This talk deals with the recently introduced class of planar and spatial Pythagorean Hodograph (PH) B-Spline curves. PH B-Spline curves are odd-degree, non-uniform, parametric B–Spline curves whose arc length is a B–Spline function of the curve parameter and can thus be computed explicitly without numerical quadrature. 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 shortly reviewing their construction and main properties we address solutions to several curve design applications, including the design of a PH B-Spline curve closest to a given reference curve, the interpolation of point and second order Hermite data as well as the construction of almost rotation minimizing spatial PH B-Spline curves as spine curves of rational tensor product B-Spline pipe surfaces.