Modélisation volumique de surfaces non-manifold

Karine Lamboglia. ( 1994 )
INPL, Nancy, France

Abstract

Most of the existing solid modeling systems using the boundary representation consider only manifold geometry. For a manifold object, and more precisely 2-ma,nifold, each point has a neighbourhood homeomorphic to a 2D disc. The restriction of the representation domain constitutes a major drawback for applications handling natura.l surfaces, as in the fields of Geology and Medecine. The proposed modeling system enables to extend the representation domain by ta.king into account both manifold and non-manifold conditions. The objects used by this system are surfaces represented by triangular facets. A surface is divided in several parts of connected t.riangles called faces. \'Vhile a surface may be non-manifold, a face is always manifold. As a matter of fact, by definition, a non-manifold condition appears only at the boundaries of a face. This modeling system consists in dividing the 3D space into several distinct c10sed volumes (regions), defined by their boundaries (she11s). In order to determine the adjacent faces composing the boundary of a region, there is a need to introduce specifie structures describing the adjacency relationships between the faces. More precisely the topology of the model appears at two levels: the Macro-Topology describes the adjacencies between faces, the Micro-Topology describes the adjacencies between triangles. The a,djacency structures enable to detect and define automatically every single volume closure. Two methods for building a solid model have been developed. The first one is an interactive method using a tool for gluing surfaces, thus modifying the topology of the model by creating new adjacency relationships. The second method is entirely automatic and consists in creating the adjacency structures of the model by leaning on its actual topology.

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    BibTeX Reference

    @PHDTHESIS{Lamboglia94,
        author = { Lamboglia, Karine },
         title = { Modélisation volumique de surfaces non-manifold },
       chapter = { 0 },
          year = { 1994 },
        school = { INPL, Nancy, France },
      abstract = { Most of the existing solid modeling systems using the boundary representation consider only
    manifold geometry. For a manifold object, and more precisely 2-ma,nifold, each point has a
    neighbourhood homeomorphic to a 2D disc. The restriction of the representation domain constitutes
    a major drawback for applications handling natura.l surfaces, as in the fields of Geology
    and Medecine. The proposed modeling system enables to extend the representation domain by
    ta.king into account both manifold and non-manifold conditions.
    The objects used by this system are surfaces represented by triangular facets. A surface is
    divided in several parts of connected t.riangles called faces. \'Vhile a surface may be non-manifold,
    a face is always manifold. As a matter of fact, by definition, a non-manifold condition appears
    only at the boundaries of a face.
    This modeling system consists in dividing the 3D space into several distinct c10sed volumes
    (regions), defined by their boundaries (she11s). In order to determine the adjacent faces composing
    the boundary of a region, there is a need to introduce specifie structures describing the
    adjacency relationships between the faces. More precisely the topology of the model appears at
    two levels: the Macro-Topology describes the adjacencies between faces, the Micro-Topology describes
    the adjacencies between triangles. The a,djacency structures enable to detect and define
    automatically every single volume closure.
    Two methods for building a solid model have been developed. The first one is an interactive
    method using a tool for gluing surfaces, thus modifying the topology of the model by creating
    new adjacency relationships. The second method is entirely automatic and consists in creating
    the adjacency structures of the model by leaning on its actual topology. }
    }