| abstract |
A map in an atlas represents some part of the Earth and every point in the map corresponds unambiguously to a point on the Earth's surface. Together, all these correspondences form a function that is usually called a parameterization of the affected region. More generally speaking, a parameterization is a bijective mapping between a surface and an appropriate parameter domain. This mapping usually distorts geometric properties like angles, surface areas and lengths, and one often tries to find parameterizations that minimize these deformations. After a brief introduction to the theoretical background from differential geometry, I am going to review several methods that have been used to achieve this goal in the case that the surface is a triangle mesh.
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