Math 155 - Computer Graphics
U.C. San Diego - Winter 2001

Bezier problem set answers

1.  Handdrawn curve needd to be tangent at both endpoints to the bounding lines.

2.  q(1/2) = ( 21/8, 3/4)
     q(1/4) = (75/64, 9/16)

    For problem #2 it was necessary to show your work using the de Castaljau method.

3. Once problem #2 is done using the de Castaljau method, there is nothing left to do for problem #3, but write out the answer:

    q₁ has control points: (0,0), (1/2,1/2), (7/4,3/4), (21/8, 3/4)
    q₂ has control points: (21/8, 3/4), (7/2, 3/4), (4, 1/2), (3,0).

4.  The first half of the curve needed vertical slope at the beginning so its second control point had to lie on the positive z-axis.
     The end of the first curve needed slope -1/2, so its second control point had to lie on the line (-1/2)(3-x) = y. 

    Suggested answers for control points of first curve: (0,0), (0,1), (1,1), (3,0).  (Other answers possible.)

    The second curve had  -1/2 at its starting point and slope 1/2 at its ending point.

    Suggested answers for control points of second curve: (3,0), (3   2/3, -1/3), (4  1/3, -1/3), (5,0).