Spiral spline interpolation to a planar spiral

We derive regions for T-cubic and arc/T-cubic spirals to two-point Hermite interpolation in terms of unit tangent vectors with help of Mathematica. The use of spirals gives the designer an excellent and speedy control over the shape of curve that is produced because there are no internal curvature maxima, curvature minima, inflection points, loops and cusps in a spiral segment.