iris
Ground Plane — Distorted View (from above)
Correct Viewing Angle — What you see
Viewing Angle30°
Text Size80

Anamorphic Parameters

Viewing angle (θ) 30°
cos(θ) 0.8660
Stretch factor (1/cosθ) 1.1547×
Text height (original) 80 px
Text height (stretched) 92 px

How it works

Anamorphic art creates images that appear distorted unless viewed from a particular angle or with a special mirror. The technique has been used for centuries: one of the earliest and most famous examples is the skull in Hans Holbein the Younger's painting The Ambassadors (1533), which can only be recognized when viewed from a steep angle at the painting's right edge.

The mathematical principle is straightforward. When you view a flat surface at an oblique angle θ from the ground plane, objects along the depth axis are foreshortened by a factor of cos(θ). To compensate, anamorphic art stretches the image in the depth direction by 1/cos(θ). At a 30° viewing angle the stretch factor is about 1.15×; at 70° it reaches nearly 3×, creating dramatically elongated images on the ground that snap into perfect proportion from the intended viewpoint.

Modern street artists like Julian Beever and Kurt Wenner use this principle to create stunning 3D chalk drawings on pavement. These appear as impossible pits, floating objects, or protruding structures when photographed from the correct position, but look wildly distorted from any other vantage point. The same mathematics governs road markings: the word "SLOW" painted on roads is often stretched lengthwise so drivers can read it from their low, forward-looking angle.

Cylindrical anamorphosis is a related technique where a distorted image is painted on a flat surface and a cylindrical mirror is placed at the center. The curved mirror unscrambles the distortion, revealing the hidden image in its reflection. This was a popular parlor amusement in the 17th and 18th centuries and was sometimes used to conceal politically subversive or erotic imagery.