CS 284: CAGD 
Lecture #2 -- Tue 8/28, 2012.

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read Rockwood: pp 20-48:

You should find access to a Windows machine and download the CAGD_LAB  from:
You can also use the workstations in 349 Soda Hall. (Account forms handed out in class)

Warm-up Question for the Day


How to Draw Interpolating (Smooth) Curves

Bézier Curves

Bernstein Basis Functions

Basic Underlying Math;

Understanding the Properties of Bézier Curves

Drawing Bézier Curves:  de Casteljau Algorithm  ( "cass - tell - sho" )

New Homework: What can you do with Bézier Curves?

Use Rockwood's Interactive Curve Editor CAGD_LAB. Open the applet shown on page 52 of the book (Ch3, 70%down),
labelled "Higher Degree Bezier Curves" for the following tasks:
  1. Using a septic (heptic) Bézier 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 as possible
    {the # of times the tangent vector sweep around 360 degrees}  -- Do it at least for turning numbers 0, 1, 2.
  3. 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: THU 8/30/12, 2:40pm.
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.

Recent Homework Discussion

Quick Review of Some Important Concepts

Administrative Comments

Next Reading Assignment:

Rockwood: pp 31-58.

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