CS 284: CAGD 
Lecture #10 -- Th 9/28, 2006.

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


Read the seminal paper by Catmull and Clark on subdivision surfaces

Warm-Up:  Devise an interpolating subdivision scheme

Topics: Subdivision

Introduction to "General Subdivision (with modification)" Techniques

Conceptual Bridges to Splines, Fractals, and Affine Transformations

Topological Limitations of the B-spline Control Mesh

The Classical Subdivision Surfaces by Catmull & Clark

= foundation for all modern subdivision algorithms.

Another Subdivision Surface

Reading Assignments:

Paper by Doo and Sabin on subdivision surfaces

New Homework Assignment: Create a Subdivision Surface

Create a doubly or triply spiralling surface.
Similar to the Creative Thinking Exercise on Koch's Snowflake Curve, you should try to find a surface in 3D space that is inspired by a logarithmic spiral in the plane.
However, you must not just extrude a logarithmic spiral in a direction perpendicular to the spiral plane. You should create a surface that shows some spiralling cut lines when cut in as many different orientaions as possible. The surface will probably have to have some (spiralling?) edges -- which is good, because this will define some windows through which one can look inwards to the inner parts of the surface.

Keep your surface modular. Model as little as absolutely needed; then put multiple copies suitably re-oriented together to make the complete surface.
In addition to exploiting symmetry at one (spherical) level of the surface, you should then extend the surface inward or outward by simply making suitably scaled copies of one layer of that "onion-like" assembly. The use of one or two parameters to optimize the look of the surface is encouraged.

I have put some SLIDE starting file "spiral.slf" into the CODE directory. It has most of the basic elements that you will need to build such a surface and shows how to do mirroring, scaled instanciation, and subdivision. I also have included some token parameters so you can get started with something that already works and then do incremental modifications.

PHASE I --DUE: Tu. 10/3/2006, 2:10pm:

Plan the topology (connectivity and rims)
of your surface to get the desired spiral patterns locked in. Give me something by Tuesday at the latest that allows me to give you feedback whether you are on a good track. You can either give me a paper and pencil sketch, or a rudimentary slide file that shows the basic geometry, even though not all pieces fit together seamlessly yet. Feel free to e-mail me images or SLF files before Tuesday.

PHASE II --DUE: Th. 10/5/2006, 2:10pm:

The final  surface: SLF file and captured image.

NICE JOB ON THE LAST ASSIGNMENT !!   See my Bell Selection.

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