Skip to the sheet
Drawn Mathematics

Mathematics you can see, draw, and fold.

The Vanishing Audit

Updated

The vanishing audit is the name Drawn Mathematics gives to one procedure: compute where a painting's receding lines meet, then draw those lines back over the painting to see how closely they agree. The name is this site's own, not a standard term in art history. Every painting analysis on the site runs one audit. The first full audit extends the window edges in Vermeer's Milkmaid: 11 Traced Edges Aim Just Above Her Hand; the second extends the floor borders in Anamorphic Art: The Smear in The Ambassadors Is a Skull.

What an audit does

  1. Pick edges that should be parallel in the painted scene, such as the joints of floor tiles, the edge of a table or the frame of a window.
  2. Extend each edge across the picture and compute where the lines meet. The meeting points are calculated from the lines, not judged by eye.
  3. Lay the lines over the painting and measure how far each one misses the shared vanishing point.

The overlay is the evidence. Anyone can take the same edges and recompute the same meeting points.

Three things every audit states

  • The projection assumed. Usually linear perspective with a single vanishing point, on a flat picture surface.
  • Which lines were chosen, and why. The edges treated as parallel in the scene are named, along with the reason for treating them that way.
  • Where distortion could come from. A photograph of a painting can add lens distortion, a canvas or panel can warp, and later restoration can shift lines.

Fact and interpretation

How far the lines miss a single vanishing point is a geometric fact, measured on the overlay. Why they miss is a different question: a choice of composition, an intention or a mistake. A painter's intention is stated only when a published source supports it. Without one, the explanation is labelled as this site's interpretive hypothesis.

Laying out where a famous painting departs from a single vanishing point is not disrespect. Covering for the painter would be.

Which paintings

Audits use public-domain images only. Paintings still in copyright, which include many twentieth-century works, are not audited. Each base image is credited as public domain with its basis, and the site's license covers the overlay lines only (see Borrow these drawings). The wider checking method is on Checking the construction.