CS 284: CAGD
Lecture #14 -- Th 10/12, 2006.

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Preparation:

Labsik and Greiner: "Interpolatory Root-3 Subdivision".

Warm-Up: What did you learn from the "Root-3" paper ?

Topic: Interpolating Subdivision Schemes for Surfaces (cont.)

Discussion of the "Root-3" paper:

What are the key ideas in the paper ?
What is the topological subdivision stencil ?
What is the formula for placing the new face vertex ?
How many vertices are involved in computing the new point ?

in the regular case ?
in the irregular cases ?

Treatment of boundary edges ?
How can such interpolated regions be stitched together ?
What are soem of the NEW concepts that we have not yet discussed in class ?

Forming cusps or creases by joining two patches along a common boundary curve ... (more below)
Variable "depth" subdivision for adaptive refinement ... see: Leif Kobbelt: "Root-3 Subdivision", Siggraph 2000.
For a good topological subdivision step:

there is always an approximating scheme to place new vertices
and often there is also an interpolating scheme for vertex placement.
(see comparison list below).

Adaptive Refinement by Subdivision

Figures from: Leif Kobbelt: "Root-3 Subdivision", Siggraph 2000.
The basic root-3 scheme.
Typical mesh generated.
The "rotation" implied by a single subdivision step.
Adaptive refinement to different levels -- may cause cracks.
Bad triangles or a large "transition zone" are generated to reach a desired deep level of subdivision.
Root-3 scheme has no crack problem and generates good transition zones.
Nice adptive refinement meshes on "the bunny".
Maintaining smooth boundaries in the root-3 scheme.
Forming cusps or creases by joining two patches along a common boundary curve.
The root-3 scheme allows finer gradation of uniform subdivision than the Loop scheme.
How would you do adaptive refinement in your own quad scheme ?

Summary of Subdivision Schemes:

DOO_SABIN
-- quadratic, approximating; quadrilateral facets.
CATMULL_CLARK
-- cubic, approximating; quadrilateral facets.
LOOP
-- quartic, approximating; triangular facets.
Butterfly Scheme
-- cubic, interpolating; triangular facets.
ZORIN
-- cubic, interpolating; triangular facets.
Interpolating Root-3 Subdivision
-- cubic, interpolating; triangular facets.
Your-Own Quad-Scheme
-- cubic, interpolating; quadrilateral facets.
KOBBELT: Root-3
-- cubic, interpolating; triangular facets.
HALSTEAD: Interpolating Catmull-Clark
-- cubic, interpolating; quadrilateral facets.

When should you choose which subdivision scheme ??

Sharp Features in Subdivision Surfaces

Many objects have a combination of smooth, rounded surface elements and sharp edges and corners (examples ... ?).

Remember what we did with splines to obtain sharp kinks and corners (discuss ... !).

Now we need to do the same thing for subdivision curves and surfaces....
Key paper:
"Subdivision Surfaces in Character Animation" DeRose et al.
PREVIEW:
Start with Catmull-Clark Subdivision
Introduce sharp features: creases, edges, corners...
Add smooth variable radius fillets and blends with
a mix of sharp and smooth subdivision steps:
-- take s sharp steps and then all smooth steps afterwards.
Blend between a sharp and a smooth subdivision step.
ALSO:
Modelling of loose clothes.
Collision detection.
Smooth scalar fields for texturing.
...

Results from Spiral Surface Assignment ...

Make Your Paper Selection & Start thinking about your Course Project

==> PROJECT-PLANNING

Look at the Paper Selection List -- Pick your top five candidates -- Fill out questionaire (handout) by Tuesday 10/17.

Reading Assignment:

"Subdivision Surfaces in Character Animation" DeRose et al.
Be prepared to answer the following questions:

What subdivision scheme are they using ?
What are the key additions to that scheme that they have made ?
Why do they prefer quadrilaterals ?
What is the basic approach to creating semi-sharp edges ?
What is the underlying model for cloth simulation ?
How is excessive wrinkling of the cloth avoided ?
What are virtual threads ? -- and what is their purpose ?
What is the data structure to make collision detection efficient ?
How is made it possible to apply texture maps and procedural shaders ?
What was one of the general implementation requirements for the Pixar production environment ?

Current Homework Assignment: -- Two options to choose from:

Implement your proposed quad subdivision scheme as a team (in the language of your choice).
Hand in a report of your apporach (can be same or extended version of your first report)
and describe your findings, difficulties, insights.
Add a couple of pictures of test cases that show what your implementation can do.

OR:
Compare several different subdivision schemes in SLIDE.

Also summarize your findings in a report with pictures of crucial test cases.

DUE: TUESDAY 10/17/2006, 2:10pm.