretidak independentbergantung ofpada anystruktur metricmetrik structuremanapun. Under the projective transformations, the [[incidence structure]] and the relation of [[projective harmonic conjugate]]s are preserved. A [[projective range]] is the one-dimensional foundation. Projective geometry formalizes one of the central principles of perspective art: that [[parallel (geometry)|parallel]] lines meet at [[infinity]], and therefore are drawn that way. In essence, a projective geometry may be thought of as an extension of Euclidean geometry in which the "direction" of each line is subsumed within the line as an extra "point", and in which a "horizon" of directions corresponding to coplanar lines is regarded as a "line". Thus, two parallel lines meet on a horizon line in virtue of their possessing the same direction.
Idealized directions are referred to as points at infinity, while idealized horizons are referred to as lines at infinity. In turn, all these lines lie in the plane at infinity. However, infinity is a metric concept, so a purely projective geometry does not single out any points, lines or plane in this regard—those at infinity are treated just like any others.
