Editing Cartogram (section)

===Anamorphic Projection===
{{see also | Anamorphosis}}
This is a type of contiguous cartogram that uses a single parametric mathematical formula (such as a [[Polynomial | polynomial curved surface]]) to distort space itself to equalize the spatial distribution of the chosen variable, rather than distorting the individual features. Because of this distinction, some have preferred to call the result a ''pseudo-cartogram''.<ref name="bortins-demers">{{cite web |last1=Bortins |first1=Ian |last2=Demers |first2=Steve |title=Cartogram Types |url=http://www.ncgia.ucsb.edu/projects/Cartogram_Central/types.html |website=Cartogram Central |publisher=National Center for Geographic Information Analysis, UC Santa Barbara |access-date=15 November 2020 |archive-date=29 January 2021 |archive-url=https://web.archive.org/web/20210129215218/http://www.ncgia.ucsb.edu/projects/Cartogram_Central/types.html |url-status=dead }}</ref> [[Waldo R. Tobler|Tobler's]] first computer cartogram algorithm was based on this strategy,<ref name="tobler1963" /><ref name="tobler1973">{{cite journal |last1=Tobler |first1=Waldo R. |title=A Continuous Transformation Useful for Districting |journal=Annals of the New York Academy of Sciences |date=1973 |volume=219 |issue=1 |pages=215–220 |doi=10.1111/j.1749-6632.1973.tb41401.x|pmid=4518429 |bibcode=1973NYASA.219..215T |hdl=2027.42/71945 |s2cid=35585206 |hdl-access=free }}</ref> for which he developed the general mathematical construct on which his and subsequent algorithms are based.<ref name="tobler1963" /> This approach first models the distribution of the chosen variable as a continuous density function (usually using a [[Curve fitting|least squares fitting]]), then uses the inverse of that function to adjust the space such that the density is equalized. The Gastner-Newman algorithm, one of the most popular tools used today, is a more advanced version of this approach.<ref name="GSM-Fast-Flow-Based">{{cite journal |author = Michael T. Gastner |author2=Vivien Seguy |author3=Pratyush More |year = 2018 |title = Fast flow-based algorithm for creating density-equalizing map projections |journal = Proceedings of the National Academy of Sciences |volume = 115 |pages = E2156–E2164 |doi = 10.1073/pnas.1712674115 |pmid=29463721 |pmc=5877977 |issue = 10 |arxiv = 1802.07625  |bibcode=2018PNAS..115E2156G |doi-access=free }}</ref><ref name="gastner-newman">{{cite journal |last1=Gastner |first1=Michael T. |last2=Newman |first2=M.E.J. |title=Diffusion-based Method for Producing Density-Equalizing Maps |journal=Proceedings of the National Academy of Sciences of the United States of America |date=May 18, 2004 |volume=101 |issue=20 |pages=7499–7504 |doi=10.1073/pnas.0400280101 |jstor=3372222 |pmid=15136719 |pmc=419634 |url=|arxiv=physics/0401102 |s2cid=2487634 |doi-access=free }}</ref> Because they do not directly scale the districts, there is no guarantee that the area of each district is exactly equal to its value.