E92 -- October 2002 Art, Math, and Sculpture Connecting Computers and Creativity Carlo H. Séquin...
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Transcript of E92 -- October 2002 Art, Math, and Sculpture Connecting Computers and Creativity Carlo H. Séquin...
CHSCHSUCBUCB E92 -- October 2002E92 -- October 2002
Art, Math, and SculptureConnecting Computers and Creativity
Carlo H. Séquin
EECS Computer Science Division
University of California, Berkeley
CHSCHSUCBUCB My Professional PathMy Professional Path
65-70: Basel: Physics – Experiment design
70-76: Bell Labs: CCD – Circuit, chip design
76-82: UCB: RISC – 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
CHSCHSUCBUCB My Professional FocusMy Professional Focus
Computer-Aided Design
Design useful and beautiful objectswith the help of computers.
Develop (interactive) computer programsto make these tasks easier.
CHSCHSUCBUCB Mechanical Parts: “Octa-Gear”Mechanical Parts: “Octa-Gear”
Design (1985) Realization (FDM) (2000)
Octahedral Gear
CHSCHSUCBUCB ““Whirled White Web”Whirled White Web”
Design for the 2003 International Snow Sculpture Championship Breckenridge, CO, Jan.28 – Feb.2
CHSCHSUCBUCB Roots of My Passion for SculptureRoots of My Passion for Sculpture
My love for geometry and abstract sculptureemerged long long before I learned to play with computers.
Thanks to: Alexander Calder, Naum Gabo,Max Bill, M.C. Escher, Frank Smullin, ...
CHSCHSUCBUCB Leonardo -- Special IssueLeonardo -- Special Issue
On Knot-Spanning Surfaces: An Illustrated Essay on Topological ArtWith an Artist’s Statement by Brent Collins
George K. Francis with Brent Collins
CHSCHSUCBUCB Brent Collins: Early SculpturesBrent Collins: Early Sculptures
All photos by Phillip Geller
CHSCHSUCBUCB My Fascination with...My Fascination with...
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”
Brent Collins’ Abstract Geometric Art:
CHSCHSUCBUCB Scherk’s 2nd Minimal SurfaceScherk’s 2nd Minimal Surface
Normal“biped”saddles
Generalization to higher-order saddles(monkey saddle)
CHSCHSUCBUCB ““Hyperbolic Hexagon” by B. CollinsHyperbolic 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 ?
CHSCHSUCBUCB Collins - Séquin CollaborationCollins - 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.
CHSCHSUCBUCB Brent Collins’ Prototyping ProcessBrent Collins’ Prototyping Process
Armature for the "Hyperbolic Heptagon"
Mockup for the "Saddle Trefoil"
Time-consuming ! (1-3 weeks)
CHSCHSUCBUCB Collins’ Fabrication ProcessCollins’ 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 marksand 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 !
CHSCHSUCBUCB Collins’ Fabrication ProcessCollins’ Fabrication Process
Lamination process to make an overall shape that withincontains the final sculpture.
Example: “Vox Solis”
CHSCHSUCBUCB ““Sculpture Generator I”Sculpture Generator I”
Prototyping & Visualization tool forScherk-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.
CHSCHSUCBUCB The Basic ElementThe Basic Element
Scherk’s 2ndminimal surface
3-story tower,trimmed, thickened
180 degreesof twist added
CHSCHSUCBUCB Toroidal Warp into Collins RingToroidal Warp into Collins Ring
8-story tower warped into a ring 360º twist added
CHSCHSUCBUCB A Simple Scherk-Collins ToroidA 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
CHSCHSUCBUCB Also a Scherk-Collins ToroidAlso 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
CHSCHSUCBUCB A Scherk Tower A Scherk Tower (on its side)(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
CHSCHSUCBUCB 1-story Scherk Tower1-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
CHSCHSUCBUCB 180º Arch = Half a Scherk Toroid180º 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
CHSCHSUCBUCB How to Obtain a Real Sculpture ?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.
CHSCHSUCBUCB Slices through “Minimal Trefoil”Slices through “Minimal Trefoil”
50% 10%23%30%
45% 5%20%27%
35% 2%15%25%
CHSCHSUCBUCB Profiled Slice through the SculptureProfiled Slice through the Sculpture
One thick slicethru “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, 3/4of one board.
CHSCHSUCBUCB Heptoroid Heptoroid ( from Sculpture Generator I )( from Sculpture Generator I )
Cross-eye stereo pair
CHSCHSUCBUCB Emergence of the “Heptoroid” (1)Emergence of the “Heptoroid” (1)
Assembly of the precut boards
CHSCHSUCBUCB Emergence of the “Heptoroid” (2)Emergence of the “Heptoroid” (2)
Forming a continuous smooth edge
CHSCHSUCBUCB Emergence of the “Heptoroid” (3)Emergence of the “Heptoroid” (3)
Smoothing the whole surface
CHSCHSUCBUCB Advantages of CAD of SculpturesAdvantages 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
CHSCHSUCBUCB Sculpture Design: “Solar Arch”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
CHSCHSUCBUCB Séquin’s “Minimal Saddle Trefoil”Séquin’s “Minimal Saddle Trefoil”
Stereo-lithography master
CHSCHSUCBUCB Séquin’s “Minimal Saddle Trefoil”Séquin’s “Minimal Saddle Trefoil”
bronze cast, gold plated
CHSCHSUCBUCB
Minimal Trefoils -- cast and Minimal Trefoils -- cast and finished by Steve Reinmuthfinished by Steve Reinmuth
CHSCHSUCBUCB New PossibilitiesNew Possibilities
Developing Parameterized,
Procedurally Generated Sculpture Families
CHSCHSUCBUCB Higher-order Trefoils Higher-order Trefoils (4th order saddles)(4th order saddles)
W=1 W=2
CHSCHSUCBUCB Exploring New IdeasExploring New Ideas
Going around the loop twice ...
… resulting in an interwoven structure.
CHSCHSUCBUCB 9-story Intertwined Double Toroid9-story Intertwined Double Toroid
Bronzeinvestment casting from wax original made on 3D Systems’“Thermojet”
CHSCHSUCBUCB Stepwise Expansion of HorizonStepwise 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
CHSCHSUCBUCB Keeping up with Brent ...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.
CHSCHSUCBUCB SLIDESLIDE
SLIDE = Scene Language for Interactive Dynamic Environments
Developed as a modular rendering pipelinefor our introductory graphics course CS184.
Primary Author: Jordan Smith
Based on OpenGL and Tcl/tk.
Good combination of interactive 3D graphicsand parameterizable procedural constructs.
CHSCHSUCBUCB SLIDE Example: Klein BottleSLIDE Example: Klein Bottle
Final Project CS 184, Nerius Landys & Shad Roundy
CHSCHSUCBUCB SLIDE Example Bug’s LifeSLIDE Example Bug’s Life
Final Project CS 184, David Cheng and James Chow
CHSCHSUCBUCB SLIDE as a Design ToolSLIDE 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”
CHSCHSUCBUCB Capturing the ParadigmCapturing 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.
CHSCHSUCBUCB Sculptures by Naum GaboSculptures by Naum Gabo
Pathway on a sphere:
Edge of surface is like seam of tennis ball;
==> 2-period Gabo curve.
CHSCHSUCBUCB 2-period Gabo curve2-period Gabo curve
Approximation with quartic B-splinewith 8 control points per period,but only 3 DOF are used.
CHSCHSUCBUCB ““Pax Mundi” RevisitedPax Mundi” Revisited
Can be seen as:
Amplitude modulated, 4-period Gabo curve
CHSCHSUCBUCB ““Viae Globi” Family Viae Globi” Family (Roads on a Sphere)(Roads on a Sphere)
L2 L3 L4 L5
CHSCHSUCBUCB Extending the Paradigm (again)Extending the Paradigm (again)
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”
Circle Splines on the SphereCircle Splines on the Sphere
CHSCHSUCBUCB ““Maloja” Maloja”
( FDM part )( FDM part )
A very winding Swiss mountain pass road in the upper Engadin.
CHSCHSUCBUCB ““Lombard”Lombard”
A very famous crooked street in San Francisco
Note that I switched to a flat ribbon.
CHSCHSUCBUCB Who am I ? (1)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 …
CHSCHSUCBUCB Who am I ? (2)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
CHSCHSUCBUCB Sculpture EngineeringSculpture 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
CHSCHSUCBUCB ConclusionsConclusions
Computers are becoming important tools – even in the field of art.
Virtual Prototyping can save time and can tackle sculptures of a complexitythat 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.
CHSCHSUCBUCB Career Advice (1)Career Advice (1)
Find out what you really enjoy doing.
Find a job that pays you to do just that !
CHSCHSUCBUCB Career Advice (2)Career Advice (2)
Acquire solid technical foundations.
Stay flexible; keep learning new things.
Keep your eyes open for new opportunities.