🚀 go-pugleaf

The Nyquist theorem does not require equal spaced points.  Equal
spacing is convenient, and good in terms of S/N ratio.  If your
samples are infinitely narrow (points in time), then, theory says 
that if you multiply each point by a dirac delta function centered
at that time, and filter it through the appropriate band limiting
filter, you will get the same result as the original signal 
through such band limiting filter.  If the points are not equally
spaced, then errors in the position of those points are magnified
in the final result.  If you have velocity or acceleration,
you use first or second derivative of the dirac delta function,
I believe.  (I have never actually tried this.)  

As a side thought, if you know all the derivatives of a function
at a single point in time, you can find the value of the
function for all times.  The problem is you have to know them
exactly.