of Prof. Yau's lecture, Monday, April 2 [with additional references and remarks] (for people who missed the lecture) A geometric structure on a manifold is a cover by coordinate systems [a " sub-atlas " ] in which the transition functions from one coordinate system to another are not arbitrary mappings but rather belong to some specific set of mappings from (open subsets of) Euclidean space to ...

2D Simulation and Mapping using the Cauchy-Green Complex Barycentric Coordinates Conformal maps are especially useful in geometry processing for computing shape preserving deformations, image warping and manipulating harmonic functions. The Cauchy-Green coordinates are complex-valued barycentric coordinates, which can be used to parameterize a space of conformal maps from a planar domain bounde...