CS 284: CAGD 
Lecture #4 -- Wed 9/09, 2009.

PREVIOUS < - - - - > CS 284 HOME < - - - - > CURRENT < - - - - > NEXT


Rockwood: 59-73 (Lagrange Interpolation)

Warm-up Exercises: Bézier Curves

Main Lecture Topic:

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

Options that we will discuss:
-- stiching together Bézier curve segments;
-- Hermite Splines;
-- Lagrange Interpolation.

All these splines are polynomial based; all of them are invariant under affine transformations,
thus for all of them each coordinate component can be dealt with individually.
All of these spline types have some unconstrained DoFs that can be used for optimization.

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

Comments on SLIDE and Tcl -- Q&A

Don't forget to load those TCL files in the CODE directory into your working directory!


SLIDE will be set up in 330 Soda on the 6 machine on the wall opposite the entry doors.
The door of 330 is open during the day; in the eveing your key card should give you access if you are enrolled in a CS course.
You need an account to use these machines. I can expedite this if you send me your e-mail and your student ID,
  which I will then forward to the EECS Instructional Support Group.

(Cubic) Hermite Splines

Higher-Order Hermite Splines

Preview of Lagrange Interpolation

New Homework Assignment: G1-Stitching of Bezier Curves

Assuming that you have been able to install SLIDE on your computers,
or have access to some machine where you and your buddy can play with SLIDE,

your first 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.

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


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

PREVIOUS < - - - - > CS 284 HOME < - - - - > CURRENT < - - - - > NEXT
Page Editor: Carlo H. Séquin