3. The following set of data is to be "best fit" using a quadratic (degree 2) B-spline. The number of control points to be used is 5. Since there are more data points compared to control points a least squares best-fit solution is required. Assume the data points will be assigned to parametric (u) values that are spaced evenly from 0 to 1. The B-spline is to be non-periodic (the end-points pass thru the first and last controls points). Note that in general none of the data may actually lie on the best-fit curve. (a) Determine the control point locations. Note data is 2D (x and y coordinates only) so the z component of the control point can be considered as zero for all control points. (10 pts) (b) Plot the data points and best fit B-spline curve (plot Y versus X). (10 pts) (c) Determine the length and centroid location of the curve using 1 point, 2 point and 3 point Gauss quadrature rule(10 pts) Data Point 0. 0.50 1 0. 2. 4 4 9. 12. 15 18 3.5 5. 4.5 3. The following set of data is to be "best fit" using a quadratic (degree 2) B-spline. The number of control points to be used is 5. Since there are more data points compared to control points a least squares best-fit solution is required. Assume the data points will be assigned to parametric (u) values that are spaced evenly from 0 to 1. The B-spline is to be non-periodic (the end-points pass thru the first and last controls points). Note that in general none of the data may actually lie on the best-fit curve. (a) Determine the control point locations. Note data is 2D (x and y coordinates only) so the z component of the control point can be considered as zero for all control points. (10 pts) (b) Plot the data points and best fit B-spline curve (plot Y versus X). (10 pts) (c) Determine the length and centroid location of the curve using 1 point, 2 point and 3 point Gauss quadrature rule(10 pts) Data Point 0. 0.50 1 0. 2. 4 4 9. 12. 15 18 3.5 5. 4.5