CS 284: CAGD 
Lecture #16 -- Mo 10/20, 2003.

Preparation:

Remarks on Homework: Designing a Genus-4 Smooth Surface

Some select examples of the models in stage 3, first some shapes seen in previous rounds:
the "organic" shape by Irena, the complex design by Aleksey, the tangible model by Young, and the very symmetrical model by Hayley;
and a new intriguing shape by Alan,

Side Remark: Triangular Surfaces Patches

We can also deal with triangular patches, but need a different interpolation scheme:
Barycentric coordinates: three numbers, but with constraint that they must sum to 1.0.
DeCasteljau evaluation technique can also be applied to triangular patches.
 

Functional Optimization

• What is the overall goal ?
• What is the high-level approach ?
• What is novel, innovative, reusable in other contexts ?
• What are the results obtained ?
• What else should you remember about this paper ?

Curve Optimization

• Desirable properties
• Optimization functionals: MEC, MVC, Si-MEC, Si-MVC
• Curve evolution to global minimum, and what slows it down
• Curve representation: quintic hermite
• Optimization procedure
• What are the best "primitives"?
• Does this work in 3D ?

Surface Optimization

• What carries over from curve optimization ?
• What are new issues ?
• The surface functionals: MES, MVS, Si-MVS
• The "ideal" zero-cost surfaces
• Surface representations: bi-quintic hermite
• Constraint initialization
• Optimization procedure: first network, then paches
• Results for unconstrained low genus surfaces
• Can we do better ?

Start preparing your Project Proposals --> Tentative Ideas due by Wednesday.

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Current Homework Assignment: (to be done individually)

Evaluate Various Surface Subdivision Schemes

Use the SLIDE file CS284/CODE/subdivision.slf and test many of the subdivision schemes accessible from the menu that do NOT have the word "SELECTIVE" in their name. In particular take a close look at:

1. SLF_SUBDIVISION_DOO_SABIN

- Doo-Sabin quadratic, it must be a closed mesh.
2. SLF_SUBDIVISION_SHARP_CATMULL_CLARK

- Catmull-Clark cubic, anything goes including sharp tags.
 
3. SLF_SUBDIVISION_CORNER_CUTTING

- All of the CORNER_... schemes generalize the Loop topological split for arbitrary polygons
   by creating a triangle at each corner by connecting the two adjacent midpoints.
4. SLF_SUBDIVISION_CORNER_ROUNDING
5. SLF_SUBDIVISION_CORNER_ROUNDING_SHARP_LOOP

- Loop quartic scheme (if the input is all triangles), sharp tags ok.
6. SLF_SUBDIVISION_CORNER_ROUNDING_BUTTERFLY

- Butterfly interpolating scheme, must be a closed object.
7. SLF_SUBDIVISION_CORNER_ROUNDING_ZORIN

- Zorin's enhanced interpolating scheme, must be a closed object.
 
8. SLF_SUBDIVISION_TRIANGLE_LOOP

- All of the TRIANGLE_... schemes are the same as the CORNER_... schemes,
   but they insert a vertex in the center of non-triangles to triangulate them on the first step
   and then they run the classic subdivision schemes.
9. SLF_SUBDIVISION_TRIANGLE_BUTTERFLY
10. SLF_SUBDIVISION_TRIANGLE_ZORIN

A.)  Do a qualitative examination on three different objects, one of which should be  "gHexPrism1", given in the starter file.
You can activate different objets by "un-commenting" different instance commands in lines 300-340 in the subdivision.slf file.
Pick a second object of your choice.
Check out the on-line SLIDE web page on Tcl-Packages, the "slideui", and "geometry.tcl" to learn more about these packages and the different objects.
The third test object should be your own design of a genus 4 object (this is obviously non-convex -- how does this affect the various methods?)
Report your qualitative observations on these test runs, in particular, which scheme performs the best, and what geometrical features cause the most problems with what subdivision schemes.

B.)  As a second way of focusing on the capabilities of the different schemes -- and using very much what you learned from the four papers -- consider the following task:
Assume you have been given the 20 vertices of a regular dodecahedron and would like to have a very finely tessellated, sphere-like, subdivision surface that interpolates these 20 vertices exactly. Study how to do this with two different subdivision schemes: an interpolating one and an approximating one. Give SLIDE descriptions of the initial two control meshes for the case there the 20 vertices lie on a sphere of radius 1.0.

• Provide two images that show the initial control meshes and
• (reasonably) smooth versions of the two resulting surfaces (don't push SLIDE too far!).
• Comment on the advantages and difficulties of the two methods, and on the qualities of the final surfaces.
• Bring your reports to class on Wednesday 10/22/2003.

Next Reading Assignment: