Génération de maillages de simplexes pour la modélisation d'objets naturels

Joël Conraud. ( 1997 )
INPL, Nancy, France

Abstract

The geometric modelling of natural abjects, in medical area as well as in geosciences areas, is based on discrete data structures, the meshes. They partition the region of interest into basic geometric primitives. These meshes are used for modellings taking into account physical properties of the studied objects. In three dimensions, two primitives are especially used for describing domains with complicated geometry: the triangle (the simplex in the plane), for surface meshes, and the tetrahedron (the simplex in space), for volume meshes. Simplicial mesh generation problems are presented. Due to the nature of the problems arisen in the domain of application, rabustness and ability to take into account feedback from the specialist are privileged in the presented algorithms. Original methods are proposed for: • Building a triangulated surface bounding a simple volume from a pomtset. • Building a triangulated surface from a 3D polygon. • Optimizing a constrained DELAUNAY triangulation or tetrahedralization by adding points in order to improve element shapes. • Building a triangulated surface from two contours. • Building a triangulated surface joining contours lying on two parallel planes. • Finding connections between contours on seriaI cross-sections. • Filling with tetrahedra a volume defined by its triangulated boundary ; this boundary can be the union of polyhedral regions. In tetrahedralization issues, the notion of lazily canstrained tetrahedralizatian is introduced. By lazily taking into account triangles, we can reduce the number of points added inside the volume mesh only for respecting them.

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    BibTeX Reference

    @PHDTHESIS{Conraud97GMS,
        author = { Conraud, Joël },
         title = { Génération de maillages de simplexes pour la modélisation d'objets naturels },
       chapter = { 0 },
          year = { 1997 },
        school = { INPL, Nancy, France },
      abstract = { The geometric modelling of natural abjects, in medical area as well as in geosciences areas, is based on
    discrete data structures, the meshes. They partition the region of interest into basic geometric primitives.
    These meshes are used for modellings taking into account physical properties of the studied objects.
    In three dimensions, two primitives are especially used for describing domains with complicated geometry:
    the triangle (the simplex in the plane), for surface meshes, and the tetrahedron (the simplex in
    space), for volume meshes.
    Simplicial mesh generation problems are presented. Due to the nature of the problems arisen in the domain
    of application, rabustness and ability to take into account feedback from the specialist are privileged
    in the presented algorithms.
    Original methods are proposed for:
    • Building a triangulated surface bounding a simple volume from a pomtset.
    • Building a triangulated surface from a 3D polygon.
    • Optimizing a constrained DELAUNAY triangulation or tetrahedralization by adding points in order
    to improve element shapes.
    • Building a triangulated surface from two contours.
    • Building a triangulated surface joining contours lying on two parallel planes.
    • Finding connections between contours on seriaI cross-sections.
    • Filling with tetrahedra a volume defined by its triangulated boundary ; this boundary can be the
    union of polyhedral regions.
    In tetrahedralization issues, the notion of lazily canstrained tetrahedralizatian is introduced. By lazily taking
    into account triangles, we can reduce the number of points added inside the volume mesh only for
    respecting them. }
    }