What is meant by C1 continuity? I saw this defined somewhat in discussion but it'd be great if someone could explain why this particular case has C1 continuity (vs C2, etc.)
lhagaman
C^n continuity means that the nth derivative is continuous. So C1 continuity means that the tangent vectors are the equal on each side of each boundary between splines (intuitively, it looks smooth and there are no kinks).
julialuo
So here since the interpolation is cubic everywhere other than the joining points, the joining points are only guaranteed to be C1 continuous but the rest are infinitely continuous? Are cubics and other polynomials infinitely continuous?
afang-story
Polynomials are smooth functions and C-n continuous for any n since you can take the nth derivative of it for any n.
What is meant by C1 continuity? I saw this defined somewhat in discussion but it'd be great if someone could explain why this particular case has C1 continuity (vs C2, etc.)
C^n continuity means that the nth derivative is continuous. So C1 continuity means that the tangent vectors are the equal on each side of each boundary between splines (intuitively, it looks smooth and there are no kinks).
So here since the interpolation is cubic everywhere other than the joining points, the joining points are only guaranteed to be C1 continuous but the rest are infinitely continuous? Are cubics and other polynomials infinitely continuous?
Polynomials are smooth functions and C-n continuous for any n since you can take the nth derivative of it for any n.