CS 284: CAGD 
Lecture #3 -- Wed 9/02, 2009.

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Rockwood: pp 31-58.

Warm-up Exercise: Draw Bézier Curves ...

Tomorrow, Thu, Sep. 3, 12:30pm-1:30pm in 380 Soda Hall:
PhD dissertation talk by Raph Levien:
From Spiral to Spline: Optimal Techniques in Interactive Curve Design.

Lecture Topics:  Bézier Curves

Understanding the Properties of Bezier Curves

Homework Discussion: What can you do with Bézier Curves?

Bernstein Basis Functions

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

Working with Bézier Curves

Stitching Bezier Curves Together

New Reading Assignment:

Rockwood: pp 59-73 (Lagrange Interpolation)

New Homework Assignment: G1-Stitching of Bezier Curves

In this first programming assignment you will be introduced (gently) to SLIDE and to the Tcl language. Your actual programming will be less than ten lines of code (most of the expressions you will need have already been provided), but it encourages experimentation and thinking.  The hard part is to actually get Slide to load an function properly on your computer. SLIDE is very particular about having all the paths set up properly, the variables in the right place, and using exactly the right version of Tcl. But it will be worth the effort, because we can then do many instructive experiements quite quickly. Good luck!

The first such experiment using SLIDE is to learn how to stitch cubic Bezier segments together to make a smooth, pleasing-looking, interpolating curve that behaves well even for rather ragged control polygons with irregularly spaced control points (like the example we did in class by hand).

Your assignment is to find a robust expression for the placement for the inner control points of each Bezier segment, involving only information from the nearest neighbor points, and which guarantees a G1-continuous overall curve.

Information on how to install SLIDE on your computer can be found at:

The first file that you should try to run is:
Make sure that you have in the same directory the files: MATH.tcl, MOVIE.tcl, SLFCONSTS.tcl, SLIDEUI.tcl
Then you may try other files in that same directory: Instancing.slf, IcosaGen.slf, SweepDemol.slf, GearMovie.slf

DUE: Wed Sept. 9, 2009:   Have SLIDE installed and the provided version of "pa1.slf" running.

For your first programming assignment, the code that you should modify and execute, can be found at:

DUE: Mon Sept. 14, 2009:   Have your modification of "pa1.slf" running. Hand in:

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