Concept

Ground line — where it appears

Where the picture plane meets the ground, along which a construction lays out the true widths it will project.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

246VPcorrect from 26 cm, at 160 mm wide34° across

The measuring point, and the step the method leaves out

Laying out equal depths correctly needs a second vanishing point that most treatments never introduce — the one belonging to the diagonals. With it the construction lands on the projected divisions to eighty femtopixels. Without it, depth is placed by judgement and the drawing depicts something nobody chose.

construction · measuring
the panelhorizon — the centric point's heightthe section — the eye, the panel, the ground470 px — the viewing distancethree routes agree to 6e-14 pxsection, distance point, and a pinhole camera

Alberti draws a pavement, and chooses where the reader stands

The costruzione legittima of 1435 is exact. Run as a construction — with drawn rays and drawn intersections rather than the formula it turns out to satisfy — it agrees with a pinhole camera to six parts in a hundred trillion of a pixel. And it has one free parameter that the recipe never names, which is the distance from the eye to the panel.

construction · alberti
three side intersections, collinear to 3e-13 pxcentrethree sides paired, three pointscollinear to 3e-13 px

Two triangles and the line nobody drew

Desargues' theorem is the reason a hand-drawn shadow construction closes. An object and its shadow are two figures in perspective from the lamp; the theorem says their corresponding sides meet, pairwise, on one line — which is the ground line. So the closure a draughtsman treats as confirmation that the work is accurate is a theorem they cannot violate.

foundations · desargues

Named alongside it

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

Centric pointcostruzione legittimaFocal lengthViewing distancebracciocentre of projectionDemonstrationDesarguesDiagonal pointHarmonic conjugateHorizonLateral section

All concepts