CS 284: CAGD 
Lecture #9 -- Tu 9/26, 2006.

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Review Rockwood pp. 94-117: B-Splines
Study handout: B+B+B: Effect of Knot Multiplicities

Creative Thinking

Topic:  B-Splines (cont.)

Reviewing some key aspects of B-Splines

Vertex Multiplicities

Non-uniform B-Splines

Knot Multiplicities

Knot Insertion (Curve Refinement)

Topics: Surface Patches

Preparation:  Rockwood Chapter 8: pp 133-151: Surfaces

From Curves to Surfaces Patches

Triangular Surfaces Patches

We can also deal with triangular patches, but need a different interpolation scheme:
Barycentric coordinates: three numbers, but with the constraint that they must sum to 1.0.
DeCasteljau evaluation technique can also be applied to triangular patches.

Reading Assignment:

Read the seminal paper by Catmull and Clark on subdivision surfaces

Current Homework Assignment: Construct a Parameterized Bell

Your task is to design a curved thin (metal) surface of finite thickness that has a chance of emitting a nice sound when struck and used as a bell.
There are many different ways in which such a surface could be defined: Some possible approaches to composing a Bell shape.
For this assignment you should concentrate of using a sweep in some form and using some spline for either the cross secition or for the guide curve, or for both.
{ Check out the code segment circle_sweep.txt in the CODE directory, for a practical way to make a circlar/cylindrical sweep around the z-axis}.
There should be from 3 to 5 parameters with wich you can change the shape of the bell interactively without loosing continuity in the overall surface.
Let yourself be inspired by this collection of pictures and references, but keep your shape simple!

Create a SLIDE file with all parameters set to their preferred values.
Capture your design pictorially using the screen saver.

DUE: Thu. 9/28/2006, 2:10pm.

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