MOTIVATING  GEOMETRY THROUGH
COMPUTATION  AND  VISUALIZATION
funded by NSF-CCLI grant DUE-0126687

 Principal Investigator
David L. Finn
Associate Professor of Mathematics
Rose-Hulman Institute of Technology
Finn's Page | CCLI Info | Applets | Materials | Course Notes | Publications
EXERCISES to EXPLORE with this APPLET
In this applet, you place control points to create a polynomial curve by de Casteljau's algorithm. The t slider illustrates the construction of the curve by de Casteljau's algorithm.
  1. Create a cubic curve. How much does each control point effect the shape of the curve?
  2. Create an inventory of cubic curve shapes. How do the relative positions of the control points affect the shape of the curve. How many "different" shapes can you create with a single cubic curve?
  3. For what values of t does the first control point p0 have an affect on the shape of the curve?
  4. For what values of t do the other control points have an affect on the shape of the curve?
  5. Can you use the intermediate points in de Casteljau's algorithm to determine the tangent line to the curve at a point? What about the derivative of c(t)?
  6. Play with de Casteljau's algorithm. Create some higher order curves and repeat the above exercises.