Using fairly simple language, what is Hermite data? I encountered it here, http://www.frankpetterson.com/publications/dualcontour/dualcontour.pdf and could not get an answer on standard StackExchange, who 'referred' me to here.
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Hermite data is the value of a function and all its derivatives up to some order at all points of a data set. It is used in Hermite interpolation.
If you do not supply all the derivatives for all points, then you have Birkhoff data, also called Hermite–Birkhoff, which of course is used in Birkhoff interpolation.