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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
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]
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.
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
The lasso (or "free form selection") is an editing tool available, with minor variations, in most digital image editing software [1] and some specific strategy games.It is often accessed from the standard main menu (in Photoshop, [2] Paint Tool SAI, [3] and GIMP, [4] as common examples), by clicking the icon of a dotted line shaped like a rope lasso, from which the common name arises.
Many non-Adobe commercial graphics applications also support Photoshop-compatible plugins – Paint Shop Pro, [4] PhotoImpact, and Corel PhotoPaint are some of the better-known ones. There are several dozen more plugin hosts, including lesser-known products like Chasys Draw IES, the free-software image editor GIMP, and viewers like IrfanView. [5]
Euler's Tonnetz. The Tonnetz originally appeared in Leonhard Euler's 1739 Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae.Euler's Tonnetz, pictured at left, shows the triadic relationships of the perfect fifth and the major third: at the top of the image is the note F, and to the left underneath is C (a perfect fifth above F), and to the right is A (a ...
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.