---
res:
  bibo_abstract:
  - The construction of anisotropic triangulations is desirable for various applications,
    such as the numerical solving of partial differential equations and the representation
    of surfaces in graphics. To solve this notoriously difficult problem in a practical
    way, we introduce the discrete Riemannian Voronoi diagram, a discrete structure
    that approximates the Riemannian Voronoi diagram. This structure has been implemented
    and was shown to lead to good triangulations in $\mathbb{R}^2$ and on surfaces
    embedded in $\mathbb{R}^3$ as detailed in our experimental companion paper. In
    this paper, we study theoretical aspects of our structure. Given a finite set
    of points $\mathcal{P}$ in a domain $\Omega$ equipped with a Riemannian metric,
    we compare the discrete Riemannian Voronoi diagram of $\mathcal{P}$ to its Riemannian
    Voronoi diagram. Both diagrams have dual structures called the discrete Riemannian
    Delaunay and the Riemannian Delaunay complex. We provide conditions that guarantee
    that these dual structures are identical. It then follows from previous results
    that the discrete Riemannian Delaunay complex can be embedded in $\Omega$ under
    sufficient conditions, leading to an anisotropic triangulation with curved simplices.
    Furthermore, we show that, under similar conditions, the simplices of this triangulation
    can be straightened.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Jean-Daniel
      foaf_name: Boissonnat, Jean-Daniel
      foaf_surname: Boissonnat
  - foaf_Person:
      foaf_givenName: Mael
      foaf_name: Rouxel-Labbé, Mael
      foaf_surname: Rouxel-Labbé
  - foaf_Person:
      foaf_givenName: Mathijs
      foaf_name: Wintraecken, Mathijs
      foaf_surname: Wintraecken
      foaf_workInfoHomepage: http://www.librecat.org/personId=307CFBC8-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-7472-2220
  bibo_doi: 10.1137/17m1152292
  bibo_issue: '3'
  bibo_volume: 48
  dct_date: 2019^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0097-5397
  - http://id.crossref.org/issn/1095-7111
  dct_language: eng
  dct_publisher: Society for Industrial & Applied Mathematics (SIAM)@
  dct_title: Anisotropic triangulations via discrete Riemannian Voronoi diagrams@
...