Visual Plane
every picture states the point it is correct from
Concept

Plane at infinity — where it appears

The set of directions in space, treated as a plane whose points are the directions themselves. A camera images it once and for all: a vanishing point is a direction's image on it, and a plane's vanishing line is the image of where that plane meets it.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

horizonprincipal pointv_zorthocentre: 812.7691 px · vᵀωu = 0: 812.7691 pxconjugacy residual 5.9e-10 in focal-length unitscorrect from 19 cm, at 160 mm wide46° across

One conic calibrates the camera

This site has recovered a focal length from two perpendicular vanishing points since its first phase, by an orthocentre construction with a square root in it. There is a second derivation with no construction and no square root — two vanishing points of perpendicular directions must be conjugate with respect to one conic in the picture — and the two agree to the last bit. They are not two methods. The conic is what a calibrated camera is.

foundations · absoluteconic xupzthe plane of x and upthe groundthe plane of x and zthe orthocentrefocal 707.4 pxthree sides, three planes

A drawing has three horizons

The triangle three vanishing points form is not a scaffold. Each of its sides is the vanishing line of one of the three coordinate planes — the floor's horizon and two walls' — and its orthocentre is the centre of the picture. So the horizon a perspective drawing is built on is one side of a triangle, and it is special only because the ground is where things stand.

construction · threepoint

Named alongside it

The objects these essays reach for when they reach for this one.

DemonstrationOrthocentrePrincipal pointVanishing pointAbsolute conicCamera calibrationCamera matrixCamera tiltCircular pointsConicFocal lengthFocal recovery

All concepts