Editing Voronoi diagram (section)

=== Natural sciences ===
[[File:Voronoi growth euclidean.gif|thumb|A Voronoi tessellation emerges by radial growth from seeds outward.]]
*In [[biology]], Voronoi diagrams are used to model a number of different biological structures, including [[Cell (biology)|cells]]<ref>{{cite journal |last1=Bock |first1=Martin |last2=Tyagi |first2=Amit Kumar |last3=Kreft |first3=Jan-Ulrich |last4=Alt |first4=Wolfgang |title=Generalized Voronoi Tessellation as a Model of Two-dimensional Cell Tissue Dynamics |journal=Bulletin of Mathematical Biology |volume=72 |issue=7 |pages=1696–1731 |doi=10.1007/s11538-009-9498-3 |pmid=20082148 |year=2009 |arxiv=0901.4469v1 |bibcode=2009arXiv0901.4469B |s2cid=16074264}}</ref> and [[Cancellous bone|bone microarchitecture.]]<ref>{{cite journal |author=Hui Li |editor2-first=Robert |editor2-last=Sitnik |editor1-first=Atilla M |editor1-last=Baskurt |title=Spatial Modeling of Bone Microarchitecture |journal=Three-Dimensional Image Processing (3Dip) and Applications II |volume=8290 |pages=82900P |year=2012 |bibcode=2012SPIE.8290E..0PL |doi=10.1117/12.907371 |s2cid=1505014}}</ref> Indeed, Voronoi tessellations work as a geometrical tool to understand the physical constraints that drive the organization of biological tissues.<ref name="Sanchez-Gutierrez 77–88">{{Cite journal |last1=Sanchez-Gutierrez |first1=D. |last2=Tozluoglu |first2=M. |last3=Barry |first3=J. D. |last4=Pascual |first4=A. |last5=Mao |first5=Y. |last6=Escudero |first6=L. M. |date=2016-01-04 |title=Fundamental physical cellular constraints drive self-organization of tissues |journal=The EMBO Journal |volume=35 |issue=1 |pages=77–88 |doi=10.15252/embj.201592374 |pmc=4718000 |pmid=26598531}}</ref>
*In [[hydrology]], Voronoi diagrams are used to calculate the rainfall of an area, based on a series of point measurements. In this usage, they are generally referred to as Thiessen polygons.
*In [[ecology]], Voronoi diagrams are used to study the growth patterns of forests and forest canopies, and may also be helpful in developing predictive models for forest fires.
*In [[ethology]], Voronoi diagrams are used to model domains of danger in the [[selfish herd theory]].
*In [[computational chemistry]], ligand-binding sites are transformed into Voronoi diagrams for [[machine learning]] applications (e.g., to classify binding pockets in proteins).<ref>{{cite book |last1=Feinstein |first1=Joseph |contribution=Bionoi: A Voronoi Diagram-Based Representation of Ligand-Binding Sites in Proteins for Machine Learning Applications |date=2021 |url=https://doi.org/10.1007/978-1-0716-1209-5_17 |title=Protein-Ligand Interactions and Drug Design |pages=299–312 |editor-last=Ballante |editor-first=Flavio |series=Methods in Molecular Biology |place=New York, NY |publisher=Springer US |language=en |doi=10.1007/978-1-0716-1209-5_17 |isbn=978-1-0716-1209-5 |access-date=2021-04-23 |last2=Shi |first2=Wentao |last3=Ramanujam |first3=J. |last4=Brylinski |first4=Michal |volume=2266 |pmid=33759134 |s2cid=232338911}}</ref> In other applications, Voronoi cells defined by the positions of the nuclei in a molecule are used to compute [[partial charge|atomic charge]]s. This is done using the [[Voronoi deformation density]] method.
*In [[astrophysics]], Voronoi diagrams are used to generate adaptative smoothing zones on images, adding signal fluxes on each one. The main objective of these procedures is to maintain a relatively constant [[signal-to-noise ratio]] on all the images.
*In [[computational fluid dynamics]], the Voronoi tessellation of a set of points can be used to define the computational domains used in [[finite volume]] methods, e.g. as in the moving-mesh cosmology code AREPO.<ref>{{cite journal |title=E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh |last=Springel |first=Volker |year=2010 |journal=MNRAS |volume=401 |issue=2 |pages=791–851 |doi=10.1111/j.1365-2966.2009.15715.x |doi-access=free |bibcode=2010MNRAS.401..791S |arxiv=0901.4107 |s2cid=119241866}}</ref>
*In [[computational physics]], Voronoi diagrams are used to calculate profiles of an object with [[Shadowgraph]] and proton radiography in [[High energy density physics]].<ref>{{Cite journal |last=Kasim |first=Muhammad Firmansyah |date=2017-01-01 |title=Quantitative shadowgraphy and proton radiography for large intensity modulations |journal=Physical Review E |volume=95 |issue=2 |pages=023306 |doi=10.1103/PhysRevE.95.023306 |pmid=28297858 |arxiv=1607.04179 |bibcode=2017PhRvE..95b3306K |s2cid=13326345}}</ref>