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

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

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

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

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

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

Metal Sculpture at SIGGRAPH 2006

Artistic Geometry Brent Collins 1997

Sutardja Dai Hall, 2009

Inspiration: Brent Collins’ Pax Mundi (1997)

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

Many Related Sculptures May Emerge

The Assembly is Too Squat !!

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

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

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

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...

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

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

Globally Regular Maps on Genus 5

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

More …

World of Wild and Wonderful Tori

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

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

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 …

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

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

Architectural Geometry Volution blocks as modular wall elements

Architectural Geometry Möbius Bridge and Möbius House

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