CHS UCB E92 -- October 2002 Art, Math, and Sculpture Connecting Computers and Creativity Carlo H.
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CHS UCB
E92 -- October 2002
Art, Math, and Sculpture
Connecting Computers and Creativity Carlo H. Séquin EECS Computer Science Division University of California, Berkeley
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My Professional Path
65-70: Basel: Physics – Experiment design
70-76: Bell Labs: 76-82: UCB: RISC CCD – Circuit, chip design – CPU architecture design
80-??: Graphics – Modeling & Rendering SW
82-90: VLSI CAD – CAD algorithm design
87-94: Soda Hall – Building design, VR
92-98: Architecture – ArchCAD tool design
95-??: Mech. Eng. – Develop SIF, CyberCut
96-??: Sculpture – Virtual Prototyping
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My Professional Focus Computer-Aided Design
Design useful and beautiful objects with the help of computers.
Develop (interactive) computer programs to make these tasks easier.
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CCD Camera, Bell Labs, 1972
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Integrated Circuits: “RISC I”, 1981
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Mathematical Models “Granny Knot” Lattice Berkeley UniGrafix (1982)
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Buildings: Soda Hall, 1992
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Mechanical Parts: “Octa-Gear” Octahedral Gear Design (1985) Realization (FDM) (2000)
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Geometrical Sculpture (virtual) (Since 1995)
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Geometrical Sculpture (real) “Cohesion” 2002
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“Whirled White Web”
Design for the 2003 International Snow Sculpture Championship Breckenridge, CO, Jan.28 – Feb.2
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Roots of My Passion for Sculpture My love for geometry and abstract sculpture emerged long long before I learned to play with computers.
Thanks to: Alexander Calder, Naum Gabo, Max Bill, M.C. Escher, Frank Smullin, ...
CHS UCB Leonardo -- Special Issue
On Knot-Spanning Surfaces: An Illustrated Essay on Topological Art With an Artist’s Statement by Brent Collins
George K. Francis with Brent Collins
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Brent Collins: Early Sculptures
All photos by Phillip Geller
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My Fascination with...
Brent Collins’ Abstract Geometric Art:
Beautiful symmetries Graceful balance of saddle surfaces Superb craftsmanship Intriguing run of the edges What type of knot is formed ?
Mystery: one-sided or two-sided ?
==> Focus on “Chains of Saddles”
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Brent Collins: Stacked Saddles
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Scherk’s 2nd Minimal Surface Normal “biped” saddles Generalization to higher-order saddles (monkey saddle)
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“Hyperbolic Hexagon” by B. Collins
6 saddles in a ring
6 holes passing through symmetry plane at ±45º
“wound up” 6-story Scherk tower
What would happen,
if we added more stories ?
or introduced a twist before closing the ring ?
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Closing the Loop straight or twisted
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Collins Séquin Collaboration
Discuss ideas on the phone
Exchange sketches
Vary the topological parameters
But how do you know whether it is beautiful ? Need visual feedback.
Making models from paper strips is not good enough.
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Brent Collins’ Prototyping Process Armature for the "Hyperbolic Heptagon" Mockup for the "Saddle Trefoil" Time-consuming ! (1-3 weeks)
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Collins’ Fabrication Process Building the final sculpture (2 - 3 months):
Take measurements from mock-up model, transfer parallel contours to 1” boards.
Roughly precut boards, leaving registration marks and contiguous pillars for gluing boards together.
Stack and glue together precut boards, remove auxiliary struts.
Fine-tune overall shape, sand and polish the surface.
A big investment of effort !
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Collins’ Fabrication Process Lamination process to make an overall shape that within contains the final sculpture.
Example: “Vox Solis”
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“Sculpture Generator I” Prototyping & Visualization tool for Scherk-Collins Saddle-Chains.
Slider control for this one shape-family,
Control of about 12 parameters.
Main goal: Speed for interactive editing.
Geometry part is about 5,000 lines of C;
10,000 lines for display & user interface.
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Sculpture Generator, GUI
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The Basic Element
Scherk’s 2nd minimal surface 3-story tower, trimmed, thickened 180 degrees of twist added
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Toroidal Warp into Collins Ring
8-story tower warped into a ring 360º twist added
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Edge Treatment
square, flat cut semi-circular bulging out
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Embellishment of Basic Shape
color texture background
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A Simple Scherk-Collins Toroid
branches = 2 storeys = 1 height = 5.00
flange = 1.00
thickness = 0.10
rim_bulge = 1.00
warp = 360.00
twist = 90 azimuth = 90 textr_tiles = 3 detail = 8
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Also a Scherk-Collins Toroid
branches = 1 storeys = 5 height = 1.00
flange = 1.00
thickness = 0.04
rim_bulge = 1.01
warp = 360 twist = 900 azimuth = 90 textr_tiles = 1 detail = 20
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A Scherk Tower (on its side)
branches = 7 storeys = 3 height = 0.2
flange = 1.00
thickness = 0.04
rim_bulge = 0 warp = 0 twist = 0 azimuth = 0 textr_tiles = 2 detail = 6
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1-story Scherk Tower
branches = 5 storeys = 1 height = 1.35
flange = 1.00
thickness = 0.04
rim_bulge = 0 warp = 58.0
twist = 37.5
azimuth = 0 textr_tiles = 8 detail = 6
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180º Arch = Half a Scherk Toroid
branches = 8 storeys = 1 height = 5 flange = 1.00
thickness = 0.06
rim_bulge = 1.25
warp = 180 twist = 0 azimuth = 0 textr_tiles = e detail = 12
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“Hyperbolic Hexagon II” (wood)
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How to Obtain a Real Sculpture ?
Prepare a set of cross-sectional blue prints at equally spaced height intervals , corresponding to the board thickness that Brent is using for the construction.
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Slices through “Minimal Trefoil” 50% 30% 23% 10% 45% 27% 20% 5% 35% 25% 15% 2%
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Profiled Slice through the Sculpture
One thick slice thru “Heptoroid” from which Brent can cut boards and assemble a rough shape.
Traces represent: top and bottom, as well as cuts at 1/4, 1/2, 3/4 of one board.
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Heptoroid ( from Sculpture Generator I )
Cross-eye stereo pair
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Emergence of the “Heptoroid” (1)
Assembly of the precut boards
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Emergence of the “Heptoroid” (2)
Forming a continuous smooth edge
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Emergence of the “Heptoroid” (3)
Smoothing the whole surface
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“Heptoroid”
Collaboration by Brent Collins & Carlo S équin
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Advantages of CAD of Sculptures
Exploration of a larger domain
Instant visualization of results
Eliminate need for prototyping
Create virtual reality pictures
Making more complex structures
Better optimization of chosen form
More precise implementation
Rapid prototyping of maquettes
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Sculpture Design: “Solar Arch”
branches = 4 storeys = 11 height = 1.55
flange = 1.00
thickness = 0.06
rim_bulge = 1.00
warp = 330.00
twist = 247.50
azimuth = 56.25
mesh_tiles = 0 textr_tiles = 1 detail = 8 bounding box: xmax= 6.01, ymax= 1.14, zmax= 5.55, xmin= -7.93, ymin= -1.14, zmin= -8.41
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Competition in Breckenridge, CO
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We Can Try Again … in L.A.
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FDM Maquette of Solar Arch
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Various “Scherk-Collins” Sculptures
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Fused Deposition Modeling (FDM)
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Galapagos-6 in the Making
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Galapagos-6 (v6)
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Séquin’s “Minimal Saddle Trefoil”
Stereo lithography master
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Séquin’s “Minimal Saddle Trefoil”
bronze cast, gold plated
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Minimal Trefoils -- cast and finished by Steve Reinmuth
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Brent Collins’ Trefoil
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New Possibilities
Developing Parameterized, Procedurally Generated Sculpture Families
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Family of Symmetrical Trefoils
W=2 W=1 B=1 B=2 B=3 B=4
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Higher-order Trefoils (4th order saddles) W=1 W=2
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Exploring New Ideas
Going around the loop twice ...
… resulting in an interwoven structure.
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9-story Intertwined Double Toroid Bronze investment casting from wax original made on 3D Systems’ “Thermojet”
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Stepwise Expansion of Horizon
Playing with many different shapes and
experimenting at the limit of the domain of the sculpture generator,
stimulates new ideas for alternative shapes and generating paradigms.
Swiss Mountains
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Note:
The computer becomes an amplifier / accelerator for the creative process.
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Inspiration: Brent Collins’ “Pax Mundi”
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Keeping up with Brent ...
A warped “Scherk tower” is not able to describe a shape like “Pax Mundi.”
Need a broader paradigm !
Use the SLIDE modeling environment (developed at U.C. Berkeley by J. Smith); it provides a nice combination of procedural modeling and interactivity.
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SLIDE
SLIDE = Scene Language for Interactive Dynamic Environments Developed as a modular rendering pipeline for our introductory graphics course CS184.
Primary Author: Jordan Smith
Based on OpenGL and Tcl/tk.
Good combination of interactive 3D graphics and parameterizable procedural constructs.
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SLIDE Example: Klein Bottle Final Project CS 184, Nerius Landys & Shad Roundy
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SLIDE Example Bug’s Life Final Project CS 184, David Cheng and James Chow
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SLIDE as a Design Tool
SLIDE has been enhanced to serve as a procedural modeling (CAD) tool.
Recently added:
Spline curves and surfaces
Morphing sweeps along such curves
3D warping module (Sederberg, Rockwood)
Many types of subdivision surfaces
These are key elements for “Sculpture Generator II”
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Capturing the Paradigm The first task when trying to construct a generator for a new family of sculptures is to understand and define its underlying logic.
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Sculptures by Naum Gabo Pathway on a sphere: Edge of surface is like seam of tennis ball; ==> 2-period Gabo curve.
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2-period Gabo curve
Approximation with quartic B-spline with 8 control points per period, but only 3 DOF are used.
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4-period Gabo curve Same construction as for as for 2-period curve
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“Pax Mundi” Revisited
Can be seen as: Amplitude modulated, 4-period Gabo curve
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SLIDE UI for “Pax Mundi” Shapes
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“Viae Globi” Family (Roads on a Sphere) L2 L3 L4 L5
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Via Globi 3 (Stone) Wilmin Martono
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Via Globi 5 (Wood) Wilmin Martono
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Extending the Paradigm (again) Circle Splines on the Sphere Examples from Jane Yen’s Editor Program.
This is a special purpose CAD program to draw nice loopy curves onto a sphere.
“Roads on a Sphere” or “Viae Globi”
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“Maloja” ( FDM part )
A very winding Swiss mountain pass road in the upper Engadin.
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“Stelvio”
An even more convoluted alpine pass in Italy.
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“Altamont”
Celebrating American multi-lane highways.
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“Lombard”
A very famous crooked street in San Francisco
Note that I switched to a flat ribbon.
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Who am I ? (1) Am I an Artist ?
What is “ ART ” these days ??
Cute ideas
Emotional outpours
The obsession to be novel
The goal to shock and offend
A medium for political statements …
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Who am I ? (2) I am a Designer -- and an Engineer !
( and proud of it. ) In design tasks you have:
Specified goals
Ways to evaluate a design
The drive to optimize your design
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Sculpture Engineering The “Whirled White Web” is the result of such an activity.
It had to be based on a shared design with B. Collins Complexity comparable to other successful designs or, preferably, slightly higher Must be executable in snow and ice Should look dramatic, intriguing, pleasing …
Lots of engineering work ahead:
Design plan of attack, using CAD and graphics Prepare stencils to make implementation easier
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Conclusions
Computers are becoming important tools – even in the field of art.
Virtual Prototyping can save time and can tackle sculptures of a complexity that manual techniques could not conquer.
The computer is not only a great visualization and prototyping tool, it also is a generator for new ideas and an amplifier for an artist’s inspiration.
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Career Advice (1)
Find out what you really enjoy doing.
Find a job that pays you to do just that !
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Career Advice (2)
Acquire solid technical foundations.
Stay flexible; keep learning new things.
Keep your eyes open for new opportunities.
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Questions ?
THE END