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5.5 PRACTICE PROBLEMS

1. Use a Bezier spline to fit the four points below. If the curve is scaled from 0 to 1, find the point at 0.5 along the curve.

2. We plan to use a Bezier spline to fit the four points below. The curve should be scaled from 0 to 1 along the curve and be represented with matrices. Set up the matrices to calculate the coefficients for these equations. (do not solve the matrices)

3. Derive the matrix form of equations for a new type of spline that has the following properties. It is defined by three points and a derivative. The middle point ‘P2’ and the derivative ‘D’ are both at the center of the curve (0.5). The first and last points ‘P1’ and ‘P3’ are at the ends of the curves (0 and 1 respectively).

4.