With progress on both the theoretical and the computational fronts, the use of Hermite
interpolation for mathematical modeling has become an established tool in applied science …

Pythagorean–hodograph curves are characterized by the special property that their
“parametric speed”—ie, the derivative of the arc length with respect to the curve parameter …

This paper presents a cooperative trajectory-generation framework to efficiently compute a
set of spatial trajectories for a team of cooperating vehicles: in particular, for unmanned …

The problem of constructing a plane polynomial curve with given end points and end
tangents, and a specified arc length, is addressed. The solution employs planar quintic …

An aerial robot is a system capable of sustained flight with no direct human control and able
to perform a specific task. A lighter than air robot is an aerial robot that relies on the static lift …

A method for constructing rational Pythagorean-hodograph (PH) curves in R3 is proposed,
based on prescribing a field of rational unit tangent vectors. This tangent field, together with …

The past decade has witnessed sustained interest in elucidating the basic theory of
Pythagorean–hodograph (PH) curves, developing construction algorithms, formulating …

A unique feature of polynomial Pythagorean–hodograph (PH) curves is the ability to
interpolate G 1 Hermite data (end points and tangents) with a specified total arc length …

In the machining of complex parts with free-formed surfaces, robots are widely employed
due to their advantages of a large operating space and high flexibility. The industrial robot …

Methods are developed to identify whether or not a given polynomial curve, specified by
Bézier control points, is a Pythagorean-hodograph (PH) curve—and, if so, to reconstruct the …