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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

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

### Who got the "gold"?

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:

### More on Mug Tiling...

Brandon's latest submission...

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## Assignments for Thu. Nov. 1, 2012:

Study: **
Texture Synthesis over Arbitrary Manifold Surfaces**

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