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. This is a generalization of the method to construct a parabola using three points as P(t) = (1-t)2 P0 + 2t(1-t) P1 + t2 P2. The t slider illustrates the construction of the curve by de Casteljau's algorithm, constructing specific points p01(t), p11(t), p02(t) to construct a parabola. This will be explained in full detail next week.
  1. Create a parabolic segment. How does each point effect the shape of the curve? [Move one point, and examine the change of the curve.]
  2. For what values of t does the first control point P0 have an affect on the shape of the curve?
  3. For what values of t do the other control points have am affect on the shape of the curve?