CS 284: CAGD 
Lecture #11 -- Tu 10/3, 2006.


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Preparation:

Paper by Doo and Sabin on Behavior of subdivision surfaces near extraordinary points

Warm-Up Discussion:  How to design a "Multi-Spiral Surface"?

How to get started: ... with pipe cleaners:  Net1 ... Net2 ... with paper models ...
Design phases.

Topics: Subdivision (cont.)

Conceptual Bridges to Splines, Fractals, and Affine Transformations

Topological Limitations of the B-spline Control Mesh

Doo, Sabin Paper: Focus on a quadratic subdivision surface

Subdivision Masks for Surfaces


Reading Assignments:

Chapter 2 and 3 from:
C. Loop, "Smooth Subdivision Surfaces Based on Triangles", Master's thesis, University of Utah, Department of Mathematics, 1987.

(! Large Document -- perhaps read on-line !)

Current 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, Noon!:

PHASE III --DUE: Tu. 10/10/2006, Noon!:



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



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