Exercise set 5: B-splines
Feel free to use the built-in BSplineBasis[] function, but nothing more advanced!

1. Plot the B-spline basis of degree 3 with the following knot vectors:
1.1 {0,0,0,0,1,2,3,4,5,6,7,7,7,7}
1.2 {0,0,0,0,4/3,2,3,13/3,5,6,7,7,7,7}
1.3 {0,0,0,0,1,1,2,3,4,5,6,6,6,6}
1.4 {0,0,0,0,1,1,1,2,3,4,5,5,5,5}
1.5 {0,0,0,0,1,1,1,1,2,3,4,4,4,4}

2. Plot B-spline curves (Subscript[c, 1]), (Subscript[c, 2]), (Subscript[c, 3]), (Subscript[c, 4]), (Subscript[c, 5]) of degree 3 using the knot vectors from previous exercise and the following control points:
{{0,0},{1,0},{2,-1},{3,1},{4,2.5},{5,3},{6,5},{5,6},{3,6},{0,5}}

3. Plot a B-spline curve (Subscript[c, 6]) with the knot vector {0,0,0,0,1,1,1,2,3,4,5,5,5,5} and the following control points:
{{0,0},{1,0},{2,-1},{3,1},{7,3},{5,3},{6,5},{5,6},{3,6},{0,5}}
3.1 Plot curves (Subscript[c, 4]) and (Subscript[c, 6]) in the same picture and compare them.

4. Translate the curve (Subscript[c, 4]) by {-3, -1} and rotate it by ((7π)/23) around the point {5,3}. Plot the resulting curve.

5. Write a function for the knot insertion algorithm.
5.1 Insert knot (Subscript[t, 0])=3 into the curve (Subscript[c, 7]) of degree 3 with knots {0,0,0,0,1,2,4,7,8,9,10,10,10,10} and control points {{0,0},{1,1},{1,2},{0,3},{-2,3},{-3,2},{-4,0},{-4,-2},{-3,-3},{0,-3}}.
5.2 Find the point (Subscript[c, 7])((22/3)) using the knot insertion algorithm. Find the tangent at this point.
5.3 Divide the curve (Subscript[c, 7]) at the point (Subscript[t, 0])=3 into two curves (using the knot insertion algorithm).