We are given the following boundary conditions for a 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 the 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) (15 points) Given Mgeom as specified above, derive the 4 by 4 matrix Mspline.

(b) (10 points) Given your solution for Mspline write out the blending functions for this curve.

(c) (10 points) Give the equation P0(u) for the tangent to this curve in terms of Mspline and Mgeom.

(d) (10 points) Do adjacent segments satisfy C1 continuity? Give a mathematical justification.

(e) (10 points) Do adjacent segments satisfy C2 continuity? Give a mathematical justification.

### Recently Asked Questions

- How much will a $ 28,100 EE savings bond cost when you initially purchase it? Assuming the bond earns 1.58 percent annually, approximately how long

- QUESTION 11 Under the Uniform Commercial Code, a "note" is best defined as: An obligation that is conditioned upon the occurrence of a future event. A document

- At a meeting, over drinks, a member asks Gazelle if she knows anything about the relationship between beer consumption and income. She takes her cocktail