Adobe Systems, Strategic Visit, 11/1/06 Artistic Geometry Carlo H. Séquin University of California,...
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Transcript of Adobe Systems, Strategic Visit, 11/1/06 Artistic Geometry Carlo H. Séquin University of California,...
![Page 1: Adobe Systems, Strategic Visit, 11/1/06 Artistic Geometry Carlo H. Séquin University of California, Berkeley.](https://reader035.fdocuments.us/reader035/viewer/2022062511/551816e75503469d318b468c/html5/thumbnails/1.jpg)
Adobe Systems, Strategic Visit, 11/1/06Adobe Systems, Strategic Visit, 11/1/06
Artistic Geometry
Carlo H. Séquin
University of California, Berkeley
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A designer for 30 years…A designer for 30 years…
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Geometry is my true love !Geometry is my true love !
Optical paths through prism
Integrated circuit layouts
Building floor plans
CAD drawings
Visualizations ...
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Fascination with Geometrical Patterns:Fascination with Geometrical Patterns: Escher TilingsEscher Tilings
in the plane on the sphere on the torus
M.C. Escher Jane Yen, 1997 Young Shon, 2002
Can we do this on surfaces of higher genus ?
serious distortions,
not all tiles are the same.Difficulties:
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““Infinite” Tiling Infinite” Tiling on the on the PoincarPoincaréé DiskDisk
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MappedMappedonto aonto agenus-3genus-3surfacesurface
168 auto-morphisms
Felix Klein (1878)
next:Hurwitz group of order 504
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The 2D Hilbert Curve (1891)The 2D Hilbert Curve (1891)A plane-filling Peano curve
Fall 1983: CS Graduate Course: “Creative Geometric Modeling”
Do This In 3 D !
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Metal Sculpture at SIGGRAPH 2006Metal Sculpture at SIGGRAPH 2006
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Since 1994: CAD for ArtistsSince 1994: CAD for Artists
How can we use the visualization power offered by computer graphics and by computer-controlled rapid prototyping for the design of geometrical sculptures?
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Geometric SculptureGeometric Sculpture
Brent Collins
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Art - Math ConnectionArt - Math Connection
ISAMA & Bridges Conferences
MOSAIC 2000 (David Salesin, Univ. of WA)
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Many Math Models and SculpturesMany Math Models and Sculptures
CAD tools are still inadequate
for free-form 3D designs !
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Ongoing Research InterestOngoing Research Interest
CAD tools for Ideation, Informal Prototyping: Mimick the best of: clay, wire, paper, scotch-tape, styrofoam …
Without the adversity of: messy glue, gravity, strength limits …
Make available pseudo-physical materials that bend as nicely as steel wire, and stretch like a nylon hose, but are strong as titanium, and as transparent as quartz …
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Recent Project with Prof. McMains (Recent Project with Prof. McMains (ME)ME)
Develop a haptic, immersive VR work station for telecollaborative design across the internet
See in 3D,Touch, feel,Annotate,Modify,Share, Discuss …
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Research with Prof. WrightResearch with Prof. Wright (ME) (ME)
Physical Rapid Prototypes:
For early user testingand hands-on feedbackin application context.
Zcorp 3D-printer FDM
“From Art to Part”
“Contact-Compact”
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Current Research (Pushkar Joshi)Current Research (Pushkar Joshi)
Based on optimization of a functionalby using all free DOFs.
Fewer controls to manipulate
Explicit consideration of constraints
Automatic attainment of some quality objectives.
Better Surface Design Tools:
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(Future) Surface Optimization Module(Future) Surface Optimization Module Built into future CAD environments!
User specifies all boundary conditions as well as any other constraints.
User selects a suitable “beauty” functional.
CAD system finds best solution in seconds.
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““Beauty Functionals”Beauty Functionals”Comparison MES Comparison MES MVS MVS ..
Things get worse for MES as we go to higher genus
Genus-5 MES MVSkeep nice toroidal arms
3 holes pinch off
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Pushkar Joshi’s WorkPushkar Joshi’s Work
Build a robust evaluation environmentfor curvature-based surface functionals.
Create a catalog of minimizing shapesfor the various beauty functionals.
Find good approximations using discrete curvature operators for polyhedra.
Integrate that into an interactive CAD environment.
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Minimum Variation CurvesMinimum Variation Curves
They minimize the arc-length integralof the square of the change of curvature.
Very nice overall properties,but depends on global optimization.
A change in one place may affect the shape everywhere !
Local support is preferable... Circle Splines Clothoids
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Current Research (Raph Levien)Current Research (Raph Levien)
Clothoids (Euler spirals, Cornu spirals)
for interactive font design (and other CAD)
k s
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Clothoid as a General CAD PrimitiveClothoid as a General CAD Primitive
Advantageous features:
Smooth variation of curvature.
Approximates behavior of MVC,but with localized support and control.
Yields circles when allowed by constraints.
Easy calculation of offset curve: clothoid-like.
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Raph Levien’s Clothoid Tool KitRaph Levien’s Clothoid Tool Kit
Composite curve of Clothoid segmentsto interpolate given data points
Interactive design toolto draw curves withingiven constraints:position, tangent,and curvature.
Conversion of Clothoidsto Bezier segments withspecified precision. error = 1e-5
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ConclusionConclusion
ART
CAD
MATH
Acrobat Reader / Photoshop / FrameMaker
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Light Field of Genus-6 Tiffany LampLight Field of Genus-6 Tiffany Lamp
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E X T R A SE X T R A S
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A Graph-Embedding ProblemA Graph-Embedding Problem
Draw K12 (= complete graph with 12 vertices) crossing-free onto a smooth surface of genus 6 with as much symmetry as possible.
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Prof. Bokowski’s ModelsProf. Bokowski’s Models
Physical goose-neck model
Partial virtual model
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My Own Rapid-Prototype ModelMy Own Rapid-Prototype Model
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Virtual Genus-6 Map (shiny metal)Virtual Genus-6 Map (shiny metal)
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Light Field of Genus-6 Tiffany LampLight Field of Genus-6 Tiffany Lamp
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SLIDE-UI for “Viae Globi” ShapesSLIDE-UI for “Viae Globi” Shapes
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Viae Globi: “Maloja” -- FDM partViae Globi: “Maloja” -- FDM part
A rather winding Swiss mountain pass road in the upper Engadin.
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My Agenda within BIDMy Agenda within BID
Teaching Applicable Design Skills
Developing Better CAD Tools & Methods.
Tight coupling: Research Instruction
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DoingDoing Design Design In my courses on graphics and on geometrical design, I found that
students often acquire a decent overview of various CAD tools & design techniques – but only at a textbook level.
When asked to design a plastic spoon, they are completely stumped or come up with totally impractical design plans.
My goal is to remedy this situation.
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(my)(my) “BID Manifesto” “BID Manifesto”
The proof of any new methods lies in their application to relevant design problems.
Apply new theories & methods of design.
Have the students actually design things – which then (hopefully) prove to be demonstratively better than earlier design.