Dürer Machines Running Back and Forth:

a workshop on anamorphosis

This is a companion web page for my 2020 Bridges Workshop Dürer Machines Running Back and Forth .

Bridges 2020 was supposed to happen in Finland but due to pandemic troubles it will happen online through the Zoom platform. You can attend the workshop for free by registering here until July 30th. My workshop is scheduled for August 4th, 10:00am EDT (3:00pm in Lisbon, Portugal)


Materials for the workshop

Requirements (minimal): A4 sheets of paper and a pencil + eraser.

The minimal requirements will allow you to follow the proceedings and understand what is going on, but you won't be able to actually build a functional anamorphosis. You'll just learn how to make one later on with proper equipment. Namely:

Requirements (fancy): If you want to draw an actual working anamorphosis during the workshop then you need a larger setup: pencil+ eraser + marker or pen + A3 paper + large ruler or straightedge (about 50 cm long) + square ruler (for drawing perpendiculars) + tape + mobile phone (for seeing/photographing the illusion). Scissors optional.

If you don't have A3 paper you can just tape two A4s to get an A3. Even when using A3 it is a good idea to have several A3 sheets and tape, as A3 is still a bit small, and most likely you'll have to extend your drawing as it flows out of the first sheet.

Due to the limitations of an online demo, I will be using Geogebra to make my drawing. If you have a big screen and you are a Geogebra buff then you can follow along using it also. But I recommend you do it on paper instead, to get an actual physical anamorphosis you can shoot with your phone camera at the end.

What is the workshop about

You can read the details in the workshop paper, but to summarize:

You probably have seen the picture of a Dürer perspective machine (Fig. 1). They allow you to plot the perspective image Q of a point P, projecting it back towards the viewpoint O until it touches the vertical picture plane.

However, in this workshop, we will use them in reverse, to plot the oblique anamorphic image R of the same point, by pushing it forward towards the horizontal plane.


Fig. 1. Dürer anamorphosis machine (a mod of a perspective machine)

In this way we will explore the creation of anamorphoses of simple, box-like objects using Dürer machines, made of thread (Fig. 2) as well as virtual machines made of descriptive geometry diagrams (Fig. 3).

In the original workshop plan we were supposed to do the physical machine (Fig. 2) together. Since we are working online, however, this can't be done in 90 minutes. So I will just show you how you can do it later at your own leisure.

Instead, we will do the diagram construction of a cube using a diagram such as the one of Fig. 3, and discuss the properties of the illusions we can obtain in this way. Then I will show you how this can be generalized to work with curvilinear anamorphoses such as those of Fig. 4, and their relation with spherical perspectives and VR panoramas.


Fig. 2. Oblique anamorphosis of a cube using a physical Dürer machine.

Fig. 3. Oblique anamorphosis of a cube using descriptive geometry diagram (student work by Manuel Flores).

We will use these constructions for various purposes:

...or just to have fun constructing amazing illusions that expose the ambiguities of our visual perception:


Fig. 4. Anamorphosis of a cube onto a cylinder.

See you soon!

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António B. Araújo, DceT, Universidade Aberta. Email: Antonio.Araujo@uab.pt

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