Note that in general, if we want to find a degree-3 polynomial, we need 4 values to determine a unique one. Here we pick these four points that are at endpoints and are easy to work with.
killawhale2
@kingdish I think the phrase "four points" is not correct in this context as the four independent conditions are 2 points and 2 derivatives at the said points. I'm pretty sure that the points are picked first and THEN a cubic polynomial is interpolated meaning that we don't pick the endpoints, rather we consider the points that we picked as the endpoints of some cubic polynomial in the sampled interval. Please correct me if I'm wrong.
Note that in general, if we want to find a degree-3 polynomial, we need 4 values to determine a unique one. Here we pick these four points that are at endpoints and are easy to work with.
@kingdish I think the phrase "four points" is not correct in this context as the four independent conditions are 2 points and 2 derivatives at the said points. I'm pretty sure that the points are picked first and THEN a cubic polynomial is interpolated meaning that we don't pick the endpoints, rather we consider the points that we picked as the endpoints of some cubic polynomial in the sampled interval. Please correct me if I'm wrong.