BID Lunch, May 13, 2014BID Lunch, May 13, 2014
Pecha Kucha Style Presentation:Pecha Kucha Style Presentation:
Carlo H. Séquin and Raymond Shiau
University of California, Berkeley
Physically Correct Rendering of Pacioli’s Rhombicuboctahedron
““Ritratto di Frà Luca PacioliRitratto di Frà Luca Pacioli”” (1495) (1495)
Museo e Gallerie di Capodimonte in Naples, Italy
RCO = Rhombi-cuboctahedronRCO = Rhombi-cuboctahedron
Archimedean solid: 8 triangles, 18 square faces
RCO “Leonardo style”
Praise of the Pacioli RCOPraise 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]
How Accurate Is the Rendering ?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]
Comparison to a Physical ModelComparison to a Physical Model
Model by Claude Boehringer
-- quite different surroundings.
Do a Computer Graphics Rendering!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 GeometryMatching the Viewing Geometry
Front view Side view
Depicting Surface ReflectionsDepicting 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 WaterSimple 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-EventsMultiple Refraction- & Mirror-Events Limiting the depth of the ray-trace tree:
M=1 R=2
M=1 M=8R=2 R=8
M
>3R
Glass / Water InterfaceGlass / Water Interface
Water half-cube behind glass half-cube
water/gap/glass water/glass (fused)
view
Water Half-cube Water Half-cube behind behind Glass Half-cubeGlass Half-cube
Tracing ray-bundles Properly fused interface
Water Half-cube Water Half-cube behind behind Glass Half-cubeGlass Half-cube
Ray-bundles Properly fused interface Ray-bundles
The Complete RCOThe Complete RCO
The various materials and interfaces:Opaque filler (O), Water (W), Glass (G), G/W-interface (I)
Modeling the Whole RCOModeling the Whole RCO
M=1 R=3
Modeling the Whole RCOModeling the Whole RCO
R=4 M=1, R=4
Modeling the Whole RCOModeling the Whole RCO
M=1, R=6 M=R=10 (max)
= “ground truth” ?
RCO in Pacioli’s RoomRCO in Pacioli’s Room
Slightly exaggerated tinting
Set-up
Final ComparisonFinal Comparison
1495 Painting 2014 Computer Rendering
