CS 284: CAGD 
Lecture #15 -- We 10/15, 2003.

Preparation:

Discussion of Homework: Designing a Genus-4 Smooth Surface

Some select examples of the models in stage 2:
the "organic" shape by Irena, the complex design by Aleksey, the tangible model by Young, and a very symmetrical model by Hayley.

Any problems encountered when subjecting your design to Catmull-Clark subdivision ?
 

Comparison of different starting frames for the genus 3 case:

Paper Assignments and Presentations

Interpolating Subdivision Surface for Triangulated Control Polyhedra

• What are the key ideas: (Section 1, six bullets in right column)
• The construction of new edge midpoints: (Section 3.2)
• what are the actual region of influence ?
• why does it make sense to ignore the neighbors to the right of S1 and S6 in Figure 3b ?
• The modified subdivision scheme: (Section 3.3: four cases)
• Improvements over Butterfly scheme: (Fig. 4a)
• How can such interpolated regions be stiched togehter ?

 

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.

New 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

!! Change the method selection at least once before you start, there is something funny going on with the displayed label !!

Within this slide program, compare the capabilities of the various schemes to make smooth, evenly rounded objects with as few concavities as possible for convex starting objects. One of the tougher test objets is "gHexPrism1" because of the many coplanar facets and the sharp edges in the input net.

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 observations on these test runs..

As a second way of focusing on the capabilities of the different schemes -- and using very much what you may learn from the four papers -- consider the following task:
Assume you have 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. Try to do this with two different subdivision schemes: an interpolating one and an approximating one.
Which two schemes would you use ? -- Why ? -- How ?
Describe the initial control mesh complete with a value for the circum-radius for each of the chosen schemes. Discuss the trade-offs of the resulting surfaces. Provide 2 images that show the control mesh and a (reasonably) smooth version of the surface (i.e., don't push SLIDE to the limit ...).

Bring your reports to class on Wednesday 10/22/2003.

Please place your "sphere" .slf files on your Windows account  (i.e. \\fileservice\cs284\fa03  in the directory ~/cs284/hw/pa5).

Next Reading Assignment:

Also: Start thinking about your Project Proposals