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- W2884604114 abstract "For any (real) algebraic variety $X$ in a Euclidean space $V$ endowed with a nondegenerate quadratic form $q$, we introduce a polynomial $mathrm{EDpoly}_{X,u}(t^2)$ which, for any $uin V$, has among its roots the distance from $u$ to $X$. The degree of $mathrm{EDpoly}_{X,u}$ is the {em Euclidean Distance degree} of $X$. We prove a duality property when $X$ is a projective variety, namely $mathrm{EDpoly}_{X,u}(t^2)=mathrm{EDpoly}_{X^vee,u}(q(u)-t^2)$ where $X^vee$ 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 $Xcup(X^veecap Q)^vee$." @default.
- W2884604114 created "2018-08-03" @default.
- W2884604114 creator A5034482984 @default.
- W2884604114 creator A5060402032 @default.
- W2884604114 date "2018-07-26" @default.
- W2884604114 modified "2023-09-27" @default.
- W2884604114 title "The Distance Function from a Real Algebraic Variety" @default.
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