🚀 go-pugleaf

> create an essentialy straight line.  It seems to me that it should be possible
> to reverse the subdivision algo, and go back a given number of iterations, to
> arrive at a set of control points, that would generate a curve that passes
> through the data points.


No, it doesn't work that way.  The reason cubic curves have 4 controls 
is because you have to completely specify 4 coefficients in the cubic 
polynomial that gives the curve.  If you glue two cubics together, then 
you have 8 controls (although there may be constraints introduced by
whatever order of continuity you are interested in), but that does
mean that you get a 7th-order polynomial as a result.  YOu are now
faced with the problem of approximating a 7th-degree polynomial with
a cubic, which is harder than the original problem of apporximating
a set of data points with a cubic, before you can proced to the next
stage of `unsubdivison'.  I agree though: like much of numerical work,
it IS a pity!
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