Geometri projektif tidaklah begitu mengungkung bila dibandingkan dengan [[geometri euklides]] atau [[geometri afin]]. Ia secara intrinsik merupakan geometri non-[[metrik (matematika)|metrik]], yang fakta-faktanya tidak bergantung pada struktur metrik manapun. UnderDi thebawah projectivetransformasi transformationsprojektif, the [[incidencestruktur structureinsidensi]] and the relationdan ofrelasi [[projectivesekawan harmonicharmonik conjugateprojektif]]sare preserveddipelihara. A [[projectiveRentang rangeprojektif]] isadalah thedasar one-dimensionalsatu foundationdimensi. ProjectiveGeometri geometryprojektif formalizesmemformalkan onesalah ofsatu theprinsip centralsentral principlesseni of perspective artperspektif: thatbahwa garis-garis [[parallelparalel (geometrygeometri)|parallelsejajar]] linesbertemu meet atdi [[infinitytak hingga|ketakhinggaan]], anddan thereforeoleh arekarenanya drawndigambarkan thatseperti wayitu. In essenceIntinya, ageometri projectiveprojektif geometrydapat maydipikirkan besebagai thoughtperluasan ofgeometri aseuklides andi extension of Euclidean geometry in which themana "directionarah" oftiap-tiap eachgaris linedimasukkan iske subsumeddalam withingaris the line as an extrasebagai "pointtitik" ekstra, anddan indi whichmana asebuah "horizoncakrawala" ofarah directionsyang correspondingberpadanan todengan coplanargaris-garis lineskoplanar isdipandang regarded as asebagai "linegaris". ThusDengan demikian, two parallel lines meetdua ongaris asejajar horizonbertemu linepada ingaris virtuemendatar ofkarena theirmereka possessingmemiliki thearah sameyang directionsama.
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.
