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

PREVIOUS < - - - - > CS 284 HOME < - - - - > CURRENT < - - - - > NEXT

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:

More eversion movies at:

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


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...

Assignments for Thu. Nov. 1, 2012:

Study:   Texture Synthesis over Arbitrary Manifold Surfaces

PREVIOUS < - - - - > CS 284 HOME < - - - - > CURRENT < - - - - > NEXT
Page Editor: Carlo H. Séquin