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Physically Correct Rendering of Pacioli's Rhombicuboctahedron

Explore the accuracy of rendering techniques in depicting Pacioli's Rhombicuboctahedron through PechaKucha style presentation.

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Physically Correct Rendering of Pacioli's Rhombicuboctahedron

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

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

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

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

  5. How Accurate Is the Rendering ? • … 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. • … 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 M=1 R=2 M • Limiting the depth of the ray-trace tree: M=1 M=8R=2 R=8 >3R

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

  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

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