# Digital geometry > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Digital_geometry > Markdown URL: https://mediated.wiki/source/Digital_geometry.md > Source: https://en.wikipedia.org/wiki/Digital_geometry > Source revision: 1326158764 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) Geometry Projecting a sphere to a plane Branches Euclidean Non-Euclidean Elliptic Spherical Hyperbolic Non-Archimedean geometry Projective Affine Synthetic Analytic Algebraic Arithmetic Diophantine Differential Riemannian Symplectic Discrete differential Complex Finite Discrete/Combinatorial Digital Convex Computational Fractal Incidence Noncommutative geometry Noncommutative algebraic geometry Concepts Features Dimension Straightedge and compass constructions Angle Curve Diagonal Orthogonality (Perpendicular) Parallel Vertex Congruence Similarity Symmetry Zero-dimensional Point One-dimensional Line Line segment Ray Curve Length Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram Square Rectangle Rhombus Rhomboid Trapezoid Kite Circle Radius Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron cuboid Cube Octahedron Dodecahedron Icosahedron Pyramid Solid of revolution Sphere Great circle Cylinder Cone Four - other-dimensional 4-polytope Simplex 5-cell Hypercube Tesseract n-sphere Hypersphere Geometers by name Aida Aryabhata Ahmes Alhazen Apollonius Archimedes Atiyah Baudhayana Bolyai Brahmagupta Cartan Chern Coxeter Descartes Euclid Euler Gauss Gromov Hilbert Huygens Jyeṣṭhadeva Kātyāyana Khayyám Klein Lobachevsky Manava Minkowski Minggatu Pascal Pythagoras Parameshvara Poincaré Riemann Sakabe Sijzi al-Tusi Veblen Virasena Yang Hui al-Yasamin Zhang List of geometers by period BCE Ahmes Baudhayana Manava Pythagoras Euclid Archimedes Apollonius 1–1400s Zhang Kātyāyana Aryabhata Brahmagupta Virasena Alhazen Sijzi Khayyám al-Yasamin al-Tusi Yang Hui Parameshvara 1400s–1700s Jyeṣṭhadeva Descartes Pascal Huygens Minggatu Euler Sakabe Aida 1700s–1900s Gauss Lobachevsky Bolyai Riemann Klein Poincaré Hilbert Minkowski Cartan Veblen Coxeter Chern Present day Atiyah Gromov v t e Deals with digitized models or images of objects of the 2D or 3D Euclidean space This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (January 2015) (Learn how and when to remove this message) **Digital geometry** deals with [discrete](/source/Discrete_space) sets (usually discrete [point](/source/Point_(geometry)) sets) considered to be [digitized](/source/Digitizing) [models](/source/Scale_model) or [images](/source/Image) of objects of the 2D or 3D [Euclidean space](/source/Euclidean_space). Simply put, *digitizing* is replacing an object by a discrete set of its points. The images we see on the TV screen, the [raster](/source/Raster_graphics) display of a computer, or in newspapers are in fact [digital](/source/Digital_data) images. Its main application areas are [computer graphics](/source/Computer_graphics) and [image analysis](/source/Image_analysis). Main aspects of study are: - Constructing digitized representations of objects, with the emphasis on precision and efficiency (either by means of synthesis, see, for example, [Bresenham's line algorithm](/source/Bresenham's_line_algorithm) or digital disks, or by means of digitization and subsequent processing of digital images). - Study of properties of digital sets; see, for example, [Pick's theorem](/source/Pick's_theorem), digital convexity, [digital straightness](https://en.wikipedia.org/w/index.php?title=Digital_straightness&action=edit&redlink=1), or digital planarity. - Transforming digitized representations of objects, for example (A) into simplified shapes such as (i) skeletons, by repeated removal of simple points such that the [digital topology](/source/Digital_topology) of an image does not change, or (ii) medial axis, by calculating local maxima in a distance transform of the given digitized object representation, or (B) into modified shapes using [mathematical morphology](/source/Mathematical_morphology). - Reconstructing "real" objects or their properties (area, length, curvature, volume, surface area, and so forth) from digital images. - Study of digital curves, digital surfaces, and [digital manifolds](/source/Digital_manifold). - Designing tracking algorithms for digital objects. - Functions on digital space. - Curve sketching, a method of drawing a curve pixel by pixel. Tracing a curve on a triangular mesh Digital geometry heavily overlaps with [discrete geometry](/source/Discrete_geometry) and may be considered as a part thereof. ## Digital space A 2D digital space usually means a 2D grid space that only contains integer points in 2D Euclidean space. A 2D image is a function on a 2D digital space (See [image processing](/source/Image_processing)). In Rosenfeld and Kak's book, digital connectivity are defined as the relationship among elements in digital space. For example, 4-connectivity and 8-connectivity in 2D. Also see [pixel connectivity](/source/Pixel_connectivity). A digital space and its (digital-)connectivity determine a [digital topology](/source/Digital_topology). In digital space, the digitally continuous function (A. Rosenfeld, 1986) and the [gradually varied function](/source/Gradually_varied_surface) (L. Chen, 1989) were proposed, independently. A digitally continuous function means a function in which the value (an integer) at a digital point is the same or off by at most 1 from its neighbors. In other words, if *x* and *y* are two adjacent points in a digital space, |*f*(*x*) − *f*(*y*)| ≤ 1. A gradually varied function is a function from a digital space Σ {\displaystyle \Sigma } to { A 1 , … , A m } {\displaystyle \{A_{1},\dots ,A_{m}\}} where A 1 < ⋯ < A m {\displaystyle A_{1}<\cdots