The distance function from a real algebraic variety
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Computer Aided Geometric Design, Volume 82
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)∨.Description
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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