Bezier-curves with curvature and torsion continuity

One of the main problems in computer-aided design is how to input shape information to the computer. In the analytic description and approximation of arbitrary shaped curves the Bezier-curves are of great importance (see A Bezier-curve is a segmented curve. The segments X/(u): = E^0 6 m/ +; JSf*(w -w// W/+1 -u/) of a Bezier-curve of degree m over the parameter interval U/ ^ u ^ W/-I-1 use the Bernstein-polynomials as blending functions. The coefficients b m/ +t are called Bezier points. They form the so called Bezier polygon, which implies the Bezier-curve.