The reconstruction of the Merz Building was based on the stereometric analysis
of three wide-angle shots dating from 1932.
The axes of the three photographs are positioned at an angle of between
80 and 100 degrees; certain elements of the pictures are found in two out
of three shots, and one (single) corner appears in all three. This was enough
to provide the basis for a three-dimensional reconstruction.
There were various practical difficulties: both the optical capability
and the standpoint of each camera was unknown, and so was the size of the
room. The room itself is incidentally only faintly discernible in two places
in the photos, since the Merz Building grew rampantly into the middle of the
room. After receiving various kinds of misleading information (for instance
a sheet showing a house plan, dating from the war years and indicating emergency
accommodation), the plan of an apartment was found which was identified by
the artist’s son, Ernst Schwitters, as a hand-sketch made by his grandfather.
When his grandfather had measured out the room, it was still empty; thus we
finally discovered its exact size.
The optical conditions of the photographs (shifts in the subject’s position,
the tilt of planes of both image and lens) proved extraordinarily complex;
however, the main difficulty was to determine the aperture of the lens.
The solution was provided by the stereometric registration of a particular
object that appears in two of the three photographs, namely the ‘planing bench’
(all the different parts of the Merz Building have been named, some by Schwitters,
others by me). Moreover, the cameras ‘see one another simultaneously’, which
means each camera’s standpoint can be analogously defined as a point within
the other two pictures.
These two facts suggest the following principle of action: If the perspective
lines of the edges of the planing bench are drawn as geometric projections
from the points in the pictures while taking all possible manipulations into
account (focus, camera tilt, tilt of planes, etc.), at the right aperture
they appear vertically aligned.
(Got that? . . .)
Only after these mental steps, and only at this point, did I take up on
my iterative path (that is in my infinite approach to a sought-after figure)
the aid of a programmable pocket calculator (model HP 41), to give a mathematical
and therefore more precise rendition of the solution in my drawing.
The figure I arrived at gave me an aperture of 14.08 cm. An unbelievable
size! But further research at the ETH in Zurich, in old catalogues of the
Institute of Photography, proved the existence of a Zeiss lens called ‘Protar’,
in use since 1892 and a favourite of professional photographers, which had
a maximum aperture of 14.1 cm.
Eureka ! !
Now all that was needed was the ‘fine-tuning’. After months of pushing,
tilting, lifting and calculating, the approximation to the camera standpoints
became so close that each individual spot in the photographs could be retrospectively
projected, plotted, measured and, since it was defined by more than one source,
back-checked. ...
Peter Bissegger, 1988