CS 284: CAGD
Lecture #20 -- Tue 10/30, 2012.

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Preparation: Study: Anisotropic Polygonal Remeshing

Warm-Up: Answer some key questions about today's paper

Results of: "Venture Capitalist Rally" or "NSF Proposal Review"

Who got the "gold"?

Paper Presentation:

Eric leads the discussion on: Anisotropic Polygonal Remeshing

Why is such a re-parametrization desirable ?
How is the curvature field sampled, constructed ?
Why is there a restriction to genus 0 on page 2 ?
What routines, programs is the algorithm built upon ?
What is the key advice about implementation given in the paper ?

A genus-3 object with suitably aligned quadrilateral parametrization. (close-up view).

Another Application where the shape of the parameterization mesh plays a crucial role:

If we start with an ordinary torus with a 360-degree twist in its surface parameterization,
that twist can be relieved by deforming the sweep path of the torus into a figure-8 shape.
Some demos:
http://www.cs.berkeley.edu/~sequin/TALKS/2011_Bridges_Tori-Story_/F8warp_twisting.avi
http://www.cs.berkeley.edu/~sequin/TALKS/2011_Bridges_Tori-Story_/F8warp_minTorsion.avi
More eversion movies at:
http://www.cs.berkeley.edu/~sequin/TALKS/2011_Bridges_Tori-Story_/

A study to demonstrate the untwisting effect on tori and on tubes with a circular profile:
Bending and Torsion Minimization of Toroidal Loops (EECS-2012-165) Avik Das

Generalization?

Can we find an energy functional that takes surface parameterization into account in such a way
that the torus would automatically undergo such as twist reducing deformation?

Could such an energy functional aslos show how to smoothly undo a Klein bottle mouth
of the "Inverted Double-Sock" type into a twisted tube with a figure-8 profile?
Some pictures to explain this problem: