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CS 284: CAGD

Lecture #16 -- Tue 10/16, 2012.

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Preparation: **Read:

Ken Brakke's **"Surface Evolver"**** ** [ skip Sections 3.4, 3.5, 4.2, 4.8, 5.4, 5.5, 6.2, 6.7, 9, 10.]

**and Henry Moreton's ****"Functional Optimization for Fair Surface Design"**.

# Warm-up Questions:

# What applications of "surface optimization" do you know of?

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**Laura and Michael**** **discussing: **Ken Brakke's ****"Surface Evolver"**** **

1.) What is the basic representation of a surface in the Evolver?

2.) What kind of constraints can be specified on these surfaces?

3.) What kind of energies can be specified to guide the surface optimization?

4.) What is a Willmore surface.

5.) For soap films suspended in wire frames, the mean curvature has to be minimized;

-- how is this step discretized to work with the above representation?

6.) By how much does a vertex move in each iteration?

7.) For closed soap bubbles the mean curvature is (obviously) not zero;

-- what does it depend on?

8.) What processes are there to make a surface smooth and "well-behaved"?

Discussion of the salient points of the papers: Data structures, algorithms, difficulties ...

A Current Modeling Research Problem:

How to smoothly undo a Klein bottle mouth of the "Inverted Double-Sock" type into a twisted tube with a figure-8 profile?

Now we also need to have energy terms to penalize twisted or sheared parameter grids.

In other applications we may want to have the parameterization as uniform as possible,

or aligned with the prinicpal curvatures (can be done by re-meshing).

## Discussion of any Subdivision Problems -- ?

Brandon's Mug

**Issues Arising with Texture Mapping (cont.):**

**What factors affect the quality of the generated texture?**

How do the sizes of the triangles in the original (level 0) mesh affect the outcome of the generated texture pattern?

Can you use the "fish" tiles shown above to texture map you mug? -- What issues might arise?

### Example pictures of triangle tiles with different sides:

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# Your Project Ideas ...

Send me a refined, concrete proposal by Thursday!

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## Assignments for Thu. Oct. 18, 2012:

Read: **Surface Simplification Using QEM and ****Progressive Meshes**

**Programming: Continue implementing your dyadic triangle subdivision:**

1.) Add some rounding/smoothing scheme and demonstrate it on your mug. Send me pictures by Tuesday, October 16.

2.) Add some "interesting" texture, i.e., the tiles should have some
"directionality" and should not fit together with arbitrary rotations or with
every possible pairing of sides. For instance, try to use the square
"fish" tile or the triangular "lizard tile" shown above.

Get this to work by **Tuesday, October 23.**

## COURSE PROJECTS:

By Thursday, Oct. 18, e-mail me a refined concrete proposal.

**Thursday Oct. 25: "Venture Capitalist Rally" or "NSF Proposal Review"**

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