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Tong Lai Yu
Homework 2, due 2/25/2019 ( Mon ), 11:00 am

  1. ( 10 points ) Write a program that finds the knot vector ( u0, ..., un-1 ) of a B-spline. It asks for 'number of control points' and 'degree of spline' as inputs and prints out the knot vector.

  2. ( 10 points ) Write a program that plots all the blending functions of degree 3 ( m = 4 ) on the same screen.

  3. ( 10 points ) Cubic interpolating polynomial is used to find a point for a certain value of the parameter u. Suppose the points at u = 0, 1/3, 2/3, 1 are: P(0) = ( 0, 0, 0 )
    P(1/3) = ( 1, 2, 2 )
    P(2/3) = ( 2, 3, 4 )
    P(1) = ( 4, 5, 8 )
    Find the point at u = 0.8.

  4. ( 20 points ) Write a program that uses B-splines and some control points to generate a profile and then use the profile and surface of revolution to generate a graphic chess piece like the one shown in class notes. ( You can choose any chess piece. You can gain extra credit by doing more than one piece. )

  5. ( 20 points ) Find a Frenet frame for the toroidal spiral given by

    x(t) = [1 + 0.5 * cos ( 7t )] cos ( t )
    y(t) = [1 + 0.5 * cos ( 7t )] sin ( t )
    z(t) = 0.5 * sin ( 7t )
    Write a program that generates a tube using the above curve.



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