References

Most of this week's material are from classical differential geometry, except the concept of geometric continuity. Barsky and DeRose's papers are highly recommended for the concept of geometric continuity. If you need a good companion of classic differential geometry, you ming consider Struik's. Farin's book also contains chapters on classical differential geometry, written by W. Boehm. Finally, Casey's book has some very interesting discussions and experiments about curvature.

• Brian A. Barsky and Tony D. DeRose, Geometric Continuity of Parametric Curves: Three Equivalent Characterizations, IEEE Computer Graphics & Applications, Vol. 9 (1989), No. 6 (November), pp. 60-68.
• Brian A. Barsky and Tony D. DeRose, Geometric Continuity of Parametric Curves: Constructions of Geometrically Continuous Splines, IEEE Computer Graphics & Applications, Vol. 10 (1910), No. 1 (January), pp. 60-68.
• James Casey, Exploring Curvature, Friedr. Vieweg & Sohn, Braunschweig/Wiesbaden, 1996.
• Gerald Farin, Curves and Surfaces for CAGD: A Practical Guide, fourth edition, Academic Press, 1997.
• Dirk J. Struik, Lectures on Classical Differential Geometry, second edition, Dover, New York, 1950.