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A plane transformation process is included in AutoCAD Release 12. This process permits a user to do single-photo photogrammetry, that is, to obtain measurements of a flat surface from a photograph of that surface. One must survey the locations of at least four points that are on the surface in question and visible in the photograph; with that information one may determine the location of any other point on the surface. The procedures will work only on a flat surface; all points - the surveyed points as well as the new points to be measured - must lie on that surface.
This process is sometimes referred to as photo rectification, and it was tested in Pompeii in June. Not only did the process work well, it permitted a great deal of information to be retrieved from photographs - both on site or after the staff had returned to the U.S.
The basic principle is that each undistorted representation of a flat surface, whether head-on or oblique, isometric or perspective, follows a set of mathematical principles. Therefore, a formula can be derived to translate the position of a point on a surface in a photograph into a position on that surface in three-dimensional space, as if one had measured its position with a tape. The math required is not particularly difficult or arcane, and it is also a straight-forward process to determine the formulae to apply. One need only have surveyed the positions of four points on the surface that can be identified in the photograph. (Widely spaced points make the math work better, and more than four may be used.) After the photo is placed on a digitizing tablet and the surveyed points have been located, the program can relate the surveyed coordinates of the points to their positions on the tablet. Those relationships allow the program to determine the angle and type of view as well as the formulae required to convert positions in the photograph into absolute positions on the surface in question.
To accomplish our purposes at Pompeii, we photographed each of the walls of the Sanctuary of the Genius of Augustus. Because the space was rather tight, a wide-angle lens was used, and the long walls were divided in half, two photos each. Four points on the wall in each photograph were surveyed. Initially, we surveyed points which we thought we could identify in the photos by describing them carefully (e.g., the upper right corner of the brick at the far left of the first course . . .). We quickly realized that a better system would involve putting markers in the photos; so white arrow-shaped tabs were taped on the walls before the later photos were taken, and the corners to which they pointed were surveyed.
The film was developed and enlargements were made in Pompeii (one roll of film only), and one photo was used to be sure the system was working properly. It was, but the time required and equipment taken to the site were such that further use of the system awaited our return to the U.S. The remaining rolls of film were developed and appropriate enlargements made.
For each enlargement to be used, the surveyed points were determined, and those surveyed points were added to the model (as icons - AutoCAD blocks - with labels for identification) before the photograph was put to use. The photo was then taped on the digitizing tablet, the known points on the photograph were selected, and their locations were entered (from the keyboard); then the surface to be surveyed could be oriented by AutoCAD. Once the relationship of photo to model had been determined, any marks, blocks, cracks, or holes could be traced as lines, polygons, or surface boundaries directly into the model. (We found that the relatively coarse cross-hairs on the portable digitizer taken to Pompeii made the selection of points somewhat difficult, especially compared to the selections made at CSA's office with very fine cross-hairs and a magnifying glass mounted on our lamp.)
Results of the first work on the sanctuary may be seen in figures. 1 and 2. The drawing in figure 2 is a three-dimensional (orthogonal, not perspective) view of the area shown in figure 1; the angle is different, however, looking down on the area rather than up to it. The area shown was modeled with survey points, measured points, and points determined with photogrammetry.
Astute readers will note that there are three roughly parallel planes on the wall - the back plane of the recesses, the intermediate plane of the piers, and the front plane of the pilasters. Each had to be dealt with separately in the photogrammetric process. Four points had to be located on each surface, and the photograph had to be re-oriented for each surface. Information about each surface was added to the model independently, with the result being a complex three-dimensional model of the whole wall.
The drawing in figure 2 is just one drawing from the model of the building. Any number of different three-dimensional views could be generated by AutoCAD, and the views could include any other portions of the building.
The photogrammetric process made it possible to add considerable detail to the model with relative ease, and the work could be done conveniently, well after we returned to the U.S. It is an important tool to add to others for surveying and is especially valuable when dealing with details such as cracks, surface changes or patterns, plaster areas, and the like.
For other Newsletter articles concerning the applications of CAD modelling in archaeology and architectural history or Pompeii, consult the Subject index.
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Table of Contents for the November, 1994 issue of the CSA Newsletter (Vol. 7, no. 3)
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