The power diagram, also known as the Laguerre diagram or the Dirichlet-Voronoi diagram, is a geometric structure that represents the partition of a Euclidean space into regions based on a set of weighting points. Alternatively, it can be described as a tessellation of space that is determined by the power function associated with each weighting point. Other synonyms for power diagram include the Laguerre-Voronoi diagram, Dirichlet tessellation, weighted Voronoi diagram, and energy-based segmentation. These terms are often used interchangeably in the fields of computational geometry, computer vision, and pattern recognition. Each synonym highlights a different aspect of the power diagram, but they all refer to the same mathematical construct.