CS 284: CAGD 
Lecture #4 -- Th 9/07, 2006.

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Read:  RC pp 59-73.

Warm-up Exercises: Bézier Curves

Main Lecture Topic:

How to make interesting, complex, smooth curves that interpolate given points.

Last lecture: How to use Bézier curve segments, properly stitched together, to make an interpolating spline.
This lecture: Other approaches: Hermite Splines; Lagrange Interpolation.
All types of splines thus far, are polynomial based; all of them are invariant under affine transformations,
thus for all of them each coordinate component can be dealt with individually.
For a given curve interpolation problem, all of these spline types have some unconstrained DoF that can be used for optimization.

Stitching Bézier Curves Together -- what choices do we have ?

Comments on SLIDE and Tcl -- Q&A

Also load those TCL files in the CODE directory!

(Cubic) Hermite Splines

Higher-Order Hermite Splines

Preview of Lagrange Interpolation

Current Homework Assignment: G1-Stitching of Bézier 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 goal 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.

DUE: Sept. 12, 2006, 2:10pm. -- Hand in:

The code that you should modify and execute, can be found at:

Also copy the TCL files:  MATH.tcl, SLFCONSTS.tcl,  SLIDEUI.tcl  to the directory in which your run your SLIDE file.

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

Reading Assignment:

Read again:  RC pp 59-73  and  pp 93-97; 108-112 (preview of B-Splines)

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