4 research outputs found
Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics,
It is shown that, depending upon the orientation of the end tangents \t_0,
\t_1 relative to the end point displacement vector \Delta\p=\p_1-\p_0, the
problem of Hermite interpolation by PH cubic segments may admit zero,
one, or two distinct solutions. For cases where two interpolants exist, the
bending energy may be used to select among them. In cases where no solution
exists, we determine the minimal adjustment of one end tangent that permits a
spatial PH cubic Hermite interpolant. The problem of assigning tangents to a
sequence of points \p_0,\ldots,\p_n in , compatible with a
piecewise--PH--cubic spline interpolating those points, is also briefly
addressed. The performance of these methods, in terms of overall smoothness
and shape--preservation properties of the resulting curves, is illustrated by
a selection of computed examples