microsoft mosaic microsymposium 2000 analysis and synthesis of intuitively conceived geometrical art...
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UCBUCB Microsoft MOSAIC Microsymposium 2000Microsoft MOSAIC Microsymposium 2000
Analysis and Synthesis of Intuitively Conceived Geometrical Art
Carlo H. Séquin
University of California, Berkeley
Brent Collins
Gower, Missouri
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UCBUCB Roots of My PassionRoots of My Passion
My love for geometry and abstract sculptureemerged long long before I learned to play with computers.
Acknowledgement to the artists who have strongly influenced me ...
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Appreciation of Simple Appreciation of Simple Geometric Forms (`50s, `60s )Geometric Forms (`50s, `60s )
Alexander Calder,
Naum Gabo,
Max Bill:
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UCBUCB Intro to Computer Graphics (`70s)Intro to Computer Graphics (`70s)
Ken Knowlton, Lillian Schwarz (at Bell Labs)
Frank Smullin (at D.A.Conference):
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UCBUCB Complex Compositions (‘80s)Complex Compositions (‘80s)
M. C. Escher,
Bruce Beasly,
George Rickey,
Alan Holden:
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UCBUCB Recent Interactions (`90s)Recent Interactions (`90s)
Charles Perry,
Helaman Ferguson,
Robert Longhurst:
• Brent Collins: Collaboration since 1995
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UCBUCB Leonardo FoilLeonardo Foil
On Knot-Spanning Surfaces: An Illustrated Essay on Topological ArtWith an Artist’s Statement by Brent Collins
George K. Francis with Brent Collins
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UCBUCB Early Brent Collins SculpturesEarly Brent Collins Sculptures
All photos by Phillip Geller
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UCBUCB ==> BRENT COLLINS’ Presentation==> BRENT COLLINS’ Presentation
Early work with saddles ...
through “Hyperbolic Hexagon”
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UCBUCB My Fascination with...My Fascination with...
Brent Collins’ Abstract Geometric Art Beautiful symmetries Graceful balance of the 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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UCBUCB Scherk’s 2nd Minimal SurfaceScherk’s 2nd Minimal Surface
Normal“biped”saddles
Generalization to higher-order saddles(monkey saddle)
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UCBUCB ““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 ?
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UCBUCB 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.
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UCBUCB Brent Collins’ Prototyping ProcessBrent Collins’ Prototyping Process
Armature for the "Hyperbolic Heptagon"
Mockup for the "Saddle Trefoil"
Time-consuming ! (1-3 weeks)
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UCBUCB 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 !
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UCBUCB Collins’ Fabrication ProcessCollins’ Fabrication Process
Lamination process to make an overall shape that withincontains the final sculpture.
Example: “Vox Solis”
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UCBUCB ““Sculpture Generator I”Sculpture Generator I”
Prototyping 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.
==> VIDEO
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UCBUCB Base Geometry: One Scherk StoryBase Geometry: One Scherk Story
Hyperbolic Slices ==> Triangle Strips
precomputed -- then warped into toroid
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UCBUCB Slices through the SculptureSlices through the Sculpture
One thick slicethru “Heptoroid”from which Brent can cut boards and assemble a rough shape.
Shown are top andbottom as well ascuts at 1/4, 1/2, 3/4of one board.
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UCBUCB Our First “Joint” SculptureOur First “Joint” Sculpture
Six monkey saddles in a ring with no twist
(like Hyperbolic Hexagon)
azimuth = –30°, flange 1.5
(aesthetics)
size, thickness (fabrication consideration)
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UCBUCB Heptoroid Heptoroid ( from Sculpture Generator I )( from Sculpture Generator I )
Cross-eye stereo pair
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UCBUCB Emergence of the “Heptoroid” (1)Emergence of the “Heptoroid” (1)
Assembly of the precut boards
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UCBUCB Emergence of the “Heptoroid” (2)Emergence of the “Heptoroid” (2)
Forming a continuous smooth edge
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UCBUCB Emergence of the “Heptoroid” (3)Emergence of the “Heptoroid” (3)
Smoothing the whole surface
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UCBUCB ==> BRENT COLLINS’ Presentation==> BRENT COLLINS’ Presentation
Hyperbolic Heptagon
Trefoils
Hyperbolic Hexagon II, and Heptoroid
Pax Mundi, Egg, Vox Solis
Atomic Flowers
Pieces with Positive Curvature
(Bronze casting will be described at MOSAIC talk)
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UCBUCB 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
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UCBUCB Sculpture DesignSculpture Design
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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UCBUCB SFF Maquettes of Future SculpturesSFF Maquettes of Future Sculptures
Monkey-SaddleCinquefoil
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UCBUCB Séquin’s “Minimal Saddle Trefoil”Séquin’s “Minimal Saddle Trefoil”
Stereo-lithography master
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UCBUCB Séquin’s “Minimal Saddle Trefoil”Séquin’s “Minimal Saddle Trefoil”
bronze cast, gold plated
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Minimal Trefoils cast and Minimal Trefoils cast and finished by Steve Reinmuthfinished by Steve Reinmuth
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UCBUCB Higher-order Trefoils Higher-order Trefoils (4th order saddles)(4th order saddles)
W=1 W=2
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UCBUCB 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
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UCBUCB Exploring New IdeasExploring New Ideas
Going twice around the loop ...
Resulting in an interwoven structure.
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UCBUCB 9-story Intertwined Double Toroid9-story Intertwined Double Toroid
Bronzeinvestment casting from wax original made on 3D Systems“Thermojet”
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UCBUCB Keeping up with Brent ...Keeping up with Brent ...
Bent “Scherk towers” is not able to describe a shape like “Pax Mundi.”
Need a broader paradigm !
Use SLIDE modeling environment,it provides a nice combination of procedural modeling and interactivity.
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UCBUCB SLIDESLIDE
SLIDE = Scene Language for Interactive Dynamic Environments
Developed as a modular rendering pipelinefor our introductory graphics course.
Primary Author: Jordan Smith
Based on OpenGL and Tcl/tk.
Good combination of interactive 3D graphicsand parameterizable procedural constructs.
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UCBUCB SLIDE Example: Klein BottleSLIDE Example: Klein Bottle
Final Project CS 184, Nerius Landys & Shad Roundy
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UCBUCB SLIDE Example Bug’s LifeSLIDE Example Bug’s Life
Final Project CS 184, David Cheng and James Chow
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UCBUCB SLIDE as a Design ToolSLIDE as a Design Tool
SLIDE is being enhanced currentlyto serve as a front-end for CyberBuild.
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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UCBUCB Conclusions 1Conclusions 1
Interactive computer graphics is a novel (to artists) medium that can play an important role -- even for traditional artists.
Virtual Prototyping can save time and can tackle sculptures of a complexitythat manual techniques could not conquer.
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UCBUCB Conclusions 2Conclusions 2
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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UCBUCB Conclusions 3Conclusions 3
What makes a CAD tool productive for this kind of work ?
Not just “virtual clay,”
partly procedural;
fewer parameters that need to be set.
Keep things aligned, joined;
guarantee symmetry, regularity,
watertight surfaces.
Interactivity is crucial !
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========= SPARE ========= ========= SPARE ========= ==================================================
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UCBUCB Preparation of Blue PrintsPreparation of Blue Prints
Cut geometrical shape into slices parallel to one axis:
Assemble several profile lines for each board,
and print out on separate sheet at 1:1 size.
==> (Examples from printer on wall)
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UCBUCB The role of the computerThe role of the computer
Eliminate need for prototyping
Exploration of larger domain
Making more complex structures
Better optimization
Precise blue prints
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UCBUCB SLA Maquette of “Solar Arch”SLA Maquette of “Solar Arch”
Back-lighting and photo by Philip Geller
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UCBUCB My Contorted Professional PathMy Contorted 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 Sculpture – CAD, Virtual Prototyping
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UCBUCB ==Abstract==Abstract
Brent Collins is a professional artist living in Gower, MO,who has been carving abstract geometrical structures from solid wood blocks or from laminated assemblies. Many of his sculptures comprise minimal surfaces which form an intricate composition of tunnels and saddles.Carlo Séquin is a professor at U.C. Berkeley, teachingcomputer graphics, geometric modeling, and computer aided design.Since 1995 he has been collaborating with Collins in the conceptionand design of intricate geometrical shapes that expand the originalwork of Collins. He has developed several procedural generatorprograms that recreate some of the shapes conceived by Collinsand can expand the basic concept in several possible directions.His interactive "sculpture generator" allows a quick perusal ofsome domain of the configuration space, and an optimization ofa given design along the axes of several parameters.Shapes of high artistic merits can then be sliced into 1-inch slabsand a corresponding set of cross sections printed out.Brent Collins uses these templates to precut a set of wood boardsand to preassemble a rough shape from which the final sculptureis then carved. In this way, the intuitive genius of the artist can beamplified by a computer tool that assists with the visualization and faithful reproduction of complex geometrical shapes.
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UCBUCB The Need for a Prototyping ToolThe Need for a Prototyping Tool
Intriguing Conceptual Idea: Turn the Hyperbolic Hexagon into a Heptagon Goals: Give it more variety;
Make different hole-angles visible from one direction by adding twist before closure.
Results: Surface becomes single-sided;
The four separate edges join into a torus knot.
Question: Will it look beautiful ? What can we do if it doesn’ t ?
Perhaps more twist can save it ?
What is the best size for the holes, the flanges ?
How can we find out quickly ?