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

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

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

4. 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]

5. 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]

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

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

8. Matching the Viewing Geometry Front view Side view

9. 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!

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

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

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

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

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

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

16. Modeling the Whole RCO M=1 R=3

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

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

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

20. Final Comparison 1495 Painting 2014 Computer Rendering