CS 284: CAGD 
Lecture #7 -- Thu 9/13, 2012.

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Read:  Rockwood:  pp 76-83; pp 89-92 (basic labeling scheme for Blossoming)

Read:  Rockwood:  pp 94-103 (basics of B-splines)

Warm-up Exercise: Designing a C2-continuous interpolating curve

Questions about Homework Assignment?

Blossoms (cont.)

A geometrical view of iterated "multi-level" inter-/extra-polation,
which allows us to see the various spline types in a unified manner and to convert easily between them.

Topic:  B-Splines

The deBoor Algorithm (= deCasteljau for B-splines)

Multi Segmented B-Splines

B-Spline Basis Functions

The Behavior of B-Splines

Non-uniform B-Splines

Knot Multiplicities (an extreme case of non-uniform knot spacings!)

Circle Splines, Spiral Splines, Minimum-Variation Curves (MVC)

These are curves that are not subject to the "Linear-Precision Collapse"
Motivation: you want to obtain nice round loops with gradual change in curvature

"Fair, G2- and C2-Continuous Circle Splines," by C. H. Séquin, Kiha Lee, and Jane Yen (2005).

"From Spiral to Spline: Optimal Techniques in Interactive Curve Design" Ph.D. thesis by Raph Levien (2009).

"Minimum Curvature Variation Curves, Networks, and Surfaces for Fair Free-Form Shape Design" Ph.D. thesis by Henry Moreton (1993).

Homework Assignments:

Review: Rockwood pp. 94-117: B-Splines .

Study handout: B+B+B: "Effect of Knot Multiplicities" and answer this question:
-- What is the key difference in the result (if any) of piling multiple knot values on top of each other and placing multiple control points on top of each other?

Read: "Fair, G2- and C2-Continuous Circle Splines," by C. H. Séquin, Kiha Lee, and Jane Yen.  Then write a few sentences on the following issues:
-- What are the one or two key lessons learned from this paper, regarding the design/introduction of a new CAD technique (such as a new curve type)?

Send your answers to both questions to me by e-mail by Monday, September 17, 2012,  8pm. -- Thanks.

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