The following sub-sections give an idea of the steps performed to carry out the project, and briefly present the results.

Step 1: the acquisition of the point clouds

Fig.3 shows the point clouds acquired in correspondence with the head of the statue. Following the requirement of the archaeologist staff, the digitizer has been configured to acquire at the highest resolution, even at the expense of a considerable number of views and of an increased complexity of the alignment process. In the figure, 41 views are shown after the alignment (performed in means of the PolyWorks IM_Align module). Each one is characterised by a lateral resolution of 0.2mm, and a height resolution from 0.1mm to 0.3mm, depending on the quality of the measurement. The measurement error spans from 0.050mm to 0.2mm: this variability mainly depends on the colour of the surface and on the presence of numerous undercuts, holes, and shadow regions.

The body of the statue has been acquired at lower resolutions, depending on the different body segments. Special care has been taken to avoid misalignment between the views, especially considering that the registration process was very complex, due to the high number of point clouds (more than 500) needed to fully digitise the statue. The measurement was performed in two steps: in the former, the skeleton was acquired (few, large views at low resolution, along suitable paths around the statue), to minimise the alignment error. In the latter, a high number of small views was captured and aligned to the skeleton. At the end of the process, the skeleton was eliminated.

Step2: the creation of the triangle models

The IM_Merge module of Polyworks has been used to generate the polygon model from the measured data. Preliminarily, proper filtering, decimation and fusion of the partial views were carried out. Models characterised by different levels of adherence to the original point cloud have been created. Fig. 4 shows that one at the highest accuracy that has been used by the archaeologists to perform the measurements between the pairs of fiduciary points. The measurement is very easy: the operator only selects on the display the two triangles representative of the fiduciary points and the software automatically evaluates and displays the corresponding distance. The measurement is very precise, due to (i) the high quality of the original data, (ii) the availability of the colour information acquired with the range data, and (iii) the density of the triangles within each single marker, as highlighted in the zoom of the figure. The results of this study have been recently published (see the References list to know more).
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Step 3: the editing of the triangle models

The Polyworks IM_Edit module was very useful for the editing of the triangle models. The objective was to eliminate holes, and in general all the topological irregularities deriving from the invalid measured data. As an example, Fig. 5 shows the appearance of the high-resolution triangle model of the head before and after the editing operation. It is easy to note how all the holes disappeared, resulting in a very appealing rendering of the surface. This model, when the colour information is added, as in Fig. 6, is suited also for applications different with respect to the original, metrological one. These are, for example, the virtual musealization of the statue, and the creation of a topologically closed STL model, that allows us the creation of the copy of the statue.

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Step 4: the creation of scaled reproductions of the statue

This step has resulted in the achievement of a number of copies of the ‘Vittoria Alata’. In Fig. 7 the 1:8 scaled copy of the head of the statue is shown . The work has been accomplished in the framework of the collaboration between our Laboratory and the Laboratory of Fast Prototyping of the University of Udine. A rapid prototyping machine has been used to produce the model, by means of the stereolithography technique. The CIBATOOL SL 5190 has been used as the material. The overall dimension of the prototype is 140mm x 110mm x 133mm. The memory occupation of the original STL file was 10MB: it has been sent via the Internet to the Laboratory located in Udine. The time required to obtain the copy was 0.20 hours for the elaboration of the data, plus 15 hours for the prototypisation.

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A suite of copies of the whole statue has been obtained in the framework of the collaboration between the Direzione Civici Musei di Arte e Storia of Brescia and the EOS Electro Optical Systems GmbH, located in Munich, Germany. The work led to the development of two 1:1 scaled copies of the statue have been produced. For them, the Laboratory has provided the high resolution STL file shown in Fig. 8 (16 millions of triangles).  The model was segmented into sub-parts, that were separately prototyped. Figure 9 shows the copy of the statue that is currently placed in the hall of EOS gmbh, Robert-Stirling-Ring 1, 82152 Krailling Munchen DE.

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Further experimentation dealing with the generation of the mathematics of the surfaces has been carried out. Obviously, we did not want to ‘redesign’ the shape of the statue: instead, the objective was to verify the feasibility of the generation of the CAD model of the surfaces, in view of its use mainly in two applications. The former is the reconstruction of lost parts (for example, the fingers of the hands), the latter is the virtual modification of the relative position of sub-parts of the body. For example, this is the case of the position of the head of the statue, which seems excessively inclined with respect to the bust.Step 5: the creation of the CAD models

The feasibility study has been performed on the head. The Raindrop Geomagic Studio 3.1 has been used. The triangle models of these two body segments have been imported as STL files from the PolyWorks Suite. The Geomagic environment elaborated them and generated the CAD model in three steps. The first one allowed the determination of the patch layout (in a fully automatic way); the second one automatically identified a proper number of control points within each patch, the third one fitted the NURBS surfaces to the control points. Fig. 10 shows the process in the case of the head of the statue. It is worth noting the regularity of the surfaces at the borders of each patch (Fig. 10.a), the complexity of the CAD model (Fig. 10.b) and the adherence of the mathematics to the triangle model (Fig. 10.c).

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