Differential and Computational Geometry

ED 5310Differential and Computational Geometry

Course Contents:

Differential geometry of curves and surfaces: Tangent vector, normal plane, principal normal, binomial, osculating plane, moving trihedron, curvature and torsion, Arc length, First and second fundamental forms, tangent plane, principal curvatures, geodesics, umbilical points, point classification, characteristic tests, relational properties, intersection of surfaces, offsets and bisectors.
Topology: Homeomorphism, Topology of Surfaces, Invariants of Surfaces, Surfaces as Manifolds.
Computational Geometry: Polygon triangulation and partitioning, Convex hull in two and three dimensions, Voronoi diagram and Delaunay triangulation, and Arrangements.

Text Books:

1. Differential geometry of curves and surfaces, Monfredo P. do Carmo, Prentice Hall,1976.
2. Goemetric Modeling, Michael E. Mortenson, Industrial Press Inc., 2006.
3. Computational Geometry in C, Joseph O’Rourke, Cambridge University Press, 1998
4. M A Armstrong, Basic Topology, Springer, 1980.


1. Computational Geometry: Algorithms and Applications, Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars, Springer-Verlag, 2008.
2. Curves and surfaces for CAGD, Gerald Farin, Morgan Kaufmann Publishers
Inc., 2002
3. Computational Geometry: An Introduction, Franco P. Preparata and Michael Ian Shamos, Springer, 1985
4. Alfred Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, CRC Press Ltd., 1996
5. I.D. Faux. and M. J Pratt, Computational Geometry for Design and Manufacture, Jhon Wiley & Sons, NY, 1979