Editing Cartogram (section)

===Shape-warping contiguous cartograms===
[[File:PaullHennig2016WorldMap.OAha.CC-BY-4.0.jpg|thumb|upright=1.35|Contiguous cartogram (Gastner-Newman) of the world with each country rescaled in proportion to the hectares of certified [[organic farming]]<ref name=Atlas>Paull, John & Hennig, Benjamin (2016) [https://www.academia.edu/25648267/Atlas_of_Organics_Four_maps_of_the_world_of_organic_agriculture  Atlas of Organics: Four Maps of the World of Organic Agriculture]  Journal of Organics. 3(1): 25–32.</ref>]]
Also called ''irregular cartograms'' or ''deformation cartograms'',<ref name="markowska2019" /> This is a family of very different algorithms that scale and deform the shape of each district while maintaining adjacent edges. This approach has its roots in the early 20th Century cartograms of Haack and Weichel and others, although these were rarely as mathematically precise as current computerized versions. The variety of approaches that have been proposed include [[Cellular automaton|cellular automata]], [[Quadtree | quadtree partitions]], [[cartographic generalization]], [[Medial axis|medial axes]], spring-like forces, and simulations of inflation and deflation.<ref name="nusrat2016" /> Some attempt to preserve some semblance of the original shape (and may thus be termed ''homomorphic''),<ref name="kocmoud1998">{{cite book |last1=House |first1=Donald H. |last2=Kocmoud |first2=Christopher J. |title=Proceedings Visualization '98 (Cat. No.98CB36276) |chapter=Continuous cartogram construction |date=October 1998 |pages=197–204 |doi=10.1109/VISUAL.1998.745303 |isbn=0-8186-9176-X |s2cid=14023382 |chapter-url=https://www.researchgate.net/publication/3788051}}</ref> but these are often more complex and slower algorithms than those that severely distort shape.