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The distance function from a real algebraic variety

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Ottaviani, Giorgio
dc.contributor.author Sodomaco, Luca
dc.date.accessioned 2020-11-30T08:20:07Z
dc.date.available 2020-11-30T08:20:07Z
dc.date.issued 2020-10
dc.identifier.citation Ottaviani , G & Sodomaco , L 2020 , ' The distance function from a real algebraic variety ' , COMPUTER AIDED GEOMETRIC DESIGN , vol. 82 , 101927 . https://doi.org/10.1016/j.cagd.2020.101927 en
dc.identifier.issn 0167-8396
dc.identifier.other PURE UUID: debb71c0-20dc-4f86-aca0-db6824f6afba
dc.identifier.other PURE ITEMURL: https://research.aalto.fi/en/publications/the-distance-function-from-a-real-algebraic-variety(debb71c0-20dc-4f86-aca0-db6824f6afba).html
dc.identifier.other PURE LINK: http://www.scopus.com/inward/record.url?scp=85089890037&partnerID=8YFLogxK
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/61815
dc.description.abstract For any (real) algebraic variety X in a Euclidean space V endowed with a nondegenerate quadratic form q, we introduce a polynomial EDpolyX,u(t2) which, for any u∈V, has among its roots the distance from u to X. The degree of EDpolyX,u is the Euclidean Distance degree of X. We prove a duality property when X is a projective variety, namely EDpolyX,u(t2)=EDpolyX∨,u(q(u)−t2) where X∨ is the dual variety of X. When X is transversal to the isotropic quadric Q, we prove that the ED polynomial of X is monic and the zero locus of its lower term is X∪(X∨∩Q)∨. en
dc.language.iso en en
dc.publisher Elsevier
dc.relation.ispartofseries COMPUTER AIDED GEOMETRIC DESIGN en
dc.relation.ispartofseries Volume 82 en
dc.rights embargoedAccess en
dc.title The distance function from a real algebraic variety en
dc.type A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä fi
dc.description.version Peer reviewed en
dc.contributor.department University of Florence
dc.contributor.department Department of Mathematics and Systems Analysis
dc.subject.keyword Euclidean distance
dc.subject.keyword Euclidean Distance degree
dc.subject.keyword Euclidean Distance polynomial
dc.subject.keyword Isotropic quadric
dc.subject.keyword Polar degrees
dc.subject.keyword Real algebraic variety
dc.identifier.urn URN:NBN:fi:aalto-2020113020660
dc.identifier.doi 10.1016/j.cagd.2020.101927
dc.date.embargo info:eu-repo/date/embargoEnd/2022-08-28

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