CS 284: CAGD 
Lecture #8 -- Tue 9/18, 2012.

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Preparation: Read: "Fair, G2- and C2-Continuous Circle Splines," by C. H. Séquin, Kiha Lee, and Jane Yen. 

Warm-up Exercise: Comparison of Different Splines

Wrap-up:  B-Splines

Vertex Multiplicities on Uniform B-Splines (different from Knot Multiplicities, see below)

Playing with the Knots: Non-Uniform B-Splines

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

Goal:  To obtain nice round loops with gradual change in curvature.
Basic idea:  If circles are your ideal shape, build on circular primitives.

Key difference: These are curves that are not subject to the "Linear-Precision Collapse"
"Fair, G2- and C2-Continuous Circle Splines," by C. H. Séquin, Kiha Lee, and Jane Yen (2005).
Comparison of different interpolation schemes an the interpolation task in "B+B+B", Chapter 3:
Comparison of those schemes on the more challenging example task used at the beginning of this course: Going beyond Circle Splines:

"From Spiral to Spline: Optimal Techniques in Interactive Curve Design" Ph.D. thesis by Raph Levien (2009).
A summary of some of the above findings:
Interpolating Splines: Which is the fairest of them all?  by Raph Levien and C. H. Séquin (2009)

"Minimum Curvature Variation Curves, Networks, and Surfaces for Fair Free-Form Shape Design" Ph.D. thesis by Henry Moreton (1993).
We will talk about this in the context of optimized surfaces.

Bottom Line:  Polynomials are not the only possible primitives !

Homework Assignments:

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

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