Adobe Systems, Strategic Visit, 11/1/06 Artistic Geometry Carlo H. Séquin University of California, Berkeley
A designer for 30 years…
Geometry is my true love ! u Optical paths through prism u Integrated circuit layouts u Building floor plans u CAD drawings u Visualizations...
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 ? u serious distortions, u not all tiles are the same. Difficulties:
Infinite Tiling on the Poincaré Disk
Mapped onto a genus-3 surface 168 auto- morphisms Felix Klein (1878) next: Hurwitz group of order 504
The 2D Hilbert Curve (1891) A plane-filling Peano curve Fall 1983: CS Graduate Course: Creative Geometric Modeling Do This In 3 D !
Metal Sculpture at SIGGRAPH 2006
Since 1994: CAD for Artists u How can we use the visualization power offered by computer graphics and by computer-controlled rapid prototyping for the design of geometrical sculptures?
Geometric Sculpture Brent Collins
Art - Math Connection ISAMA & Bridges Conferences MOSAIC 2000 (David Salesin, Univ. of WA)
Many Math Models and Sculptures CAD tools are still inadequate for free-form 3D designs !
Ongoing Research Interest CAD tools for Ideation, Informal Prototyping: l Mimick the best of: clay, wire, paper, scotch-tape, styrofoam … l Without the adversity of: messy glue, gravity, strength limits … l 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 …
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 …
Research with Prof. Wright (ME) Physical Rapid Prototypes: For early user testing and hands-on feedback in application context. Zcorp 3D-printer FDM From Art to Part Contact-Compact
Current Research (Pushkar Joshi) l Based on optimization of a functional by using all free DOFs. l Fewer controls to manipulate l Explicit consideration of constraints l Automatic attainment of some quality objectives. Better Surface Design Tools:
(Future) Surface Optimization Module u Built into future CAD environments! u User specifies all boundary conditions as well as any other constraints. u User selects a suitable beauty functional. u CAD system finds best solution in seconds.
Beauty Functionals Comparison MES MVS. Things get worse for MES as we go to higher genus Genus-5 MES MVS keep nice toroidal arms 3 holes pinch off
Pushkar Joshis Work u Build a robust evaluation environment for curvature-based surface functionals. u Create a catalog of minimizing shapes for the various beauty functionals. u Find good approximations using discrete curvature operators for polyhedra. u Integrate that into an interactive CAD environment.
Minimum Variation Curves u They minimize the arc-length integral of the square of the change of curvature. u Very nice overall properties, but depends on global optimization. u A change in one place may affect the shape everywhere ! u Local support is preferable... Circle Splines Clothoids
Current Research (Raph Levien) u Clothoids (Euler spirals, Cornu spirals) u for interactive font design (and other CAD) k s
Clothoid as a General CAD Primitive Advantageous features : u Smooth variation of curvature. u Approximates behavior of MVC, but with localized support and control. u Yields circles when allowed by constraints. u Easy calculation of offset curve: clothoid-like.
Raph Leviens Clothoid Tool Kit u Composite curve of Clothoid segments to interpolate given data points u Interactive design tool to draw curves within given constraints: position, tangent, and curvature. u Conversion of Clothoids to Bezier segments with specified precision. error = 1e-5
Conclusion ART CAD MATH Acrobat Reader / Photoshop / FrameMaker
Light Field of Genus-6 Tiffany Lamp
E X T R A S
A Graph-Embedding Problem u Draw K 12 (= complete graph with 12 vertices) crossing-free onto a smooth surface of genus 6 with as much symmetry as possible.
Prof. Bokowskis Models Physical goose-neck model Partial virtual model
My Own Rapid-Prototype Model
Virtual Genus-6 Map (shiny metal)
Light Field of Genus-6 Tiffany Lamp
SLIDE-UI for Viae Globi Shapes
Viae Globi: Maloja -- FDM part u A rather winding Swiss mountain pass road in the upper Engadin.
My Agenda within BID u Teaching Applicable Design Skills u Developing Better CAD Tools & Methods. Tight coupling: Research Instruction
Doing Design u 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. u 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.
(my) BID Manifesto The proof of any new methods lies in their application to relevant design problems. u Apply new theories & methods of design. u Have the students actually design things – which then (hopefully) prove to be demonstratively better than earlier design.