**Alexis Angelidis**

This document contains reading notes on differential geometry for curves and surfaces, in the purpose of understanding the minimal information required to specify the smoothness of a surface at points only. The reconstruction of the surface from these points is not discussed. A surface is sometimes called smooth when it is mathematically , which sometimes does not make sense: a 'cube' with extremely small rounded edges shouldn't be called smooth.

- Curves

- Surfaces
- Notations
- Observations
- Parameterization properties
- Tangent plane
- Normal
- Weingarten map
- First fundamental form
- Second fundamental form
- Third fundamental form
- Surface area
- Normal curvature
- Principal curvatures and directions
- Mean curvature
- Gaussian curvature

- Surfaces deformation

- Bibliography
- About this document ...

Alexis Angelidis (PhD) 2004-02-09