Reproduction of a relief perspective model by Ludwig Burmester

Can you believe your eyes? In view of Ludwig Burmester's arched hall, this question arises involuntarily. At first glance, you think you are looking at a model of small-scale architecture on a rectangular floor plan. Only up close and from the side do you realize that it is a strangely distorted object, a so-called relief perspective.

Since the Renaissance, architectural elements and other objects have been depicted with distorted perspectives in reliefs. The relief is so artfully constructed towards a point of view that the objects appear undistorted when viewed from that point of view. This impression is partly due to the fact that we interpret the true shape of the objects in the relief based on our visual experience. Users of the relief perspective are sculptors and set designers. In 1883, Ludwig Burmester wrote the text "Grundzüge der Reliefperpective nebst Anwendungen zur Herstellung reliefperspectivischer Modelle" (Principles of relief perspective and applications for the production of relief perspective models) specifically for teaching at art academies and arts and crafts schools in order to familiarize them with the geometric principles of relief perspective. Burmester was the first Chair of Geometry at the TUD Dresden University of Technology, which at the time was still called the Royal Saxon Polytechnic.

With drawings and detailed descriptions, Burmester explains all the tricks of the trade that can be used to create relief perspective models from plaster. Supplementary photos show a model with basic bodies, as well as the arched hall shown here and another model depicting the interior of a basilica in relief. Unfortunately, none of the models have survived in Dresden. Like the rest of the historical collection of mathematical models, they were presumably destroyed during the bombing in February 1945. However, individual specimens still exist at the TU Vienna.

Today, the Institute of Geometry at TU Dresden once again houses a considerable collection of mathematical models. The desire to present Burmester's models in their original location led to considerations as to how the models could be reconstructed. Traditional model making was ruled out for financial reasons and due to a lack of capacity. In addition, Burmester's warnings, himself a trained precision mechanic, should be taken seriously: "Only the initiated can appreciate the manifold difficulties that arose during the practical production of the two relief models of the hall and the basilica described here; and overcoming these difficulties requires skill and patience of the highest order." Instead of taking on the challenge of craftsmanship, the author constructed the arched hall in the virtual space of the computer.

The perspective distortion is performed by an algorithm specially developed for this purpose. A rapid prototyping system, a so-called 3D printer, which is available at the Institute of Geometry, is then used for the actual model construction. The 3D printer interprets the 3D data and prints an aqueous binder layer by layer into a constantly refilled bed of fine plaster powder until the model is finished. The photo shows the arched hall during recovery from the 3D printer. Finally, the model is infiltrated with epoxy resin to make it durable. Because the 3D printer only has a build space of 20 x 25 x 20 cm, the arched hall was scaled to 80% of the original size. The model stands on a base whose inclined surface corresponds to the relief perspective image of a horizontal plane. A copy of the model is now part of the Office for Academic Heritage, Scientific and Art Collections' permanent exhibition.

Dr. Daniel Lordick
Institute of Geometry
TU Dresden

Further information:

• Collection of mathematical models of the TU Dresden
• 3D Laboratory at the Institute of Geometry (3D printer)

You can also download this article as a pdf document.