EXERCISES FOR WEEK 13

week13-1

Show that the standard knot vector for an order m = 3 B-spline curve based on eight control points is T = (0,0,0,1,2,3,4,5,6,6,6).
week13-2

What is the standard knot vector when seven control points are used for B-splines of order

  1. m = 3?
  2. m = 4?
  3. m = 5?
  4. m = 6?
  5. m = 7?
week13-3

Show that when m = L + 1 = 4 the B-spline functions are the Bernstein polynomials (the polynomials that went with the Bezier Curve.)

 
week13-4 Choose at least twenty 3D control points for a curve in space and plot them to the screen, using a fairly large point size and an appropriate color (so that you will eventually be able to distinguish them from points on the curve). Drop this into one of your previous projects that allows you to move around in the scene, so that you may be able to view the points from all directions.