Carlo H. Séquin and Raymond Shiau

EECS Department, University of California, Berkeley

Technical Report No. UCB/EECS-2015-169

June 24, 2015

http://www2.eecs.berkeley.edu/Pubs/TechRpts/2015/EECS-2015-169.pdf

The depiction of the glass rhombicuboctahedron (RCO) appearing in a famous painting of Pacioli (1495) is analyzed as to how much it might agree with a physically correct rendering of a corresponding glass container half-filled with water. This investigation shows that it is unlikely that the painter of the RCO was looking at such a physical object. The question is then raised what a proper rendering of such an object might look like. Detailed computer renderings are presented that take into account multiple internal and external reflections and refractions. A warning is issued to non-experts in the use of computer graphics tools, showing that one cannot simply plug in the geometry of the RCO into a readily accessible rendering program and expect to obtain photo-realistic results. Care must be taken to model properly the interfaces where water is in contact with the glass container; the inappropriate handling of total internal reflections will give erroneous results. Detailed rendering studies on simpler glass and water geometries are recommended to assure that the resulting renderings do not deviate too much from physical reality. Nevertheless, the painter of the RCO has clearly succeeded in providing a rendering that appears very plausible to almost all observers.

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BibTeX citation:

@techreport{Séquin:EECS-2015-169,
    Author= {Séquin, Carlo H. and Shiau, Raymond},
    Title= {Rendering Issues in Pacioli’s Rhombicuboctahedron},
    Year= {2015},
    Month= {Jun},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2015/EECS-2015-169.html},
    Number= {UCB/EECS-2015-169},
    Abstract= {The depiction of the glass rhombicuboctahedron (RCO) appearing in a famous painting of Pacioli (1495) is analyzed as to how much it might agree with a physically correct rendering of a corresponding glass container half-filled with water. This investigation shows that it is unlikely that the painter of the RCO was looking at such a physical object. The question is then raised what a proper rendering of such an object might look like. Detailed computer renderings are presented that take into account multiple internal and external reflections and refractions. A warning is issued to non-experts in the use of computer graphics tools, showing that one cannot simply plug in the geometry of the RCO into a readily accessible rendering program and expect to obtain photo-realistic results. Care must be taken to model properly the interfaces where water is in contact with the glass container; the inappropriate handling of total internal reflections will give erroneous results. Detailed rendering studies on simpler glass and water geometries are recommended to assure that the resulting renderings do not deviate too much from physical reality. Nevertheless, the painter of the RCO has clearly succeeded in providing a rendering that appears very plausible to almost all observers.},
}

EndNote citation:

%0 Report
%A Séquin, Carlo H. 
%A Shiau, Raymond 
%T Rendering Issues in Pacioli’s Rhombicuboctahedron
%I EECS Department, University of California, Berkeley
%D 2015
%8 June 24
%@ UCB/EECS-2015-169
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2015/EECS-2015-169.html
%F Séquin:EECS-2015-169