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GVGEN(1)						      General Commands Manual							  GVGEN(1)

NAME
gvgen - generate graphs SYNOPSIS
gvgen [ -dV? ] [ -in ] [ -cn ] [ -Cx,y ] [ -g[f]x,y ] [ -G[f]x,y ] [ -hn ] [ -kn ] [ -bx,y ] [ -Bx,y ] [ -mn ] [ -Mx,y ] [ -pn ] [ -rx,y ] [ -Rx ] [ -sn ] [ -Sn ] [ -tn ] [ -td,n ] [ -Tx,y ] [ -Tx,y,u,v ] [ -wn ] [ -nprefix ] [ -Nname ] [ -ooutfile ] DESCRIPTION
gvgen generates a variety of simple, regularly-structured abstract graphs. OPTIONS
The following options are supported: -c n Generate a cycle with n vertices and edges. -C x,y Generate an x by y cylinder. This will have x*y vertices and 2*x*y - y edges. -g [f]x,y Generate an x by y grid. If f is given, the grid is folded, with an edge attaching each pair of opposing corner vertices. This will have x*y vertices and 2*x*y - y - x edges if unfolded and 2*x*y - y - x + 2 edges if folded. -G [f]x,y Generate an x by y partial grid. If f is given, the grid is folded, with an edge attaching each pair of opposing corner vertices. This will have x*y vertices. -h n Generate a hypercube of degree n. This will have 2^n vertices and n*2^(n-1) edges. -k n Generate a complete graph on n vertices with n*(n-1)/2 edges. -b x,y Generate a complete x by y bipartite graph. This will have x+y vertices and x*y edges. -B x,y Generate an x by y ball, i.e., an x by y cylinder with two "cap" nodes closing the ends. This will have x*y + 2 vertices and 2*x*y + y edges. -m n Generate a triangular mesh with n vertices on a side. This will have (n+1)*n/2 vertices and 3*(n-1)*n/2 edges. -M x,y Generate an x by y Moebius strip. This will have x*y vertices and 2*x*y - y edges. -p n Generate a path on n vertices. This will have n-1 edges. -r x,y Generate a random graph. The number of vertices will be the largest value of the form 2^n-1 less than or equal to x. Larger values of y increase the density of the graph. -R x Generate a random rooted tree on x vertices. -s n Generate a star on n vertices. This will have n-1 edges. -S n Generate a Sierpinski graph of order n. This will have 3*(3^(n-1) - 1)/2 vertices and 3^n edges. -t n Generate a binary tree of height n. This will have 2^n-1 vertices and 2^n-2 edges. -t h,n Generate a n-ary tree of height h. -T x,y -T x,y,u,v Generate an x by y torus. This will have x*y vertices and 2*x*y edges. If u and v are given, they specify twists of that amount in the horizontal and vertical directions, respectively. -w n Generate a path on n vertices. This will have n-1 edges. -i n Generate n graphs of the requested type. At present, only available if the -R flag is used. -n prefix Normally, integers are used as node names. If prefix is specified, this will be prepended to the integer to create the name. -N name Use name as the name of the graph. By default, the graph is anonymous. -o outfile If specified, the generated graph is written into the file outfile. Otherwise, the graph is written to standard out. -d Make the generated graph directed. -V Verbose output. -? Print usage information. EXIT STATUS
gvgen exits with 0 on successful completion, and exits with 1 if given an ill-formed or incorrect flag, or if the specified output file could not be opened. AUTHOR
Emden R. Gansner <erg@research.att.com> SEE ALSO
gc(1), acyclic(1), gvpr(1), gvcolor(1), ccomps(1), sccmap(1), tred(1), libgraph(3) 5 June 2012 GVGEN(1)

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POLYMERGE(1gv)															    POLYMERGE(1gv)

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 Surface 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 original 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 cor- responding vertex in the original object). face description # oldvertno ... For each new face, with N vertices after reduction, the comment indicates N corresponding vertices in the original 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 different colors. Should be able to handle binary OFF objects, but this hasn't been tested. Geometry Center 25 July 1993 POLYMERGE(1gv)
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