CS 284: CAGD 
Lecture #11 -- Mon 10/5, 2009.

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Paper by Doo and Sabin on subdivision surfaces

Chapters 2 and 3 from: C. Loop, "Smooth Subdivision Surfaces Based on Triangles"
This is also a nice review of B-spline subdivision!
Some errata found in this thesis.

Warm-up: Understanding Subdivision and Its Analysis

Topic: Subdivision (cont.) 

Key points about useful subdivision schemes:

Doo, Sabin Paper: Focus on a quadratic subdivision surface

Comparing Subdivision Schemes for Surfaces

Tensor-product patches, e.g., cubic tensor-product Bezier patches;
readily do in the "u" and in "v" directions what we have learned about curves.

We can also use 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!

Evaluation / Analysis of Subdivision Schemes

How do we know whether a particular interpolation or subdivision scheme is any good ?

Testing / Evaluation by Visual Inspection

Formal Analysis of Blending / Subdivision Methods

Discussion of Your Genus-4 Designs...

Reading Assignments:

Zorin et al: "Interpolating Subdivision Meshes with Arbitrary Topology"

Optional, if you are interested in the details of analyzing a particulart subdivision scheme: 
hapters 4 and 5 from:  C. Loop, "Smooth Subdivision Surfaces Based on Triangles"

Current Homework Assignment:

Design the Control Mesh for a Smooth Genus-4 Surface.

The goal is to design a highly-symmetrical control mesh for a closed genus-4 subdivision surface based on triangles
(which could be later used for experiments in surface-energy minimization studies).
Following an iterative design process, we will do this in stages:

Paper Presentation Assignments (for the future)

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