  We introduce the new class of planar Pythagorean-Hodograph (PH) B-Spline
curves. They can be seen as a generalization of the well-known class of planar
Pythagorean-Hodograph (PH) B\'ezier curves, presented by R. Farouki and T.
Sakkalis in 1990, including the latter ones as special cases.
Pythagorean-Hodograph B-Spline curves are non-uniform parametric B-Spline
curves whose arc-length is a B-Spline function as well. An important
consequence of this special property is that the offsets of
Pythagorean-Hodograph B-Spline curves are non-uniform rational B-Spline (NURBS)
curves. Thus, although Pythagorean-Hodograph B-Spline curves have fewer degrees
of freedom than general B-Spline curves of the same degree, they offer unique
advantages for computer-aided design and manufacturing, robotics, motion
control, path planning, computer graphics, animation, and related fields. After
providing a general definition for this new class of planar parametric curves,
we present useful formulae for their construction, discuss their remarkable
attractive properties and give some examples of their practical use.
