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

costruzione legittima — where it appears

The Renaissance construction that divides a pavement in depth by a drawn section rather than by judgement. Its free parameter is the viewing distance, which the recipe never names, so two draughtsmen following it exactly can produce two pictures correct from two different places.

Named by 5 essays across one field — each of them below, with the objects they name alongside it.

horizonequal stepshalve thetaper byworst error, in metres of depthequal steps to the horizon14.72 mhalve the remaining gap228.13 mtaper by eye350.80 mcorrect 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 the distance pointAlberti's sectionthe measuring pointcorrect from 12 cm at 160 mm widethree routes, 0e+0 px apart

Three procedures, one panel

Alberti's lateral section, the distance-point construction and a pinhole camera put every transversal at the same pixel — and every reading of the finished drawing therefore returns the same number for all three. The methods are distinguishable on the desk and indistinguishable on the panel, which is the fact any attribution has to start from.

construction · Attribution the distance pointone mark on the horizonleaves another exact drawingAlberti's sectionone mark per braccio, each from the panelleaves errors each its ownthe measuring pointdividers walked along the measuring lineleaves errors that accumulatea photographnoneleaves a smooth curvethe constant ratioone ratio, applied throughoutleaves a smooth curveone hand step eachand four kinds of trace

One hand step each

Every classical perspective construction has exactly one step a person performs by hand, and the four constructions perform four different steps. That single difference decides everything a finished drawing can say about its maker, because the answers are identical and only the mistakes are not.

construction · Handerror the picture plane, in planto the observer, 208 px further downcorrect from 12 cm, at 160 mm widestation 520 px

Two rules for one pavement

Vignola set out two rules for laying a tiled floor and asserted that they agree. Executed from the same ground line and the same free parameter they agree to 2e-13 px; executed from the numbers their own wordings invite they part by 24 px. The quantity that separates them is the distance the reader has to stand at, and neither rule names it.

construction · Tworules

Named alongside it

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

TransversalViewing distanceCentric pointDistance pointMeasuring pointProcedureAttributionbraccioFocal lengthGround lineHorizonStation point

All concepts