We are given the following boundary conditions for cubic spline section:

P(0) = pk
P(1) = pk+1
P00(0) = pk-1 + pk+1 - 2pk
P00(1) = pk + pk+2 - 2pk+1

In this case Mgeom = [ pk-1 pk pk+1 pk+2 ]T and boundary conditions can be written

P(0) 0 1 0 0 Pk-1
P(1) 0 0 1 0 PK
P''(0) = 1 -2 1 0 . PK+1
P''(1) 0 1 -2 1 Pk+2

(a) Given Mgeom as specified above, deduce 4 by 4 matrix Mspline.
(b) Given your solution for Mspline write blending functions for this curve.
(c) Give equation P0(u) for tangent to this curve in terms of Mspline and Mgeom.
(d) Do adjacent segments satisfy C1 continuity? Give mathematical justification.
(e) Do adjacent segments satisfy C2 continuity? Give mathematical justification.