# splines with derivative conditions at support points

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Maximilian Dio on 6 Jul 2021
Answered: Bruno Luong on 6 Jul 2021
Hi I am trying to cubically interpolate my data but I know the derivatives at these points too. I have only found the csape function to define the derivatives at the end points -> "clamped" however I could not find how to enforce the derivatives at the support points too.
Thanks for a response..
Regards max
Are Mjaavatten on 6 Jul 2021
The cubic polynomial on the interval to must satisfy four conditions: , , and . This uniquely determines the polynomial, leaving no room for the usual requirement that the second derivative should be continuous. To obtain this, you would need quartic splines. John d'Errico's answer and comments to Clay Fulcher's question may be of help. (I do not have the Curve fitting Toolbox so I cannot test this.)
Maximilian Dio on 6 Jul 2021
Edited: Maximilian Dio on 6 Jul 2021
I can enforce the conditions in this for but I would like to have somethiing a build in function - this seems to be not so nice)
for i = 1:numberOfSegments
pp{i} = csape([x(i),x(i+1)],[y(i),y(i+1)],'complete',[dy(i),dy(i+1)]);
end
or even better a 5th order spline where the 3rd derivative is also continous...

Bruno Luong on 6 Jul 2021
There is the option point-wise constraints (pntcond) of my FEX BSFK to achieve your goal.

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