Recent technological advances have provided scholars with a host of methods to accurately record volume, surface detail and even color of artifacts and architecture [36]. A series of technology-based grants allowed for a succession of experiments over the years to develop a methodology that addresses the challenge presented by the damaged and fragmentary condition of the ruins [37]. At the time, the intent was not to provide a test of field methods—in effect, Davis [36] provides an extensive review of the costs and potentials of these developing recording technologies and their use in archaeology and heritage management—but rather to find a manner in which the confusion of carved blocks could be recorded and reassembled. For this purpose, not withstanding, we found that laser scanning or photographic digital recording, while producing accurate renderings, required a high degree of work both in the field and in the manual processing back in the lab. In the field, several different perspectives were necessary to capture all sides of an object. In the case of photogrammetry, the photographer walking around the object while taking multiple pictures could achieve this (Fig. 9). In the case of laser scanning, the process was somewhat more laborious since the station would have to be broken down, moved to a new location, and set. Thereafter, the different digital images and laser scans of the object would be stitched together in order to form a complete object, and then checked for holes or shadows in the data (areas not visible to the camera or laser scanner). If the holes or shadows were large, an additional field visit would be necessary. Outlying and unnecessary data points, sometimes called ‘noise’, such as the surrounding terrain and vegetation, needed to be removed. Except under ideal conditions, some degree of manual measurements in the field would still be necessary or at least advisable in order to determine corners and edges that were hidden or buried.

Fig. 9 Location and number of photographs taken for photogrametic reconstruction of a notable carved ashlar known as the “Maqueta” stone Full size image

Figure 9 is an example of a photogrammetry test case in near-ideal circumstances. This ashlar, known as the “Maqueta stone” appears to be an elaborate representation of a temple. The conditions for recording were ideal since there was little vegetation or any other obstructions. The total field recording and processing time was estimated to be 4 h. The results, printed on a biodegradable corn-based polyester, known as PLA (polyactic acid), suffered from various ailments, including holes or fragile areas due to the low resolution of the digital image and extraneous data that made the edges appear fuzzy or wavy (Fig. 10). In order for a 3D print to be successful, the model to be printed must be watertight—that is, the surface of the model must not contain any holes (see below).

Fig. 10 The “Maqueta” stone 3D printed based on the photogramic model Full size image

The hope that these virtual models generated from the laser scans and photogrammetry would be useful as an online archive for the site managers remains, at least at the present moment, unfulfilled since they proved to be too large to download and manipulate with the stakeholders in the rural countryside with limited Internet and computer software and hardware. To the disappointment of the stakeholders, the results were not readily available or comprehensible, and the cost of purchasing and maintaining their own equipment was prohibitive, as was the need for regular input from technicians to specialists who charge dear from their services. Consequently, the extensive laser scans of the ruins and specific sculptures is online and free to download and view but remain an unused resource for the site managers.

Essentially, these methods over-recorded the objects and, for this project, provided unneeded detailed information on surface textures and damage caused by erosion and vandalism. Depending on the number of perspectives necessary to capture the entire object, then, the final file size could be prohibitively large. (The size of the file becomes problematic not because of storage space, but because of the amount of memory required on a computer to work with such a large file). On a practical front, the equipment was expensive, required professional upkeep and a trained operator to record and process the data. Frequently, the equipment was held up in customs for interminable lengths of time; similar equipment was difficult to find in the country and, when it was, the accuracy and usability of the equipment was in serious question. The use of such specialized hardware and software was simply not sustainable in a rural environment of the high Andes, where the harsh climate could easily damage equipment. In these environmental and bureaucratic situations, breakages and technical issues, even when the fix could be relatively easy in the proper circumstances, often meant that the equipment was essentially unusable.

Fieldwork, archives and 3D modeling

For the purpose of reconstruction, we were primarily interested in the underlying geometry—not the niceties of the damaged and unfinished surfaces. The requisite amount of field data was potentially very small—the lengths of the sides of the blocks and any carved ornamentation. For example, a block could potentially require just three measurements (height, length, and width) in order to accurately model its form. Since these blocks are surprisingly geometric with planar surfaces and precise edges, the original dimensions of the sides of a block with damaged edges could be easily reconstructed using two rulers to project the surviving edges to their original meeting point (Fig. 11). In sum, acquiring the necessary information in the field to model a block could potentially be obtained in minutes.

Fig. 11 Projecting the intact edges to reconstruct the location of the missing corner Full size image

With the increased prominence and ease of use of 3D printing in the sciences and heritage management [38] and in museum exhibitions designed to engage the senses of the visitor through direct contact with accurate reproductions [39, 40], the idea of reconstructing the shattered blocks took on a new life.Footnote 2 Though the sandstone and andesite blocks have been measured on several occasions, in only a few cases was this done with a level of accuracy suitable for the virtual modeling and 3D printing technologies in this research. Consumer 3D printers have a resolution, or margin of error, ranging from 0.025 mm up to 0.3 mm depending on the type of 3D printer. This high degree of accuracy in turn necessitates a high degree of accuracy in the models to be printed. Necessary were the original field notes with the detailed measurements not included in their final publications (see Figs. 2, 12). Archival research was necessary to locate the original field notes in various museums around the world. The majority of the ashlars were modeled from the field notes of JP Protzen, who conducted his fieldwork over a number of visits in the early and mid-1990s. The field notes from Leonce Angrand (1848) and Max Uhle (1893) preserved the measurements of several blocks that had been lost in the last century. Additional ashlars that have recently surfaced were recorded using the method demonstrated by JP Protzen to members of this project.

Fig. 12 Process of creation 3D models: (1) Original field notes; (2) 3D virtual Sketchup model; (3) Translation into .stl format and checking that the model is “watertight”; (4) Printing in powder based bed: (5) Removing extra powder; (6) Applying Cyanoacrylates solution; (7) Final model Full size image

The use of 3D modeling is nearly commonplace in archaeology, and has the potential to explore phenomenological aspects of a site as 2D plans are extruded and walls and roofs are replaced, given texture, color and even inhabited by avatars [41]. The program AutoCAD, the choice of architects, and an entire suite of rendering programs that allow for realistic textures and forms, is an obvious candidate for the software. In the right hands, AutoCAD is a powerful program with the capacity to accurately model small objects to complex buildings. The downside is that the program can be expensive and has a significant learning curve, especially since many of its functions have to be adapted to the particulars of archaeology [42]. Nevertheless, this program had been previously used to good effect recording and visualizing the results of the excavation of the platform of the Pumapunku [18, 43] and even create renderings for phenomenological analysis [44].

However, this type of virtual modeling is best when it comes to extruding a 2D plan, or a site that has been nearly reduced to its foundations. In this case we were not extruding a ground plan and rendering hypothetical architecture in a realistic manner, but modeling disassociated architectural fragments. Accordingly, this project used the more intuitive and inexpensive (free to 700USD for the full package) 3D modeling software Sketchup. Though originally designed to quickly visualize 3D forms for the purpose of initial conceptualizations of form and volumes, the program does allow for accurate measurements to be entered by mouse and hand. With an hour of training, project members were able to model the more basic fragments; thereafter, the speed of modeling, and the ability to model more complex pieces, rapidly increased.

Recreating every crack and damaged edge proved to be time-consuming and did not contribute to the goal of reconstructing the intended form of the building. Where the evidence of the original form was unequivocal, damaged surfaces and edges were virtually restored to form geometric shapes. In a few cases, virtual and 3D printing anastylosis was performed; as previously mentioned, the fragmented remains of several gateways, scattered around the platform, have been refitted on several different occasions [22, 34]. Each piece was modeled, then virtually joined with the other fragments to form a single solid form. Another aspect of the blocks we judiciously choose to virtually modify were clearly unfinished aspects. For example, several of the H blocks seen in Fig. 6 had aspects that were clearly in process of being reduced. Complete examples clearly demonstrated the appearance and form of each side.

In total, 140 pieces of andesite and 17 slabs of sandstone were modeled. The time it would take for a simple unadorned block would be a short as a few minutes; the gateways, the largest, and most complex architectural pieces of this time period require additional time. For example, the gateway in Fig. 12, originally in five pieces, required approximately 5 h of modeling to restore its virtual form.

Figure 13 is a virtual reconstruction of the appearance of this area of the Pumapunku during the latter half of the nineteenth century, based on in situ authentic remains, Max Uhle’s 1893 field notes and photographs,Footnote 3 and Leonce Angrand’s 1848 series of drawings [13]. In the last century, several of the blocks were moved around, but most significantly during an unfortunate reconstruction project in 2006. Though by the mid-19th century none of the standing architecture was in place, the effort was made to virtually relocate the ashlars in their earliest known location and position since it may approximate their original place. The Additional file 1 contains the files in sketchup format (.skp) and .stl of the andsite blocks of the Pumapunku, those found in other locations of the site, and the sandstone slabs.