Optimal Transport on Discrete Domains

Many tools from discrete differential geometry (DDG) were inspired by practical considerations in areas like computer graphics and vision. Disciplines like these require fine-grained understanding of geometric structure and the relationships between different shapes—problems for which the toolbox from smooth geometry can provide substantial insight. Indeed, a triumph of discrete differential geometry is its incorporation into a wide array of computational pipelines, affecting the way artists, engineers, and scientists approach problem-solving across geometry-adjacent disciplines.