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 create a cubic Hermite curves by specifying a sequence of points and tangent vectors at the specified points. For each pair of consective points and associated tangent vectors, a cubic curve is created that passes through the desired points and has the prescribed tangent vector.
  1. Play with the applet to determine the affect of the inputs for creating one cubic curve.
  2. How can you create a straight line with a cubic Hermite curve?
  3. How can you create a closed cubic curve? Can you create a smooth closed cubic curve?
  4. Determine rough placements of points (relations between the points) that guarantee the cubic will self-intersect.
  5. Determine rough placements of points (relation between the points) that guarantee the cubic will have a cusp (a place where the curve has no defined unit tangent vector).
  6. Classify the possible shapes of cubic curves and the inputs needed to create them.
  7. How do you create a smooth closed curve using more than one cubic arc?
  8. Describe how to create an approximate circle with n cubic arcs where n = 1, 2, 3, 4, ...