Manual pages | Cast3M

$$$$ VORO     NOTICE  SH236661  13/11/25    21:15:12     7869           
                                             DATE     13/11/25

     Operateur VORONOI                       Voir aussi : TRIA
     -----------------   
     TAB1 = VORO MAIL1 MAIL2 (CHR1);

     Description :
     _____________

    The VORONOI operator builds the Voronoi tessellation of a point set
    MAIL1 limited by the closed domain MAIL2. The tessellation is stored
    in the table TAB1 described below.


     Contents :
     __________

     MAIL1 : point set (MAILLAGE type object of POI1 elements).

     MAIL2 : mesh of a closed line (boundary surface), oriented,
             connected and made up of SEG2 (TRI3) elements in 2D (3D),
             that delimits the Voronoi tessellation (MAILLAGE type
             object).

     CHR1  : CHPOINT type object, which describes the weight associated 
             to each cell sead.


     TAB1  : TABLE containing the Voronoi tessellation. The table is
             structured as follows:

       - TAB1 . 'VISU' = Mesh of all the edges of the Voronoi
                         tessellation (SEG2 elements)
       - TAB1 . 'POND' = CHPOINT type object, describes the weight  
                         associated to each cell sead

       - TAB1 . 'CELL'               = Table of Voronoi cells
       - TAB1 . 'CELL' . P1          = Table of the cell defined
                                          by the point P1
       - TAB1 . 'CELL' . P1 . 'VISU' = Mesh of the cell defined
                                          by the point P1
       - TAB1 . 'CELL' . P1 . 'FACS' = List of integers, indexes
                                          of the faces of the cell
                                          (only in 3D)
       - TAB1 . 'CELL' . P1 . 'ARTS' = List of integers, indexes
                                          of the edges of the cell
                                          (only in 2D)
       - TAB1 . 'CELL' . P1 . 'VOIS' = Neighboring points of P1

       - TAB1 . 'FACS'               = Table of the faces of the cells
       - TAB1 . 'FACS' . n1          = Table of the face n1
       - TAB1 . 'FACS' . n1 . 'VISU' = Mesh of the face n1
       - TAB1 . 'FACS' . n1 . 'ARTS' = List of integers, indexes
                                          of edges of the face n1

       - TAB1 . 'ARTS'      = Table of the edges of the cells
       - TAB1 . 'ARTS' . m1 = Mesh of the edge #m1


     Remark :
     ________
      
     * A CHPOINT type object is used to obtain a weigted Voronoi 
     tessellation. The values of these weights must verify : 
     for all pair of points (P1,P2) of weight (x1,x2), one has :
                  |(x1)**2 - (x2)**2| =< (d(P1,P2))**2
     where d(P1,P2) is the length of segment P1P2 .        


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