Triangulations and quadrics
type: Distribution
access URL: https://theses.hal.science/tel-00771335
format: HTML
issued: 2026-05-15T12:12:59.322201
modified: 2026-05-15T12:12:59.280445

Triangulations and quadrics
type: Dataset
contact point: Organization
  fn: CCSD
keyword: infoeu-reposemanticsdoctoralthesis
keyword: triangulations
keyword: optimalite
keyword: infoinfo-cgcomputer-science-cscomputational-geometry-cscg
keyword: approximations-de-surface
keyword: quadratic-functions
keyword: fonctions-quadratiques
keyword: geometrie-algorithmique
keyword: computational-geometry
keyword: surface-approximations
keyword: optimality
keyword: theses
landing page: https://theses.hal.science/tel-00771335
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.
issued: 2026-05-15T12:12:59.311808
language: fr
modified: 2026-05-15T12:12:59.311813

test_moissonnage_selune
type: Agent