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NAME
     polymerge -  merge  coincident  vertices,  collinear  edges,
     coplanar faces in an OOGL OFF object

SYNOPSIS
     polymerge   [-v   vertex_thresh]   [-e   edge_thresh]    [-f
     face_thresh] [-V] [-E] [-F] [-d] [-b] [inputfile.off]

DESCRIPTION
     Polymerge eliminates redundancies from polyhedral objects in
     OOGL's  OFF  format,  and  writes  another OFF object to its
     standard output.  (Optionally  it  can  produce  instead  an
     input file for Brakke's Evolver.)  Specifically, it combines
     nearly-coincident  vertices,  nearly-collinear  edges,   and
     nearly-coplanar  faces.   Vertices  which aren't used on any
     face are deleted, as are faces with  less  than  three  ver-
     tices.   Thresholds  for approximate equality are adjustable
     from the command line.  Options are:

     -v vertex_thresh
          Merge vertices when they're closer  than  vertex_thresh
          apart; the default is .00001.

     -V   Don't attempt to merge vertices.

     -e edge_thresh
          Merge edges where  |sin(vertex_angle)|  <  edge_thresh;
          the default is When edges are merged, the corresponding
          vertex is removed.

     -E   Don't attempt to merge edges.  (4OFF  edges  are  never
          merged.)

     -f face_thresh
          Merge faces sharing an edge where the faces are  nearly
          coplanar: when |sin(angle_between_face_normal_vectors)|
          < face_thresh.   The  default  is  .03,  or  about  two
          degrees.   Note that merging can create faces which are
          concave polygons.

     -F   Don't attempt to merge faces.  (4OFF  faces  are  never
          merged.)

     -b   Produce an output file in .fe format for Brakke's  Sur-
          face Evolver, instead of a new OFF file.

     -d   Include debugging information as comments  in  the  new
          OFF  object.   The comments indicate which vertices and
          faces in the original object correspond to which in the
          new one.  Messages include:

     # Vtx nnn->mmm
          Merged vertices nnn and mmm (both indices in the origi-
          nal object).

     # Merged face nnn into mmm (vertices vvv www) n1.n2 s
          Faces nnn and mmm in the original object  were  merged;
          their common edge joined original vertices vvv and www.
          The cosine of the angle between the face normals was s.

     vertex coordinates  # newvertno [order] # oldvertno
          Each vertex written appears with  its  new  index,  its
          order  (number  of edges touching that vertex), and its
          old index (index of a corresponding vertex in the  ori-
          ginal object).

     face description  # oldvertno ...
          For each new face, with N vertices after reduction, the
          comment  indicates N corresponding vertices in the ori-
          ginal object.

AUTHOR
     Stuart Levy, Geometry Center, University of Minnesota

SEE ALSO
     anytooff(1), offconsol(1)

BUGS
     Coplanar faces are merged even if they  were  assigned  dif-
     ferent colors.  Should be able to handle binary OFF objects,
     but this hasn't been tested.

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