http://www.cc.gatech.edu/~turk/math_gr.html

Uses Discrete geometry, and Discrete exterior calculus

http://wykobi.com/tutorial0.html

See Shape analysis course

Geometric data structures

Common queries

Neighboring vertices to a vertex

Neighboring faces to an edge

Edges adjacent to a face

Edges adjacent to a vertex

Geometric operations

Mesh smoothing

Topological operations

Vertex removal, edge collapse, face collapse

Obtaining geometry

Design software (Computer-aided design). . Half-edge is a good data structure for subdivision

Volumetric extraction. Marching cubes: isosurface extraction

Point clouds –

• Delaunay triangulation, "Delaunay Triangulation Based Surface Reconstruction: Ideas and Algorithms"
• Poisson reconstruction