Adobe Systems, Strategic Visit, 11106

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Adobe Systems, Strategic Visit, 11/1/06

• Artistic Geometry
• Carlo H. Séquin
• University of California, Berkeley

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A designer for 30 years
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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 Escher
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 ?
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Infinite Tiling on the Poincaré Disk
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Mappedonto agenus-3surface
168 auto- morphisms Felix Klein
(1878) next Hurwitz group of order 504
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The 2D Hilbert Curve (1891)

• A plane-filling Peano curve

Fall 1983 CS Graduate Course Creative
Geometric ModelingDo This In 3 D !
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Metal Sculpture at SIGGRAPH 2006
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Since 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 Sculpture
Brent Collins
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Art - Math Connection

• ISAMA Bridges Conferences
• MOSAIC 2000 (David Salesin, Univ. of WA)

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Many Math Models and Sculptures

• CAD tools are still inadequate
• for free-form 3D designs !

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Ongoing 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 (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. Wright (ME)
From Art to Part

• Physical Rapid Prototypes
• For early user testingand hands-on feedbackin
  application context.

Contact-Compact
Zcorp 3D-printer
FDM
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Current Research (Pushkar Joshi)
Better Surface Design Tools

• Based on optimization of a functionalby using
  all free DOFs.
• Fewer controls to manipulate
• Explicit consideration of constraints
• Automatic attainment of some quality objectives.

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(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 FunctionalsComparison MES ?? MVS
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pinch off
3 holes
Genus-5 MES
MVSkeep nice toroidal arms

• Things get worse for MES as we go to higher genus

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Pushkar Joshis 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 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)

• Clothoids (Euler spirals, Cornu spirals)
• for interactive font design (and other CAD)

k ? s
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Clothoid 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 Leviens Clothoid Tool Kit

• Composite curve of Clothoid segmentsto
  interpolate given data points
• Interactive design toolto draw curves
  withingiven constraintsposition, tangent,and
  curvature.
• Conversion of Clothoidsto Bezier segments
  withspecified precision.

error 1e-5
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Conclusion
ART
MATH
CAD
Acrobat Reader / Photoshop / FrameMaker
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Light Field of Genus-6 Tiffany Lamp
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E X T R A S
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A 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. Bokowskis Models
Partial virtual model
Physical goose-neck model
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My Own Rapid-Prototype Model
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Virtual Genus-6 Map (shiny metal)
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Light Field of Genus-6 Tiffany Lamp
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SLIDE-UI for Viae Globi Shapes
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Viae Globi Maloja -- FDM part

• A rather winding Swiss mountain pass road in the
  upper Engadin.

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My Agenda within BID

• Teaching Applicable Design Skills
• Developing Better CAD Tools Methods.
• Tight coupling Research ?? Instruction

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Doing 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) 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.