Prof. Carlo H. SProf. Carlo H. Séquinéquin

CAD – Geometric Modeling – Rapid Prototyping

SSééquin’s Research Interests: CAD+RPquin’s Research Interests: CAD+RPwith Paul Wright (ME)with Paul Wright (ME)

Physical Rapid Prototypes:

For early user testing,

and hands-on feedback

in application context.

Zcorp 3D-printer FDM

SSééquin’s Research Interests (cont.)quin’s Research Interests (cont.)

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 …

““Art – Math” Connection:Art – Math” Connection:

From an Idea ...From an Idea ...

Start with a crudepolyhedral object

Subdivide trianglesOptimize vertices

Repeat theprocess

Using Brakke’s Surface EvolverUsing Brakke’s Surface Evolver

... via Rapid Prototyping ...... via Rapid Prototyping ...

Fused DepositionModeling Machine

3D-Print Model,Z-Corporation

... to a Final Bronze Cast... to a Final Bronze Cast

“Volution_0” --- “Volution_5”

Minimal surfaces of different genus.

Mathematical Models:Mathematical Models: Parallel Projection of the 4D 120-CellParallel Projection of the 4D 120-Cell

Zcorp,

6” diam.,

6hrs.

Topological ModelsTopological Models

Octahedrally Linked Trefoils Knots

CAGD: SurfaceCAGD: Surface Optimization Optimization Creating the best-looking surfaces

from only the truly relevant constraints by using appropriate energy functionals

Comparison: MES Comparison: MES MVS MVS (genus 4 surfaces)(genus 4 surfaces)

Make Process Efficient:Make Process Efficient:Discrete vs. Exact FunctionalsDiscrete vs. Exact Functionals

discrete --- exact

(seconds) --- (minutes)

(Future) Surface Optimization Module(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.

Curve Optimization on Surfaces:Curve Optimization on Surfaces:LVC’s = Curves with linearly varying curvatureLVC’s = Curves with linearly varying curvature

Need more control than geodesics can offer.

Want to space the departing curves from a vertex more evenly, avoid very acute angles.

Need control over starting and ending tangent directions (like Hermite spline).

LVC Curves (instead of MVC)LVC Curves (instead of MVC)

Curves with linearly varying curvaturehave two degrees of freedom: kA kB,

Allows to set two additional parameters,i.e., the start / ending tangent directions.

A

B

CURVATURE

kA

kB

ARC-LENGTH

Fast Algorithm for Subdivision SurfacesFast Algorithm for Subdivision Surfaces Start with an approximate path from S to T.

Locally move edge crossing points ( C ) so as to even out variation of curvature:

T

CS

CV

For subdivision surfaces: refine surface and LVC path jointly !

KK1212 on a Genus-6 Surface on a Genus-6 Surface

CITRIS -- BIDCITRIS -- BID

Collaborative Design Environments

Sara McMains, Carlo Séquin, Paul Wright

Development of a tele-collaborative designand re-design environment for mechanical

and geometrical parts.

Allows designers, managers, manufacturers,located on different continents, to jointlyinspect, annotate, and modify a design.

Collaborative VR WorkstationCollaborative VR Workstation A haptic, immersive work space

for telecollaborative design across the internet

See in 3D,Touch, feel,Annotate,Modify,Share, Discuss …

Collaborative VR WorkstationCollaborative 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).