Adobe Systems, Strategic Visit, 11/1/06

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. serious distortions, • not all tiles are the same. Difficulties: 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 PoincaréDisk

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 Modeling”Do 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) Physical Rapid Prototypes: For early user testingand hands-on feedbackin application context. “From Art to Part” “Contact-Compact” Zcorp 3D-printer FDM

16. 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:

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 Functionals”Comparison MES  MVS . Things get worse for MES as we go to higher genus pinch off 3 holes Genus-5 MES MVSkeep nice toroidal arms

19. Pushkar 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.

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 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

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. Bokowski’s 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.