Interpolating function with two important characteristics


Hello!
I need an interpolating function Y=Func(Array,X) with these characteristics:

1) Passes through the points
2) At least the first-derivative must be continuos

As far as I know Catmull-Rom doesn't satisfy the 2nd point, and many other spline-like functions don't satisfy the 1st point.

Ideally, a third point would be that if the array contains a repeating pattern of 0,1,0,-1 then it should produce a sinewave.
It should produce a sine-like wave also if the repeating pattern is e.g. 1,-1 or 0,.707,1,.707,0,-.707,-1,-.707

Is it even mathematically possible? Should I give up? Or what should I Google for? :P

Many thanks,
Mike

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