CS 284: CAGD
Lecture #27 -- We Nov. 29, 2000.

Preparation

Hints for Project Presentations

Single person presentations: 10 minutes, + 2 min. for Q&A
Two person presentations: 12 minutes, + 3 min. for Q&A

Your presentation should touch upon the following points:

• (Briefly: <1min.) What the project is all about:
  - title, authors, general goal(s);
  - perhaps a conceptual picture of desired result (from proposal presentation).

• (Briefly: <1min.) Original scope and hopes:
  - what did you originally hope to achieve ?
  - what was originally promised ?

• (5-6min.) Accomplishments, status report, preliminary demos:
  - what has actually been achieved so far ?
  - what unexpected problems have been encountered ?
  - how did you (try to) overcome them ?
  - show pieces of your program that work.
  - what do you realistically believe you can achieve by Dec. 13 ?

• (2-3min.) Critical evaluation of results:
  - discuss strengths and weaknesses of the approach taken.
  - what would you do differently, if you could "rewind the clock" ?

• (Briefly: <1min.) Concluding remarks:
  - what is the (lasting?) contribution of your project ?
  - what have you learned in this project ?

A Rational Curves and NURBS

Rational Curves

• Motivation
  -- represent conic sections
  -- more design flexibility (?)
• The notion of weights
  -- their influence
• Projective interpretation
  -- review of basic facts
  -- the effect of the w coordinate

2D Rational Bezier Curves

• Formulas (p. 121)
• Qualitative influence of weights (p. 122)
• Making conic sections (p. 124)
• Difference between changing position and weight of control point (p. 129)
• DeCasteljau algorithm for rational Bezier curves (p. 129)

How to Make a Circle

• Using rational quadratic Bezier curves
• Using rational cubic Bezier curves
  -- Use Bezier degree elevation
  -- But in Projective Space !

• Using rational quadratic B-splines
  -- Can we use blossoming to convert Bezier points to deBoor points ?
• Using rational cubic B-splines
  -- Can we use B-Spline degree elevation
  -- Not so simple -- Need to do it in Projective Space

Rational B-Splines

• Formulas (p. 131)
• NURBS
• Usage examples
  -- cylinders
  -- spheres
  -- tori

New Homework Assignment:

Prepare your Project Presentations

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