1. Carlo H. Séquin u (Descriptive) Geometry – my love since high school

2. 2D Geometry (Chip Layouts) Bell Labs, 1973: U.C. Berkley 1982: CCD Camera RISC microcomputer

3. 3D Geometry Berkeley, 1994: U.C. Berkley 1996: Soda Hall CyberCut – CyberBuild (WalkThru) (RP models and toys)

4. Ph.D. Thesis by Raph Levien Interpolating Designer Curves (≈MVC) u Euler spirals (clothoids, Cornu spirals) u for interactive font design (and other CAD) k  s

5. Ph.D. Thesis by Pushkar Joshi Surface Optimization – New Functionals Things get worse for MES as we go to higher genus Genus-5 MES MVS yields nice toroidal arms 3 holes pinch off

6. Art - Math Connection ISAMA & Bridges Conferences (1998-2011…) MOSAIC 2000 (David Salesin, Univ. of WA)

7. Metal Sculpture at SIGGRAPH 2006

8. Artistic Geometry Brent Collins 1997

9. Sutardja Dai Hall, 2009

10. Inspiration: Brent Collins’ Pax Mundi (1997)

11. SLIDE-GUI for “Pax Mundi” Shapes Good combination of interactive 3D graphics and parameterizable procedural constructs.

12. Many Related Sculptures May Emerge

14. The Assembly is Too Squat !!

15. Changing the Curvature u PHYSICS is important too... not just Geometry !

16. James Hamlin: Emulation of Solstice The thick rail forms a {3,2} torus knot; there are 300 ribs inside

17. Parameter Changes u Go from {3,2} torus knot to {2,3} torus knot

18. Ph.D. Thesis of James Andrews Extracting the Generating Paradigms u Find a decomposition into simpler parameterizable entities, e.g., CSG primitives, generalized sweeps, curved surfaces...

19. Tilings on Surfaces of Higher Genus 24 tiles on genus 3 48 tiles on genus 7

20. All the Regular Maps of Genus Zero Platonic SolidsDi-hedra (=dual) Hosohedra {3,4} {3,5} {3,3} {4,3} {5,3}

21. Globally Regular Maps on Genus 5

22. Visualizing R4.2_{4,5}_6 u A transformation maintaining symmetry

23. More …

24. World of Wild and Wonderful Tori

25. 4 Generic Representatives of Tori u For the 4 different regular homotopy classes: OO O8 8O 88 Characterized by: PROFILE / SWEEP

26. Analyzing the Twist in the Ribbons The knotted lines are harder to analyze  Use a paper strip!

27. 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 …

28. More Research Interests: Design for Manufacturability, including Rapid Prototyping, and Injection-Mold Making. l Speeding up “Art to Part” (or actually: “Inspiration to Income”) l “Manufacturing-aware” CAD tools. (show limitations of fabrication process during all design phases.) Vague Idea Concept Mock-up CAD Model Proc.Plan, CNC File Prototype Part Commercial Product

30. Volution Surface of Genus 2 Suspended by 12 quarter circles on 6 cube faces

31. Architectural Geometry Volution blocks as modular wall elements

32. Architectural Geometry Möbius Bridge and Möbius House

33. Viae Globi : ( roads on a sphere ) Collins: Pax Mundi (1997)Séquin: Maloja (2001)