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Can a point have different left and right tangents? It seems like that's how we can get the spline from the previous slide to not have C2 continuity but it doesn't look like this definition allows this


Are endpoints not double differentiable?


To clarify, do we not require that endpoint positions of adjacent segments match up? It seems like we don't, since you say that we have 2n degrees of freedom for the endpoint positions, but it feels counterintuitive.


In practice, how do we define the value of the tangent at end points?


Why this does not follow C2 continunity?


For people asking why this isn't C2 continuous, look at the previous slide's f2. It's not differentiable.


What if the tangent is infinity (vertical)?