1. Prof. Carlo H. Séquin CAD – Geometric Modeling – Rapid Prototyping

2. Séquin’s Research Interests: CAD+RP with Paul Wright (ME) Physical Rapid Prototypes: l For early user testing, l and hands-on feedback l in application context. Zcorp 3D-printer FDM

3. Séquin’s Research Interests (cont.) 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 …

4. “Art – Math” Connection: From an Idea... Start with a crude polyhedral object Subdivide triangles Optimize vertices Repeat the process Using Brakke’s Surface Evolver

5. ... via Rapid Prototyping... Fused Deposition Modeling Machine 3D-Print Model, Z-Corporation

6. ... to a Final Bronze Cast “Volution_0” --- “Volution_5” Minimal surfaces of different genus.

7. Mathematical Models: Parallel Projection of the 4D 120-Cell u Zcorp, u 6” diam., u 6hrs.

8. Topological Models Octahedrally Linked Trefoils Knots

9. CAGD: Surface Optimization u Creating the best-looking surfaces from only the truly relevant constraints by using appropriate energy functionals Comparison: MES   MVS (genus 4 surfaces)

10. Make Process Efficient: Discrete vs. Exact Functionals discrete --- exact (seconds) --- (minutes)

11. (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.

12. Curve Optimization on Surfaces: LVC’s = Curves with linearly varying curvature u Need more control than geodesics can offer. u Want to space the departing curves from a vertex more evenly, avoid very acute angles. u Need control over starting and ending tangent directions (like Hermite spline).

13. LVC Curves (instead of MVC) u Curves with linearly varying curvature have two degrees of freedom: k A k B, u Allows to set two additional parameters, i.e., the start / ending tangent directions. A B CURVATURE kAkA kBkB ARC-LENGTH

14. Fast Algorithm for Subdivision Surfaces u Start with an approximate path from S to T. u Locally move edge crossing points ( C ) so as to even out variation of curvature: T C S C V u For subdivision surfaces: refine surface and LVC path jointly !

15. K 12 on a Genus-6 Surface

16. CITRIS -- BID Collaborative Design Environments Sara McMains, Carlo Séquin, Paul Wright Development of a tele-collaborative design and re-design environment for mechanical and geometrical parts. Allows designers, managers, manufacturers, located on different continents, to jointly inspect, annotate, and modify a design.

17. Collaborative VR Workstation A haptic, immersive work space for telecollaborative design across the internet See in 3D, Touch, feel, Annotate, Modify, Share, Discuss …

18. Collaborative VR Workstation A student interacting with a Ford Explorer model displayed on the workstation (simulated 3D effect showing the part where the user perceives it to be).