CS 284: CAGD 
Lecture #2 -- Th 8/31, 2006.

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Read:  RC pp 31-48.

Lecture Topics

Brain Teaser of the Day

Homework Discussion

Quick Review of Some Important Concepts

How to Draw Smooth Curves

Administrative Intermezzo

Definition of Cubic Bezier Curve

Bernstein Basis Functions

Understanding the Properties of Bezier Curves

New Homework Assignment:

Use Rockwood's Interactive Curve Editor CAGD_LAB. Open the applet shown on page 52 of the book, labelled "Higher Degree Bezier Curves" for the following tasks:
  1. Using a heptic Bezier curve {this is degree 7, order 8; using 8 ctrl pts; ==> different ways of saying the same thing},
  2. model G-1 continuous {continuous tangent directions} closed loops of as many different turning numbers
    {the # of times the tangent vector sweep around 360 degrees} as possible -- at least for turning numbers 0, 1, 2.
  3. What order Bezier curve is needed to make a (G1-smooth) loop of turning number 3 ?
  4. Using the minimum number of control points (=minimum order Bezier), make a G1-continuous "figure-8" Bezier curve with overall C2-point-symmetry
    {= 2-fold rotational symmetry around a point that will bring the figure back onto itself after a 180-degree rotation around this point}.
DUE: TU 9/5/06, 2:10pm.
Hand in: window snapshots showing your solutions;
label your figures with their turning numbers;
put your name on your hand-ins
add explanatory comments as necessary.

On the PCs you can hit Alt+PrnScrn to capture the current active window to the clipboard.
You can then paste the clipboard into a program such as "paint" and from there readily send it to the printer.
"SnagIt" is another great screen/window/region-saving application that you can download.

Next Reading Assignment:

Rockwood: pp 49-73.

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