  The construction of smooth spatial paths with Pythagorean-hodograph (PH)
quintic spline biarcs is proposed. To facilitate real-time computations of
$C^2$ PH quintic splines, an efficient local data stream interpolation
algorithm is introduced. Each spline segment interpolates second and first
order Hermite data at the initial and final end-point, respectively. In the
spline extension of the scheme a $C^2$ smooth connection between successive
spline segments is obtained by taking the locally required second-order
derivative information from the previous segment. Consequently, the data stream
spline interpolant is globally $C^2$ continuous and can be constructed for
arbitrary $C^1$ Hermite data configurations. A simple and effective selection
of the free parameters that arise in the interpolation problem is proposed. The
developed theoretical analysis proves the fourth approximation order of the
local scheme while a selection of numerical examples confirms the same accuracy
of its spline extension. In addition, the performances of the algorithm are
also validated by considering its application to point stream interpolation
with automatically generated first-order derivative information.
