Hermite interpolation of space curves using the symmetric algebra

Conditions are presented which describe the construction of a degree 5 Bézier curve which interpolates given positional, tangent, curvature, and torsion data at end points. The result is extended to provide technique for interpolation of a given curve by a sequence of Bézier segments that interpolate positional, tangent, curvature, and torsion data associated with intermediate points on the curve. It is shown that the order of approximation is O(h8), 0