Differential Geometry is an important foundation for much of graphics. Students must have a sense of the basic concepts (curvature, distortion, ...).
Parts of #1 and #2 below should provide sufficient background.
Otherwise for a good primer, see the notes (and slides) from the SIGGRAPH Discrete Differential Geometry course (particularly Lecture 2). For further details refer to the resources listed at The 2009 Advanced Graphics Course Readings.
Surface parameterization is a useful tool for many graphics applications and a setting for applying differential geometry concepts. Students should be aware of the key issues in surface parameterizations, and have some sense of the kinds of approaches available. Suggested readings (any one should be enough):
- Floater, M., & Hormann, K. (2005). Surface Parameterization: a Tutorial and Survey. In N. A. Dodgson, M. S. Floater, & M. A. Sabin (Eds.), Advances in Multiresolution for Geometric Modelling (pp. 157–186). Berlin/Heidelberg: Springer-Verlag. doi:10.1007/b138117 (author copy) - a very widely cited survey, with a nice introduction and tutorial to differential geometry that gets too mathematical too fast.
- Floater, Sheffer, and others. Mesh Parameterization SIGGRAPH Course (offered in 2008 and 2007), notes online. The Differential Geometry primer is useful not only as a tutorial on differential geometry, but also on the basic issues in parameterization.
- Sheffer, A., Praun, E., & Rose, K. (2006). Mesh Parameterization Methods and Their Applications. Foundations and Trends® in Computer Graphics and Vision, 2(2), 105–171. doi:10.1561/0600000011 (author version) - also a nice survey that covers many of the techniques. Provides an excellent survey of the applications of parameterizations and the methods for doing it - with a little less background on the issues.