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The resulting polyhedral Morse\u2013Smale complex may be regarded, on one hand, as a generalization of the Morse\u2013Smale complex of the smooth radial distance function defining a smooth, convex body, on the other hand, it could be also regarded as a generalization of the Morse\u2013Smale complex of the piecewise linear parallel distance function (measured from a plane), defining a polyhedral surface. Beyond similarities, our paper also highlights the marked differences between these three problems and it also relates our theory to other methods. Our work includes the design, implementation and testing of an explicit algorithm computing the Morse\u2013Smale complex on a convex polyhedron.<\/jats:p>","DOI":"10.1007\/s10998-024-00583-4","type":"journal-article","created":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T15:01:51Z","timestamp":1717599711000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Morse\u2013Smale complexes on convex polyhedra"],"prefix":"10.1007","volume":"89","author":[{"given":"Bal\u00e1zs","family":"Ludm\u00e1ny","sequence":"first","affiliation":[]},{"given":"Zsolt","family":"L\u00e1ngi","sequence":"additional","affiliation":[]},{"given":"G\u00e1bor","family":"Domokos","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,5]]},"reference":[{"key":"583_CR1","doi-asserted-by":"publisher","DOI":"10.1515\/9781400881802","volume-title":"Morse Theory (AM-51)","author":"J Milnor","year":"1963","unstructured":"J. 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