Geometry is a pervasive mathematical concept that appears in many places and in many
disguises. The representation of geometric entities, of their unions and intersections, and of …

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 …

The interpolation of first-order Hermite data by spatial Pythagorean-hodograph curves that
exhibit closure under arbitrary 3-dimensional rotations is addressed. The hodographs of …

The structural invariance of the four-polynomial characterization for three-dimensional
Pythagorean hodographs introduced by Dietz et al.(1993), under arbitrary spatial rotations …

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 …

Helical space curves are characterized by the property that their unit tangents maintain a
constant inclination with respect to a fixed line, the axis of the helix. Equivalently, a helix …

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

It is shown that, depending upon the orientation of the end tangents t 0, t 1 relative to the end
point displacement vector Δ p= p 1− p 0, the problem of G 1 Hermite interpolation by PH …

We construct one-frequency trigonometric spline curves with a de Boor-like algorithm for
evaluation and analyze their shape-preserving properties. The convergence to quadratic B …

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 …