BID Lunch May 13 2014 Pecha Kucha Style

BID Lunch, May 13, 2014 Pecha Kucha Style Presentation: Physically Correct Rendering of Pacioli’s Rhombicuboctahedron Carlo H. Séquin and Raymond Shiau University of California, Berkeley

“Ritratto di Frà Luca Pacioli” (1495) Museo e Gallerie di Capodimonte in Naples, Italy

RCO = Rhombi-cuboctahedron RCO “Leonardo style” u Archimedean solid: 8 triangles, 18 square faces

Praise of the Pacioli RCO u… a masterpiece of reflection, refraction, and perspective. [George Hart] u Its surface reflects a view out an open window, showing the Palazzo Ducale in Urbino. [Margaret Davis]

How Accurate Is the Rendering ? u … do the reflections show that the window is high up towards the left? Or rather towards the bottom right? Both do not really make sense. u … the way the images are formed doesn’t seem very realistic at all. [Joost Rekveld]

Comparison to a Physical Model by Claude Boehringer -- quite different surroundings.

Do a Computer Graphics Rendering! Which of these pictures is correct? There are many parameters to adjust! Difficulties with the glass/water interface.

Matching the Viewing Geometry Front view Side view

Depicting Surface Reflections 0° 170° 146° A line reflected across a non-flat dihedral angle results in a “sheared” discontinuity. Pasted-on rectangular “sticker” is wrong!

Simple Refraction in Water Painting no refraction with refraction Painter did not observe any refraction! (probably did not have a water-filled model)

Multiple Refraction- & Mirror-Events u Limiting M=1 the depth of the ray-trace tree: R=2 M M=1 R=2 M=8 R=8 >3 R

Glass / Water Interface Water half-cube behind glass half-cube view water/gap/glass water/glass (fused)

Water Half-cube behind Tracing ray-bundles Glass Half-cube Properly fused interface

Water Half-cube Ray-bundles behind Glass Half-cube Properly fused interface Ray-bundles

The Complete RCO The various materials and interfaces: Opaque filler (O), Water (W), Glass (G), G/W-interface (I)

Modeling the Whole RCO M=1 R=3

Modeling the Whole RCO R=4 M=1, R=4

Modeling the Whole RCO M=1, R=6 M=R=10 (max) = “ground truth” ?

RCO in Pacioli’s Room Set-up Slightly exaggerated tinting

Final Comparison 1495 Painting 2014 Computer Rendering