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There seems to be an answer in the article itself at your link, pp. 105-106. As I understand it, first they distill the fragments into an STL model using a 3D scanner. For ceramics they use Rhinoceros 3D software developed by McNeel & Assocciates and for metal objects they use FormZ software developed by AutoDesSys. Then, using the three-point method, the radii and centers of rotation of several horizontal sections are determined. Find the vertical axis of rotation. Then a fragment profile is obtained and rotated around a vertical axis.
How automatic? Judging by the screenshot, the radius of the dishes was set manually (17.6 cm on the top, 9.1 cm on the bottom). Further , a body of revolution is built from the fragment . This can just be done elementarily in AutoCAD, 3d Max and even in free 3d editors.
Those. no hand painting required. It is only necessary to know the radius of the body of revolution.
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