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An Eulerian trail, [note 1] or Euler walk, in an undirected graph is a walk that uses each edge exactly once. If such a walk exists, the graph is called traversable or semi-eulerian. [3] An Eulerian cycle, [note 1] also called an Eulerian circuit or Euler tour, in an undirected graph is a cycle that uses each edge exactly once
Adobe has unveiled a new attribution tool for Photoshop that will help consumers better understand the authenticity of images while giving proper credit to creators. Adobe's tool to identify ...
Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges. The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler, in 1736, [1] laid the foundations of graph theory and prefigured the idea of topology. [2]
A three-dimensional hypercube graph showing a Hamiltonian path in red, and a longest induced path in bold black. In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges).
The Euler tour technique (ETT), named after Leonhard Euler, is a method in graph theory for representing trees. The tree is viewed as a directed graph that contains two directed edges for each edge in the tree. The tree can then be represented as a Eulerian circuit of the directed graph, known as the Euler tour representation (ETR) of the tree
In computer graphics, an Euler filter is a filter intended to prevent gimbal lock and related discontinuities in animation data sets in which rotation is expressed in terms of Euler angles. These discontinuities are caused by the existence of many-to-one mappings between the Euler angle parameterization of the set of 3D rotations .
In solid modeling and computer-aided design, the Euler operators modify the graph of connections to add or remove details of a mesh while preserving its topology. They are named by Baumgart [1] after the Euler–Poincaré characteristic. He chose a set of operators sufficient to create useful meshes, some lose information and so are not invertible.
The Photoshop and illusions.hu flavors also produce the same result when the top layer is pure white (the differences between these two are in how one interpolates between these 3 results). These three results coincide with gamma correction of the bottom layer with γ=2 (for top black), unchanged bottom layer (or, what is the same, γ=1; for ...