@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-tel-00771335v1> a dcat:Dataset ;
    dct:description """
              Given a set S of data points on a surface F whose equation is z = f(x,y), we would like to triangulate the convex hull of the projection of F on the xy-plane. This triangulation determines a linear approximation of F whose quality is given by a measure of the approximation error. It has been recently proved that the Delaunay triangulation is optimal with respect to Lp-norm criteria, when used for approximating convex quadratic functions. But, little research has been carried out for non convex surfaces. This work studies the approximation, with respect to L1- and L2-norms, of a non convex surface by using a triangulation. We consider a simple case: the hyperbolic paraboloid z = x2 − y2. A construction is given for finding the separation curves of a triangle ∆, the curves limiting the planar zones where ∆ will be kept in a locally optimal triangulation of the hyperbolic paraboloid. Triangu- lation algorithms that use several heuristics based on the separation curves are amply tested and are shown to be better than the Delaunay triangulation. A comparison with globally optimal triangulations which are obtained by means of exponential programs shows that these algorithms finally give "good" trian- gulations. Our research proves that such a process can be easily extended to general quadratic functions z = αx2 + βy2 + γxy + δ1x + δ2y + δ3.
            """ ;
    dct:identifier "tel-00771335" ;
    dct:issued "2026-05-15T12:12:59.311808"^^xsd:dateTime ;
    dct:language "fr" ;
    dct:modified "2026-05-15T12:12:59.311813"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Triangulations and quadrics" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-tel-00771335v1/resource/8585ea88-cb4c-4e1f-8c1e-13d9120bd837> ;
    dcat:keyword "approximations-de-surface",
        "computational-geometry",
        "fonctions-quadratiques",
        "geometrie-algorithmique",
        "infoeu-reposemanticsdoctoralthesis",
        "infoinfo-cgcomputer-science-cscomputational-geometry-cscg",
        "optimalite",
        "optimality",
        "quadratic-functions",
        "surface-approximations",
        "theses",
        "triangulations" ;
    dcat:landingPage <https://theses.hal.science/tel-00771335> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-tel-00771335v1/resource/8585ea88-cb4c-4e1f-8c1e-13d9120bd837> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-15T12:12:59.322201"^^xsd:dateTime ;
    dct:modified "2026-05-15T12:12:59.280445"^^xsd:dateTime ;
    dct:title "Triangulations and quadrics" ;
    dcat:accessURL <https://theses.hal.science/tel-00771335> .

<https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> a foaf:Agent ;
    foaf:name "test_moissonnage_selune" .

<https://theses.hal.science/tel-00771335> a foaf:Document .