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

Inclined plane — where it appears

A plane that is not level, whose vanishing line therefore sits above or below the true horizon rather than on it. That displaced vanishing line is what a ramp has and a stair does not, because a stair is two families of surfaces neither of which slopes.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

nothing on the ramp images above its vanishing linehorizonuphilllevelcorrect from 10 cm, at 160 mm wideslope recovered 22.0000° against 22° built

The ramp has its own horizon

Every plane has a vanishing line, and a ramp's is not the ground's. Its uphill edges meet on a line above the horizon, and the angle at the eye between that meeting point and the same direction taken level is the gradient — 22.0000° recovered against 22° built, out of the picture alone, with no scale, no ruler and nothing known about the scene except that the ground is level.

construction · Inclined horizoncorrect from 20 cm, at 160 mm wide44° across

The line every nosing is on

Nothing in a staircase points up the pitch. Every surface in it is level or vertical, and its picture has a vanishing point off the horizon all the same — belonging to the line the front edges of the treads lie on. That point is not free: it is collinear with the travel point and the vertical point, and the angle it makes says the rise-to-run the builder chose.

construction · Inclined the ramp's vanishing linethe ramp's own pointthe horizoncorrect from 16 cm, at 160 mm wide3.43 m out at the sixth tread

A measuring point for a ramp

Stepping true distances along a receding line needs a measuring point, and every printed rule puts it on the horizon. On a 1 in 6.0 ramp the ramp's own point lands every tread to 1.2e-13 pixels and the ground's puts the sixth one-metre tread at 2.57 metres instead of six. A halfway construction separates the two halves of the mistake, and the wrong radius costs 0.083 metres of the 3.43.

construction · Inclined the heads' linethe horizoncorrect from 16 cm, at 160 mm wide59 px, 1.46 m at the far figure

Figures on a street that slopes

Equal-height figures have their heads on one line, and the taught rule says the line is the horizon. On a street rising at 8.33 per cent the heads are still collinear to 2.8e-14 pixels and the line is 58.9 pixels above the horizon — the street plane's own vanishing line. The taught rule loses 1.46 m of a 1.62 m figure at the far figure, and runs out of figure altogether at 19.4 m.

construction · Height

Named alongside it

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

HorizonVanishing pointPicture planesingle-view metrologyVanishing lineCollinearityFocal lengthStraightedge constructionAngle from vanishing pointsDistance pointEye levelForeshortening

All concepts