Editing Digital geometry (section)

{{Short description|Deals with digitized models or images of objects of the 2D or 3D Euclidean space}}
{{no footnotes|date=January 2015}}

'''Digital geometry''' deals with [[discrete space|discrete]] sets (usually discrete [[Point (geometry)|point]] sets) considered to be [[digitizing|digitized]] [[scale model|models]] or [[image]]s of objects of the 2D or 3D [[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 graphics|raster]] display of a computer, or in newspapers are in fact [[Digital data|digital]] images.

Its main application areas are [[computer graphics]] and [[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]] 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]], digital convexity, [[digital straightness]], 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]] 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]].
* 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 manifold]]s.
* Designing tracking algorithms for digital objects.
* Functions on digital space.
* Curve sketching, a method of drawing a curve pixel by pixel.
[[File:Simplicial.gif|thumb|right|Tracing a curve on a triangular mesh]]

Digital geometry heavily overlaps with [[discrete geometry]] and may be considered as a part thereof.