Bezier Curves Exploration: Calculus II, Fall 2003

   Bezier Curves Introduction & Examples

After reading the introduction above, experiment with the following applet and try to get a good feeling for the possible shapes that can be created with one Bezier curve:

   Bezier Curve Applet

Using the following Bezier matrix, it is easy to construct a parametric Bezier curve.  This is illustrated using the four control points for each of the four examples in the first link above. Check it out !

   Bezier Matrix Transformation

Next, use the following applet, which allows several Bezier curves to be connected together, to write your first and/or your last name in cursive.  When you are happy with how this Bezier version of your name looks, use the applet grid feature to produce a background grid under your name, and then create a screen capture of your name, paste it into MS Word, and print it out.  Finally, label the control points on the grid of this hardcopy version, and then use the Bezier matrix to find the formula for the parametric curve for each curve segment in your name.

  Connected Bezier Curves Applet

In each of the next two applets there is a cross section of an airfoil (airplane wing) that is to be modeled (by you ;-) in two different ways.  The first applet uses Bezier curves and the second uses least squares regression. There are instructions and exercises in each applet. Your task is to complete each exercise and then compare your results. Which applet produces the best model? Why? Explain.

In the following applet the directions are below the air foil image: 

  Bezier Air Foil Applet

In this one there is an Ex. 1 button at the lower right of the image: 

  Regression Air Foil Applet