Given a set of k-dimensional knots in 
and a set of intrinsic coordinates
we compute a piecewise quintic function (i.e. a quintic spline)
where each spline segment 
is in the form of a fifth-degree polynomial,
over interval 
such that not only
the resulting quintic spline goes through all knots,
but also enforces continuity up to the fourth order,
- Re-parametrize spline intrinsic coordinates according to arc length
- Support sampling of non-knot points along spline curve
- Can impose 1st and 2nd order boundary condition at both ends