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Adobe Systems, Strategic Visit, 11106

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Adobe Systems, Strategic Visit, 11/1/06. Artistic Geometry. Carlo H. S quin ... Geometry is my true love ! Optical paths through prism. Integrated circuit layouts ... – PowerPoint PPT presentation

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Title: Adobe Systems, Strategic Visit, 11106


1
Adobe Systems, Strategic Visit, 11/1/06
  • Artistic Geometry
  • Carlo H. Séquin
  • University of California, Berkeley

2
A designer for 30 years
3
Geometry is my true love !
  • Optical paths through prism
  • Integrated circuit layouts
  • Building floor plans
  • CAD drawings
  • Visualizations ...

4
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 ?
5
Infinite Tiling on the Poincaré Disk
6
Mappedonto agenus-3surface
168 auto- morphisms Felix Klein
(1878) next Hurwitz group of order 504
7
The 2D Hilbert Curve (1891)
  • A plane-filling Peano curve

Fall 1983 CS Graduate Course Creative
Geometric ModelingDo This In 3 D !
8
Metal Sculpture at SIGGRAPH 2006
9
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?

10
Geometric Sculpture
Brent Collins
11
Art - Math Connection
  • ISAMA Bridges Conferences
  • MOSAIC 2000 (David Salesin, Univ. of WA)

12
Many Math Models and Sculptures
  • CAD tools are still inadequate
  • for free-form 3D designs !

13
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

14
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
15
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
16
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.

17
(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.

18
Beauty FunctionalsComparison MES ?? MVS
.
pinch off
3 holes
Genus-5 MES
MVSkeep nice toroidal arms
  • Things get worse for MES as we go to higher genus

19
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.

20
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

21
Current Research (Raph Levien)
  • Clothoids (Euler spirals, Cornu spirals)
  • for interactive font design (and other CAD)

k ? s
22
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.

23
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
24
Conclusion
ART
MATH
CAD
Acrobat Reader / Photoshop / FrameMaker
25
Light Field of Genus-6 Tiffany Lamp
26
E X T R A S
27
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.

28
Prof. Bokowskis Models
Partial virtual model
Physical goose-neck model
29
My Own Rapid-Prototype Model
30
Virtual Genus-6 Map (shiny metal)
31
Light Field of Genus-6 Tiffany Lamp
32
SLIDE-UI for Viae Globi Shapes
33
Viae Globi Maloja -- FDM part
  • A rather winding Swiss mountain pass road in the
    upper Engadin.

34
My Agenda within BID
  • Teaching Applicable Design Skills
  • Developing Better CAD Tools Methods.
  • Tight coupling Research ?? Instruction

35
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.

36
(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.
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