Prof' Carlo H' Squin

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Prof. Carlo H. Séquin

• CAD Geometric Modeling Rapid Prototyping

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Séquins Research Interests CADRPwith Paul
Wright (ME)

• Physical Rapid Prototypes
• For early user testing,
• and hands-on feedback
• in application context.

Zcorp 3D-printer
FDM
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Séquins 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

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Art Math ConnectionFrom an Idea ...
Start with a crude polyhedral object
Subdivide triangles Optimize vertices
Repeat theprocess
Using Brakkes Surface Evolver
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... via Rapid Prototyping ...

• Fused DepositionModeling Machine

3D-Print Model,Z-Corporation
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... to a Final Bronze Cast

• Volution_0 ---
  Volution_5Minimal surfaces of different
  genus.

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Mathematical Models Parallel Projection of the
4D 120-Cell

• Zcorp,
• 6 diam.,
• 6hrs.

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Topological Models

• Octahedrally Linked Trefoils Knots

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CAGD Surface Optimization

• Creating the best-looking surfaces from only the
  truly relevant constraints by using appropriate
  energy functionals

Comparison MES ? ? MVS (genus 4 surfaces)
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Make Process EfficientDiscrete vs. Exact
Functionals

• discrete --- exact
• (seconds) --- (minutes)

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(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.

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Curve Optimization on SurfacesLVCs 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).

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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.

CURVATURE
kB
ARC-LENGTH
kA
B
A
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Fast 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

S
C
V
C
T

• For subdivision surfaces refine surface and LVC
  path jointly !

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K12 on a Genus-6 Surface
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CITRIS -- BID

• Collaborative Design Environments

• Sara McMains, Carlo Séquin, Paul Wright
• Development of a tele-collaborative designand
  re-design environment for mechanicaland
  geometrical parts.
• Allows designers, managers, manufacturers,located
  on different continents, to jointlyinspect,
  annotate, and modify a design.

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Collaborative VR Workstation

• A haptic, immersive work space for
  telecollaborative design across the internet

See in 3D, Touch, feel, Annotate, Modify, Share,
Discuss
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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).