Question about linear splines


I have a question about the linear splines option in your package. The documentation is here:

My question is about the constructor. It takes the x-vector of length N+1 this I understand.

It then takes the c0 vector of length N or N+1. Why does it not have to be of the same length as the x-vector? Why can it be of one less?

The next vector is the c1 vector of the slopes. Why do we have to provide this vector? Is it not uniquely determined by the x-vector and the c0-vector?