Answer Happy

Given the following Data Points
2 4
4 5
5 6
8 3
9 4
1. Cubic Splines
Using a pseudo-inverse, find the CubicSpline that interpolates the endpoints, and best approximates theremaining data points.
2. Bezier Curves
a) Using a pseudo-inverse, find a quadratic Bezier Curvethat best fits the data points.
b) Now, find a cubic Bezier Curve that best fits the datapoints.
c) Now, find a 4th order (quartic) Bezier Curve that best fitsthe data points.
d) Using de Castejau’s Algorithm, find the set of quadraticBezier Curves that also has five control points.
3. B-splines
a) Using a pseudo-inverse, find the best fit quadratic B-splinecurve for the data points, with an open uniform knot vector.
b) Repeat the process for a cubic B-spline curve with an openuniform knot vector.
c) Create a pair of quadratic B-splines that interpolate thedata set while maintaining slope continuity at (5,6).
4. NURBs
Using any approaches that you choose todefine the knot vector and weights, define a NURBs curve thatapproximates the data provided. Explain your approach.
5. spatial curves
Given data set
2 4 4
4 5 1
5 6 -3
8 3 1
9 4 6
a) Using a pseudo-inverse, find the Cubic Spline thatinterpolates the endpoints, and best approximates the remainingdata points.
b) Using a pseudo-inverse, find a quadratic Bezier Curve thatbest fits the data points.
c) Using a pseudo-inverse, find the best fit cubic B-splinecurve for the data points, with an open uniform knot vector.