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A primary concern of algorithmic topology, as its name suggests, is to develop efficient algorithms for solving problems that arise naturally in fields such as computational geometry, graphics, robotics, social science, structural biology, and chemistry, using methods from computable topology.
Digital topology was first studied in the late 1960s by the computer image analysis researcher Azriel Rosenfeld (1931–2004), whose publications on the subject played a major role in establishing and developing the field. The term "digital topology" was itself invented by Rosenfeld, who used it in a 1973 publication for the first time.
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
Various software packages are available, such as javaPlex, Dionysus, Perseus, PHAT, DIPHA, GUDHI, Ripser, and TDAstats. A comparison between these tools is done by Otter et al. [ 24 ] Giotto-tda is a Python package dedicated to integrating TDA in the machine learning workflow by means of a scikit-learn [1] API.
Computer graphics is a sub-field of computer science which studies methods for digitally synthesizing and manipulating visual content. Although the term often refers to the study of three-dimensional computer graphics, it also encompasses two-dimensional graphics and image processing.
Graphics represented as a rectangular grid of pixels. Rasterization Converting vector graphics to raster graphics. This terms also denotes a common method of rendering 3D models in real time. Ray casting Rendering by casting non-recursive rays from the camera into the scene. 2D ray casting is a 2.5D rendering method. Ray marching
The associated topological space of a graph is connected (with respect to the graph topology) if and only if the original graph is connected.; Every connected graph contains at least one maximal tree , that is, a tree that is maximal with respect to the order induced by set inclusion on the subgraphs of which are trees.
Animation detailing the embedding of the Pappus graph and associated map in the torus. In mathematics, topological graph theory is a branch of graph theory.It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological spaces. [1]