steveroush · January 6, 2025 02:25 · steveroush · Jul 12, 2023 · steveroush · Sep 16, 2024
diff --git a/radialLayout.gvpr b/radialLayout.gvpr
 /********************************************************************************
 RadialLayout - a radial layout engine for Graphviz

 radialLayout.gvpr takes a super-subset of Graphviz input and creates an enhanced output with explicit positioning for all nodes.  Positioning for each node is based either on new angle & distance attributes or on explicit "pos" value.  This output can be fed into `neato -n` (see https://graphviz.org/faq/#FaqDotWithNodeCoords) to route all defined edges.

 New node attributes:
  -  radialangle - angle from the origin line units:
       - radians
       - degrees
       - clock-face hour posiyion (4oc)
       - compass position (e.g. n, ne, nne, ...)
       - "fraction" (3/17) (divide 360 into 17 slices, position at 3rd).
     By default, angles are in counter-clockwise direction and are degrees.  Compass-based and clock-face-based angles are absolute.  Other angles are relative.
  -  radialdistance - distance from 0,0 in direction/angle specified by radialangle units: inches or points (in or pt). No unit defaults to inches.  (e.g. 72pt == 1in == 1)
  -  CenterOn - resets the radial center to the "pos" of an already-defined node.

 New graph attributes:

  -  radialclockwise used to request clockwise angle measurements (default is counterclockwise). Values: true or false, false is default
  -  radialstart set origin line, where default origin line is a line heading from the center of the graph to the right or (a line from 0,0 toward 999999,0) or (a line going due East). Legal values: (clock points) 1oc, 2oc, ..., 12oc and (compass points) n, s, e, w, ne, ne, se, sw, ...

 Of note:

    All nodes must have both radialangle & radialdistance values or an explicit "pos" value
    clusters do not (easily) work - a neato issue
    there is a gvpr problem setting label="" (no label).  Set a node or edge label to "" like this: `{node [label=""] X Y Z}`
    gvpr is documented here: https://graphviz.org/pdf/gvpr.1.pdf
    neato -n is documented here: https://graphviz.org/pdf/gvpr.1.pdf
    Only lightly tested!!

 How to use:
  `gvpr -c -f radialLayout.gvpr myfile.gv | neato -n -Tpng >myfile.png`

 Which Graphviz attributes do not apply?
 - attributes that only apply to a subset of the Graphviz engines (e.g. neato only)
 - attributes that affect positioning (e.g. rank, nodesep, weight)
 - attribute applicability (early guess):
 -  _background - yes
 -  Damping  - no
 -  URL - yes
 -  area - yes
 -  arrowhead - yes
 -  arrowsize - yes
 -  arrowtail - yes
 -  bgcolor - yes
 -  center - yes
 -  charset - yes
 -  class - yes
 -  clusterrank - no
 -  color - yes
 -  colorscheme - yes
 -  comment - yes
 -  compound - yes
 -  concentrate - yes
 -  constraint - no
 -  defaultdist - yes
 -  decorate - yes
 -  dim - yes
 -  dimen - yes
 -  dir - yes
 -  diredgeconstraints - yes
 -  distortion - yes
 -  dpi - yes
 -  edgeURL - yes
 -  edgehref - yes
 -  edgetarget - yes
 -  edgetooltip - yes
 -  epsilon - no
 -  esep - no
 -  fillcolor - yes
 -  fixedsize - yes
 -  fontcolor - yes
 -  fontnames - yes
 -  fontname - yes
 -  fontpath - yes
 -  fontsize - yes
 -  forcelabels - yes
 -  gradientangle - yes
 -  group - no
 -  headURL - yes
 -  headclip - yes
 -  headhref - yes
 -  headlabel - yes
 -  headport - yes
 -  headtarget - yes
 -  headtooltip - yes
 -  height - yes
 -  href - yes
 -  id - yes
 -  image - yes
 -  imagepath - yes
 -  imagepos - yes
 -  imagescale - yes
 -  inputscale - yes
 -  K - no
 -  label - yes
 -  labelURL - yes
 -  labelangle - yes
 -  labeldistance - yes
 -  labelfloat - yes
 -  labelfontcolor - yes
 -  labelfontname - yes
 -  labelfontsize - yes
 -  labelhref - yes
 -  labeljust - yes
 -  labelloc - yes
 -  labeltarget - yes
 -  labeltooltip - yes
 -  label_scheme - yes
 -  landscape - yes
 -  layer - yes
 -  layers - yes
 -  layerlistsep - yes
 -  layerselect - yes
 -  layersep - yes
 -  layout - must be neato
 -  len - no
 -  levels - no
 -  levelsgap - no
 -  lhead - yes
 -  ltail - yes
 -  margin - yes
 -  maxiter - no
 -  mclimit - no
 -  mindist - no
 -  minlen - no
 -  mode - no
 -  model - no
 -  mosek - no
 -  newrank - no
 -  nodesep - no
 -  nojustify - yes
 -  normalize - no
 -  notranslate - yes
 -  ordering - no
 -  orientation - yes
 -  outputorder - yes
 -  overlap - no
 -  overlap_scaling - no
 -  overlap_shrink - no
 -  pack - no
 -  packmode - no
 -  pad - no
 -  pagedir - yes
 -  pencolor - yes
 -  penwidth - yes
 -  peripheries - yes
 -  pin - no
 -  quadtree - no
 -  quantum - no
 -  rank - no
 -  rankdir - no
 -  ranksep - no
 -  regular - yes
 -  remincross - no
 -  repulsiveforce - no
 -  resolution - yes
 -  root - no
 -  rotate - yes
 -  rotation - no
 -  samehead - yes
 -  sametail - yes
 -  samplepoints - yes
 -  searchsize - no
 -  sep - yes
 -  shape - yes
 -  shapefile - yes
 -  showboxes - yes
 -  sides - yes
 -  skew - yes
 -  smoothing - yes
 -  sortv - no
 -  start - no
 -  style - yes
 -  stylesheet - yes
 -  tailURL - yes
 -  tailclip - yes
 -  tailhref - yes
 -  taillabel - yes
 -  tailport - yes
 -  tailtarget - yes
 -  tailtooltip - yes
 -  target - yes
 -  tooltip - yes
 -  truecolor - yes
 -  xdotversion - yes
 -  viewport - yes
 -  voro_margin - no
 -  weight - yno
 -  width - yes
 -  xlabel - yes
 -  z - yes
 ********************************************************************/
 BEGIN{
  int clockwise, absoluteAngle, noLabel[];
  float x, y, start, _CenterX, _CenterY;
  float theta, D, pi=3.14159265;
  float deg2rad=3.14159/180.;
  string numstr="?([+-])@(+([0-9])?(.*([0-9]))|\.+([0-9]))";
  string wrkStr, errStr;
  node_t cNode;
  graph_t Root;

  ////////////////////////////////////////////////////////////////////////////
  // do NOT call with direct output from sprintf
  // - there is a bug - string will be empty
  void doErrs(string eString) {
    printf(2, "(%s) Error: %s\n", $F, eString);
  }
  /////////////////////////////////////////////////////////////////////////
  // NOTE: returns string "" if invalid input (yuck)
  /////////////////////////////////////////////////////////////////////////
  string computeAngle(string Astr) {
    int Alen, Aerr;
    float Afloat;
    string Awrk, Atok[int], ASrslt;

    Aerr=0;
    Awrk=Astr;
    absoluteAngle=1;
    switch(Astr) {
    case "n":
    case "12oc":
      Afloat=90*deg2rad;
      break;
    case "1oc":
      Afloat=60*deg2rad;
      break;
    case "ne":
      Afloat=45*deg2rad;
      break;
    case "2oc":
      Afloat=30*deg2rad;
      break;
    case "e":
    case "3oc":
      Afloat=0;
      break;
    case "4oc":
      Afloat=330*deg2rad;
      break;
    case "se":
      Afloat=-45*deg2rad;
      break;
    case "5oc":
      Afloat=300*deg2rad;
      break;
    case "s":
    case "6oc":
      Afloat=270*deg2rad;
      break;
    case "7oc":
      Afloat=240*deg2rad;
      break;
    case "sw":
      Afloat=225*deg2rad;
      break;
    case "8oc":
      Afloat=210*deg2rad;
      break;
    case "w":
    case "9oc":
      Afloat=180*deg2rad;
      break;
    case "10oc":
      Afloat=150*deg2rad;
      break;
    case "nw":
      Afloat=135*deg2rad;
      break;
    case "11oc":
      Afloat=120*deg2rad;
      break;
    case "ene":
      Afloat=22.5*deg2rad;
      break;
    case "nne":
      Afloat=67.5*deg2rad;
      break;
    case "nnw":
      Afloat=112.5*deg2rad;
      break;
    case "wnw":
      Afloat=157.5*deg2rad;
      break;
    case "wsw":
      Afloat=202.5*deg2rad;
      break;
    case "ssw":
      Afloat=247.5*deg2rad;
      break;
    case "sse":
      Afloat=292.5*deg2rad;
      break;
    case "ese":
      Afloat=337.5*deg2rad;
      break;
    default:
      absoluteAngle=0;
      if (Astr=="*(?)@(r|rad|rads|radians)") {
        //print("//  RADIANs: ", Astr);
        Alen=index(Astr,"r");
        //print("//  Alen: ", Alen);
        Awrk=substr(Astr,0,Alen);
        //print("//  radians  work: ", Awrk);
        if (Awrk==numstr)
          Afloat=(float)Awrk;
        else {
          Aerr=1;
        }
      } else if (Astr=="*(?)@(d|deg|degrees)") {
        //print("//  DEGREES: ", Astr);
        Alen=index(Astr,"d");
        Awrk=substr(Astr,0,Alen);
        if (Awrk==numstr)
          Afloat=((float)Awrk)*deg2rad;
        else {
          Aerr=1;
        }
      } else if (Astr==numstr + "([/])" + numstr) {
        //print("//  Nth: ", Astr);
        split(Astr,Atok,"/");
        if ((int)Atok[1]<=0) {
          Aerr=1;
          Afloat=0;
          print("//  error bad denominator: ", Astr);
        } else {
          Afloat=2*pi*((float)Atok[0]/(float)Atok[1]);
        }
      } else if (Astr==numstr) {
        //print("//  default (degrees): ", Astr);
        Afloat=(float)Astr*deg2rad;
      } else {
        Aerr=1;
        break;
      }
    }
    if (Aerr==1) {
      print ("// error !!");
      ASrslt="";
    } else {
      ASrslt=(string)Afloat;
    }
    //print("//  returning: >", Afloat, "<");
    return ASrslt;
  }
  ////////////////////////////////////////////////////////////////////////
  float computeStartAngle(string Astr) {
    string a1;
    a1=computeAngle(Astr);
    if (a1=="") {
      errStr=sprintf("Invalid value for \"radialstart\" %s", Root.radialstart);
      doErrs(errStr);
    } else
      return (float)a1;
  }
  /////////////////////////////////////////////////////////////////////////
  float computeNodeAngle(string Astr, node_t Anode) {
    string a2;
    a2=computeAngle(Astr);
    if (a2=="") {
      errStr=sprintf("Node \"%s\" has bad radialangle attribute: %s", Anode.name, Astr);
      doErrs(errStr);
    } else
      return (float)a2;
  }
  ////////////////////////////////////////////////////////////////////////////
  // return points
  float computeDistance(string Dstr, node_t Dnode) {
    int Dlen;
    float Drslt;
    string Dwrk;

    //print("//  RAW DISTANCE: ", Dstr);
    Dwrk=Dstr;
    Dlen=length(Dstr)-1;
    if (Dstr=="*(?)@(in|inch|inches)") {
      //print("//  INCHES ", Dstr);
      Dlen=index(Dstr,"i");
      Dwrk=substr(Dstr,0,Dlen);
      //print("//  work: ", Dwrk);
      if (Dwrk==numstr)
        Drslt=72.*(float)Dwrk;  // return points
      else {
        errStr=sprintf("Node \"%s\" has bad radialdistance attribute: %s", Dnode.name, Dstr);
        doErrs(errStr);
        Drslt=0;
      }
    } else if (Dstr=="*(?)@(pt|point|points)") {
      //print("//  POINTS: ", Dstr);
      Dlen=index(Dstr,"p");
      Dwrk=substr(Dstr,0,Dlen);
      if (Dwrk==numstr)
        Drslt=((float)Dwrk);
      else {
        errStr=sprintf("Node \"%s\" has bad radialdistance attribute: %s", Dnode.name, Dstr);
        doErrs(errStr);
        Drslt=0;
      }
    } else if (Dstr==numstr) {
      //print("//  default (inches): ", Dstr);
      Drslt=72.*(float)Dstr;
    } else {
      errStr=sprintf("Node \"%s\" has bad radialdistance attribute: %s", Dnode.name, Dstr);
      doErrs(errStr);
      Drslt=0;
    }
    //print("//  DISTANCE: returning: ", Drslt);
    return Drslt;
  }

 }  // end BEGIN
 ////////////////////////////////////////////////////////////////////////////
 BEG_G{
  Root=$G;
  $G.bb="";
  clockwise=0;
  _CenterX=0;
  _CenterY=0;
  // first, determine direction /////////////////////////////////////////
  if (hasAttr($, "radialclockwise"))
    if ($.radialclockwise=="@(1|yes|true)")
      clockwise=1;
    else if ($.radialclockwise=="@(0|no|false)")
      clockwise=0;
    else {
      errStr=sprintf("Invalid value for \"radialclockwise\" %s", $.radialclockwise);
      doErrs(errStr);
    }
  // next, determine starting angle
  start=0;
  if (hasAttr($, "radialstart")) {
    wrkStr=$.radialstart;
    start=computeStartAngle(wrkStr);
  }
 }
 ////////////////////////////////////////////////////////////////////////////////
 N{
  //print("// NODE: ", $.name);
  if (hasAttr($, "label") && $.label=="") {
    print("// EMPTY label: ", $.name);
    noLabel[$]=1;
  }
  if (isAttr($G, "N", "label") && $.label=="") {
    print("// isAttr - EMPTY label: ", $.name);
    noLabel[$]=1;
  }
  if (hasAttr($, "radialangle") && $.radialangle!="") {
    theta=computeNodeAngle($.radialangle, $);
  } else if (hasAttr($, "pos") && $.pos!="") {
    continue;  // ok
  } else {
    errStr=sprintf("Node \"%s\" is missing radialangle attribute", $.name);
    doErrs(errStr);
  }
  if (hasAttr($, "radialdistance") && $.radialdistance!="") {
    D=computeDistance($.radialdistance, $);
  } else if (hasAttr($, "pos") && $.pos!="") {
    // ok
  } else {
    errStr=sprintf("Node \"%s\" is missing radialdistance attribute", $.name);
    doErrs(errStr);
  }
  if (hasAttr($, "pos") && $.pos!="") {
    continue;  // ok
  }
  if (hasAttr($, "CenterOn") && $.CenterOn!="") {
    if (isNode(Root, $.CenterOn)!=NULL) {
      cNode=node(Root, $.CenterOn);
      _CenterX=cNode.X;
      _CenterY=cNode.Y;
    }
  } else {
    // ERROR, no such node
  }
  if (absoluteAngle) {
    x=_CenterX+(D*cos(theta));
    y=_CenterY+(D*sin(theta));
  } else {
    if (clockwise==1)
      theta=-theta;  // clockwise
    x=_CenterX+(D*cos(theta+start));
    y=_CenterY+(D*sin(theta+start));
  }
  $.pos=(string)x + "," + (string)y;
 }

diff --git a/radialTest1.gv b/radialTest1.gv
 graph radialTest1 {

  graph [radialclockwise="true" radialstart="12oc"]

  label="my cool\nRadial Graph"
  
  Center[radialdistance=0 radialangle=0 label="''" style=filled fillcolor=red shape=circle fixedsize=true width=.15 height=.15]

 node[shape=point]
  b1 [radialdistance="3" radialangle="1/8"]
  b2 [radialdistance="3" radialangle="2/8" ]
  b3 [radialdistance="3" radialangle="3/8"]
  b4 [radialdistance="1.8" radialangle="4/8"]
  b5 [radialdistance="3" radialangle="5/8"]
  b6 [radialdistance="3.7" radialangle="6/8"]
  b7 [radialdistance="3" radialangle="7/8"]
  b8 [radialdistance="3" radialangle="8/8"]

 node [shape=plaintext]
  LBL1 [radialdistance="4" radialangle="1/8"]
  LBL2 [radialdistance="4" radialangle="2/8"]
  LBL3 [radialdistance="4" radialangle="3/8"]
  LBL4 [radialdistance="4" radialangle="4/8"]
  LBL5 [radialdistance="4" radialangle="5/8"]
  LBL6 [radialdistance="4" radialangle="6/8"]
  LBL7 [radialdistance="4" radialangle="7/8"]
  LBL8 [radialdistance="4" radialangle="8/8"]

 Center -- b1 [style=dashed]
 Center -- b2 [style=dashed]
 Center -- b3 [style=dotted color=green]
 Center -- b4 [style=dashed]
 Center -- b5 [color=blue]
 Center -- b6
 Center -- b7
 Center -- b8

 }
diff --git a/radialTest1.png b/radialTest1.png
diff --git a/radialTest101.gv b/radialTest101.gv
 // wrote this with gawk script
 graph RR{
  label="Graphviz - New Radial Engine Tricks (101)"
  node [shape=point colorscheme=set312]
  edge [colorscheme=set312]
  "n_0.9.0" [radialdistance=0.9 radialangle=213 color=1]
  "n_0.9.2" [radialdistance=0.9 radialangle=215 color=1]
  "n_0.9.4" [radialdistance=0.9 radialangle=217 color=1]
  "n_0.9.6" [radialdistance=0.9 radialangle=219 color=1]
  "n_0.9.8" [radialdistance=0.9 radialangle=221 color=1]
  "n_0.9.10" [radialdistance=0.9 radialangle=223 color=1]
  "n_0.9.12" [radialdistance=0.9 radialangle=225 color=1]
  "n_0.9.14" [radialdistance=0.9 radialangle=227 color=1]
  "n_0.9.16" [radialdistance=0.9 radialangle=229 color=1]
  "n_0.9.18" [radialdistance=0.9 radialangle=231 color=1]
  "n_0.9.20" [radialdistance=0.9 radialangle=233 color=1]
  "n_0.9.22" [radialdistance=0.9 radialangle=235 color=1]
  "n_0.9.24" [radialdistance=0.9 radialangle=237 color=1]
  "n_0.9.26" [radialdistance=0.9 radialangle=239 color=1]
  "n_0.9.28" [radialdistance=0.9 radialangle=241 color=1]
  "n_0.9.30" [radialdistance=0.9 radialangle=243 color=1]
  "n_0.9.32" [radialdistance=0.9 radialangle=245 color=1]
  "n_0.9.34" [radialdistance=0.9 radialangle=247 color=1]
  "n_0.9.36" [radialdistance=0.9 radialangle=249 color=1]
  "n_0.9.38" [radialdistance=0.9 radialangle=251 color=1]
  "n_0.9.40" [radialdistance=0.9 radialangle=253 color=1]
  "n_0.9.42" [radialdistance=0.9 radialangle=255 color=1]
  "n_0.9.44" [radialdistance=0.9 radialangle=257 color=1]
  "n_0.9.46" [radialdistance=0.9 radialangle=259 color=1]
  "n_0.9.48" [radialdistance=0.9 radialangle=261 color=1]
  "n_0.9.50" [radialdistance=0.9 radialangle=263 color=1]
  "n_0.9.52" [radialdistance=0.9 radialangle=265 color=1]
  "n_0.9.54" [radialdistance=0.9 radialangle=267 color=1]
  "n_0.9.56" [radialdistance=0.9 radialangle=269 color=1]
  "n_0.9.58" [radialdistance=0.9 radialangle=271 color=1]
  "n_0.9.60" [radialdistance=0.9 radialangle=273 color=1]
  "n_0.9.62" [radialdistance=0.9 radialangle=275 color=1]
  "n_0.9.64" [radialdistance=0.9 radialangle=277 color=1]
  "n_0.9.66" [radialdistance=0.9 radialangle=279 color=1]
  "n_0.9.68" [radialdistance=0.9 radialangle=281 color=1]
  "n_0.9.70" [radialdistance=0.9 radialangle=283 color=1]
  "n_0.9.72" [radialdistance=0.9 radialangle=285 color=1]
  "n_0.9.74" [radialdistance=0.9 radialangle=287 color=1]
  "n_0.9.76" [radialdistance=0.9 radialangle=289 color=1]
  "n_0.9.78" [radialdistance=0.9 radialangle=291 color=1]
  "n_0.9.80" [radialdistance=0.9 radialangle=293 color=1]
  "n_0.9.82" [radialdistance=0.9 radialangle=295 color=1]
  "n_0.9.84" [radialdistance=0.9 radialangle=297 color=1]
  "n_0.9.86" [radialdistance=0.9 radialangle=299 color=1]
  "n_0.9.88" [radialdistance=0.9 radialangle=301 color=1]
  "n_0.9.90" [radialdistance=0.9 radialangle=303 color=1]
  "n_0.9.92" [radialdistance=0.9 radialangle=305 color=1]
  "n_0.9.94" [radialdistance=0.9 radialangle=307 color=1]
  "n_0.9.96" [radialdistance=0.9 radialangle=309 color=1]
  "n_0.9.98" [radialdistance=0.9 radialangle=311 color=1]
  "n_0.9.100" [radialdistance=0.9 radialangle=313 color=1]
  "n_0.9.102" [radialdistance=0.9 radialangle=315 color=1]
  "n_0.9.104" [radialdistance=0.9 radialangle=317 color=1]
  "n_0.9.106" [radialdistance=0.9 radialangle=319 color=1]
  "n_0.9.108" [radialdistance=0.9 radialangle=321 color=1]
  "n_0.9.110" [radialdistance=0.9 radialangle=323 color=1]
  "n_0.9.112" [radialdistance=0.9 radialangle=325 color=1]
  "n_0.9.114" [radialdistance=0.9 radialangle=327 color=1]
  "n_0.9.116" [radialdistance=0.9 radialangle=329 color=1]
  "n_0.9.118" [radialdistance=0.9 radialangle=331 color=1]
  "n_0.9.120" [radialdistance=0.9 radialangle=333 color=1]
  "n_0.9.122" [radialdistance=0.9 radialangle=335 color=1]
  "n_0.9.124" [radialdistance=0.9 radialangle=337 color=1]
  "n_0.9.126" [radialdistance=0.9 radialangle=339 color=1]
  "n_0.9.128" [radialdistance=0.9 radialangle=341 color=1]
  "n_0.9.130" [radialdistance=0.9 radialangle=343 color=1]
  "n_0.9.132" [radialdistance=0.9 radialangle=345 color=1]
  "n_0.9.134" [radialdistance=0.9 radialangle=347 color=1]
  "n_0.9.136" [radialdistance=0.9 radialangle=349 color=1]
  "n_0.9.138" [radialdistance=0.9 radialangle=351 color=1]
  "n_0.9.140" [radialdistance=0.9 radialangle=353 color=1]
  "n_0.9.142" [radialdistance=0.9 radialangle=355 color=1]
  "n_0.9.144" [radialdistance=0.9 radialangle=357 color=1]
  "n_0.9.146" [radialdistance=0.9 radialangle=359 color=1]
  "n_0.9.148" [radialdistance=0.9 radialangle=361 color=1]
  "n_0.9.150" [radialdistance=0.9 radialangle=363 color=1]
  "n_0.9.152" [radialdistance=0.9 radialangle=365 color=1]
  "n_0.9.154" [radialdistance=0.9 radialangle=367 color=1]
  "n_0.9.156" [radialdistance=0.9 radialangle=369 color=1]
  "n_0.9.158" [radialdistance=0.9 radialangle=371 color=1]
  "n_0.9.160" [radialdistance=0.9 radialangle=373 color=1]
  "n_0.9.162" [radialdistance=0.9 radialangle=375 color=1]
  "n_0.9.164" [radialdistance=0.9 radialangle=377 color=1]
  "n_0.9.166" [radialdistance=0.9 radialangle=379 color=1]
  "n_0.9.168" [radialdistance=0.9 radialangle=381 color=1]
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 }
diff --git a/radialTest101.png b/radialTest101.png
diff --git a/radialTest103.gv b/radialTest103.gv
 // written by gawk script
 graph RR{
  label="Graphviz - New Radial Engine Tricks (103) (accidentally wacky)"
  node [shape=point colorscheme=set312]
  edge [colorscheme=set312]
  Center[radialdistance=0 radialangle=0 label="" style=filled  shape=point]

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  "n_3.69618_120" -- "n_2.96053_135"[color="#c96f55"]
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  "n_2.96053_135" -- "n_3.11552_150"[color="#19c8d5"]
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  "n_3.11552_150" -- "n_3.04484_165"[color="#7e6df2"]
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  "n_3.04484_165" -- "n_3.28721_180"[color="#b5281e"]
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  "n_3.28721_180" -- "n_3.63874_195"[color="#de73b4"]
  "n_1.59875_210" [radialdistance=1.59875 radialangle="210/23" color="#a5b24c"]
  "n_3.63874_195" -- "n_1.59875_210"[color="#a5b24c"]
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  "n_1.59875_210" -- "n_2.36666_225"[color="#f428cc"]
  "n_0.529552_240" [radialdistance=0.529552 radialangle="240/23" color="#8cfbd2"]
  "n_2.36666_225" -- "n_0.529552_240"[color="#8cfbd2"]
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  "n_0.529552_240" -- "n_1.69194_255"[color="#f6cb2c"]
  "n_2.27526_270" [radialdistance=2.27526 radialangle="270/23" color="#ee3405"]
  "n_1.69194_255" -- "n_2.27526_270"[color="#ee3405"]
  "n_3.39672_285" [radialdistance=3.39672 radialangle="285/23" color="#b9c232"]
  "n_2.27526_270" -- "n_3.39672_285"[color="#b9c232"]
  "n_2.99436_300" [radialdistance=2.99436 radialangle="300/23" color="#6e77c8"]
  "n_3.39672_285" -- "n_2.99436_300"[color="#6e77c8"]
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  "n_2.99436_300" -- "n_1.29514_315"[color="#18e2fa"]
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  "n_1.29514_315" -- "n_2.48285_330"[color="#2870fd"]
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  "n_2.48285_330" -- "n_3.96094_345"[color="#776cb1"]
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  "n_3.96094_345" -- "n_0.507738_360"[color="#493f92"]
  "n_2.0822_375" [radialdistance=2.0822 radialangle="375/23" color="#468688"]
  "n_0.507738_360" -- "n_2.0822_375"[color="#468688"]
  "n_2.5562_390" [radialdistance=2.5562 radialangle="390/23" color="#d00308"]
  "n_2.0822_375" -- "n_2.5562_390"[color="#d00308"]
  "n_0.366654_405" [radialdistance=0.366654 radialangle="405/23" color="#725f29"]
  "n_2.5562_390" -- "n_0.366654_405"[color="#725f29"]
  "n_1.84317_420" [radialdistance=1.84317 radialangle="420/23" color="#618807"]
  "n_0.366654_405" -- "n_1.84317_420"[color="#618807"]
  "n_2.43624_435" [radialdistance=2.43624 radialangle="435/23" color="#52c76b"]
  "n_1.84317_420" -- "n_2.43624_435"[color="#52c76b"]
  "n_0.651511_450" [radialdistance=0.651511 radialangle="450/23" color="#f9362f"]
  "n_2.43624_435" -- "n_0.651511_450"[color="#f9362f"]
  "n_0.651511_450" -- "n_3.69618_120" [color="#f9362f"]
 }
diff --git a/radialTest103.png b/radialTest103.png
diff --git a/radialTest104.gv b/radialTest104.gv
 // written by gawk script
 graph RR{
  label="Graphviz - New Radial Engine Tricks (104)"
  node [shape=point colorscheme=set312]
  edge [colorscheme=set312]
  Center[radialdistance=0 radialangle=0 label="" style=filled  shape=point]

  "n_3.69618_1" [radialdistance=3.69618 radialangle="1/23" color="#984e94"]
  "n_2.96053_2" [radialdistance=2.96053 radialangle="2/23" color="#c96f55"]
  "n_3.69618_1" -- "n_2.96053_2"[color="#c96f55"]
  "n_3.11552_3" [radialdistance=3.11552 radialangle="3/23" color="#19c8d5"]
  "n_2.96053_2" -- "n_3.11552_3"[color="#19c8d5"]
  "n_3.04484_4" [radialdistance=3.04484 radialangle="4/23" color="#7e6df2"]
  "n_3.11552_3" -- "n_3.04484_4"[color="#7e6df2"]
  "n_3.28721_5" [radialdistance=3.28721 radialangle="5/23" color="#b5281e"]
  "n_3.04484_4" -- "n_3.28721_5"[color="#b5281e"]
  "n_3.63874_6" [radialdistance=3.63874 radialangle="6/23" color="#de73b4"]
  "n_3.28721_5" -- "n_3.63874_6"[color="#de73b4"]
  "n_1.59875_7" [radialdistance=1.59875 radialangle="7/23" color="#a5b24c"]
  "n_3.63874_6" -- "n_1.59875_7"[color="#a5b24c"]
  "n_2.36666_8" [radialdistance=2.36666 radialangle="8/23" color="#f428cc"]
  "n_1.59875_7" -- "n_2.36666_8"[color="#f428cc"]
  "n_0.529552_9" [radialdistance=0.529552 radialangle="9/23" color="#8cfbd2"]
  "n_2.36666_8" -- "n_0.529552_9"[color="#8cfbd2"]
  "n_1.69194_10" [radialdistance=1.69194 radialangle="10/23" color="#f6cb2c"]
  "n_0.529552_9" -- "n_1.69194_10"[color="#f6cb2c"]
  "n_2.27526_11" [radialdistance=2.27526 radialangle="11/23" color="#ee3405"]
  "n_1.69194_10" -- "n_2.27526_11"[color="#ee3405"]
  "n_3.39672_12" [radialdistance=3.39672 radialangle="12/23" color="#b9c232"]
  "n_2.27526_11" -- "n_3.39672_12"[color="#b9c232"]
  "n_2.99436_13" [radialdistance=2.99436 radialangle="13/23" color="#6e77c8"]
  "n_3.39672_12" -- "n_2.99436_13"[color="#6e77c8"]
  "n_1.29514_14" [radialdistance=1.29514 radialangle="14/23" color="#18e2fa"]
  "n_2.99436_13" -- "n_1.29514_14"[color="#18e2fa"]
  "n_2.48285_15" [radialdistance=2.48285 radialangle="15/23" color="#2870fd"]
  "n_1.29514_14" -- "n_2.48285_15"[color="#2870fd"]
  "n_3.96094_16" [radialdistance=3.96094 radialangle="16/23" color="#776cb1"]
  "n_2.48285_15" -- "n_3.96094_16"[color="#776cb1"]
  "n_0.507738_17" [radialdistance=0.507738 radialangle="17/23" color="#493f92"]
  "n_3.96094_16" -- "n_0.507738_17"[color="#493f92"]
  "n_2.0822_18" [radialdistance=2.0822 radialangle="18/23" color="#468688"]
  "n_0.507738_17" -- "n_2.0822_18"[color="#468688"]
  "n_2.5562_19" [radialdistance=2.5562 radialangle="19/23" color="#d00308"]
  "n_2.0822_18" -- "n_2.5562_19"[color="#d00308"]
  "n_0.366654_20" [radialdistance=0.366654 radialangle="20/23" color="#725f29"]
  "n_2.5562_19" -- "n_0.366654_20"[color="#725f29"]
  "n_1.84317_21" [radialdistance=1.84317 radialangle="21/23" color="#618807"]
  "n_0.366654_20" -- "n_1.84317_21"[color="#618807"]
  "n_2.43624_22" [radialdistance=2.43624 radialangle="22/23" color="#52c76b"]
  "n_1.84317_21" -- "n_2.43624_22"[color="#52c76b"]
  "n_0.651511_23" [radialdistance=0.651511 radialangle="23/23" color="#f9362f"]
  "n_2.43624_22" -- "n_0.651511_23"[color="#f9362f"]
  "n_0.651511_23" -- "n_3.69618_1" [color="#f9362f"]
 }
diff --git a/radialTest104.png b/radialTest104.png
diff --git a/radialTest11.gv b/radialTest11.gv
 digraph radialTest11 {
  // set optional radial parameters
  graph [radialclockwise="true" radialstart="12oc"]


  label="another cool\nRadial Graph"
  
  // define Center, needed by this graph type as tail of edges
  Center[radialdistance=0 radialangle=0 label="" style=filled  shape=point]

  {
  node [shape=plaintext label=<
  <table border="0" cellborder="1" cellspacing="0">
  <tr>  <td><i>Input Foo</i></td><td> two </td>   </tr>
  <tr>  <td bgcolor="lightblue" port="1">one</td><td> two </td></tr>
  <tr>  <td port="2">two</td><td> four </td></tr>
  </table>>]

  b1 [radialdistance="3" radialangle="1/9"]
  b2 [radialdistance="3" radialangle="2/9" ]
  b3 [radialdistance="3" radialangle="3/9"]
  b4 [radialdistance="1.8" radialangle="4/9"]
  node [shape=plaintext label=<
  <table border="0" cellborder="1" cellspacing="0">
  <tr>  <td bgcolor="green1"><i>This</i></td><td>That</td>   </tr>
  <tr>  <td port="1">100</td><td>bagles</td></tr>
  <tr>  <td port="2">333</td><td>tacos</td></tr>
  </table>>]
  b5 [radialdistance="3" radialangle="5/9"]
  b6 [radialdistance="3.6" radialangle="6/9"]
  b7 [radialdistance="3" radialangle="7/9"]
  b8 [radialdistance="1.1" radialangle="8/9"]
  node [shape=ellipse label="Over\nunder"]
  b9 [radialdistance="3" radialangle="9/9"]  
  }

 edge [arrowhead=normal]  //dir=forward headclip=false]  // why is dir needed?
 Center -> b1 [style=dashed]
 Center -> b2 [style=dashed]
 Center -> b3 [style=dotted color=darkgreen]
 Center -> b4
 Center -> b5 [color=blue arrowhead=odot]
 Center -> b6 [penwidth=3 arrowhead=odot]
 Center -> b7 [headclip=false arrowhead=dot]
 Center -> b8
 Center -> b9 [style=dashed ]

 }
diff --git a/radialTest11.png b/radialTest11.png
diff --git a/radialTestAngles.gv b/radialTestAngles.gv
 graph radialAngles {

  label="Radial Angles"

 node[shape=circle style=filled fillcolor=cyan radialdistance="3"]
 
 "n" [radialangle="n"  radialdistance=3]
 "12oc" [radialangle="12oc"  radialdistance=4.4]
 "1oc" [radialangle="1oc"  radialdistance=4.4]
 "ne" [radialangle="ne"  radialdistance=3]
 "2oc" [radialangle="2oc"  radialdistance=4.4]
 "e" [radialangle="e"  radialdistance=3]
 "3oc" [radialangle="3oc"  radialdistance=4.4]
 "4oc" [radialangle="4oc"  radialdistance=4.4]
 "se" [radialangle="se"  radialdistance=3]
 "5oc" [radialangle="5oc"  radialdistance=4.4]
 "s" [radialangle="s"  radialdistance=3]
 "6oc" [radialangle="6oc"  radialdistance=4.4]
 "7oc" [radialangle="7oc"  radialdistance=4.4]
 "sw" [radialangle="sw"  radialdistance=3]
 "8oc" [radialangle="8oc"  radialdistance=4.4]
 "w" [radialangle="w"  radialdistance=3]
 "9oc" [radialangle="9oc"  radialdistance=4.4]
 "10oc" [radialangle="10oc"  radialdistance=4.4]
 "nw" [radialangle="nw"  radialdistance=3]
 "11oc" [radialangle="11oc"  radialdistance=4.4]
 "ene" [radialangle="ene"  radialdistance=3]
 "nne" [radialangle="nne"  radialdistance=3]
 "nnw" [radialangle="nnw"  radialdistance=3]
 "wnw" [radialangle="wnw"  radialdistance=3]
 "wsw" [radialangle="wsw"  radialdistance=3]
 "ssw" [radialangle="ssw"  radialdistance=3]
 "sse" [radialangle="sse"  radialdistance=3]
 "ese" [radialangle="ese"  radialdistance=3]

  {
  node[shape=circle  style=filled fillcolor=lightpink CenterOn="2oc" radialdistance="3.1"]
  AAA [ radialangle="ne"]
  node[shape=circle  style=filled fillcolor=lightpink CenterOn="AAA" radialdistance="2.1"]
  DD1 [ radialangle="n"]
  DD2 [ radialangle="ne"]
  DD3 [ radialangle="s"]
  DD4 [ radialangle="nw"]
  }
  AAA--"2oc"
  AAA--{DD1 DD2 DD3 DD4}
  {
  node[shape=circle  style=filled fillcolor=yellow CenterOn="6oc" radialdistance="3"]
  BBB [ radialangle="s"]
  node[shape=circle  style=filled fillcolor=yellow CenterOn="BBB" radialdistance="2"]
  EE1 [ radialangle="ne"]
  EE2 [ radialangle="se"]
  EE3 [ radialangle="s"]
  EE4 [ radialangle="w"]
  EE5 [ radialangle="wsw"]  
  }
  "6oc"--BBB
  BBB--{EE1 EE2 EE3 EE4 EE5}
 }
diff --git a/radialTestAngles.png b/radialTestAngles.png
diff --git a/radialTestClock4:45.gv b/radialTestClock4:45.gv
 digraph radialTestClock {
  // set optional radial parameters
  graph [radialclockwise="true" radialstart="12oc"]

  label="Clock: 4:45"
  
  // define Center, needed by this graph type as tail of edges
  Center[radialdistance=0 radialangle=0 label="" style=filled  shape=point]

  {
  node [shape=circle width=.6 radialdistance="4" ]
  1 [ radialangle="1/12"]
  2 [ radialangle="2/12"]
  3 [ radialangle="3/12"]
  4 [ radialangle="4/12"]
  5 [ radialangle="5/12"]
  6 [ radialangle="6/12"]
  7 [ radialangle="7/12"]
  8 [ radialangle="8/12"]
  9 [ radialangle="9/12"]
  10 [ radialangle="10/12"]
  11 [ radialangle="11/12"]
  12 [ radialangle="12/12"] 
  
  node[shape=point style=invis  xlabel="\N"]
  hr [radialdistance="2.1" radialangle="4.75/12"]
  min [radialdistance="3.5" radialangle="9/12" ]
 
  }
 

 Center -> hr //[style=dashed]
 Center -> min // [style=dashed]

 }
diff --git a/radialTestClock4:45.png b/radialTestClock4:45.png
diff --git a/radialTestConcentric1.gv b/radialTestConcentric1.gv
 graph radialTestClock {
  // set optional radial parameters
  graph [radialclockwise="false" radialstart="-60deg"]

  label="concentric"
  
  // define Center, needed by this graph type as tail of edges
  Center[radialdistance=0 radialangle=0 label="" style=invis  shape=point]

  {
  node [shape=circle width=.6 radialdistance="2" ]
  Aa [ radialangle="1/6"]
  Ba [ radialangle="2/6"]
  Ca [ radialangle="3/6"]
  Da [ radialangle="4/6"]
  Ea [ radialangle="5/6"]
  Fa [ radialangle="6/6"]
  }
  {
  node [shape=circle width=.6 radialdistance="4" ]
  Ab [ radialangle="1/6"]
  Bb [ radialangle="2/6"]
  Cb [ radialangle="3/6"]
  Db [ radialangle="4/6"]
  Eb [ radialangle="5/6"]
  Fb [ radialangle="6/6"]
  }  
  Aa --  Ba -- Ca --  Da --  Ea --  Fa -- Aa
  Ab --  Bb -- Cb --  Db --  Eb --  Fb -- Ab
  
  Aa -- Ab
  Ba -- Bb
  Ca -- Cb
  Da -- Db
  Ea -- Eb
  Fa -- Fb
 }
diff --git a/radialTestConcentric1.png b/radialTestConcentric1.png
diff --git a/radialTestPos.gv b/radialTestPos.gv
 graph radialAngles {

  label="Radial Angles"

 A [pos="100,100" shape=rect]
 B [pos="400,200" shape=rect]
 C [pos="700,300" shape=rect]
 D [pos="1000,400" shape=rect]

 node[shape=circle style=filled fillcolor=cyan radialdistance="3" CenterOn="A"]
 
 "n" [radialangle="n"  radialdistance=3]
 "12oc" [radialangle="12oc"  radialdistance=4.4]
 "1oc" [radialangle="1oc"  radialdistance=4.4]
 "ne" [radialangle="ne"  radialdistance=3]
 "2oc" [radialangle="2oc"  radialdistance=4.4]
 "e" [radialangle="e"  radialdistance=3]
 "3oc" [radialangle="3oc"  radialdistance=4.4]
 "4oc" [radialangle="4oc"  radialdistance=4.4]
 "se" [radialangle="se"  radialdistance=3]
 "5oc" [radialangle="5oc"  radialdistance=4.4]
 "s" [radialangle="s"  radialdistance=3]
 "6oc" [radialangle="6oc"  radialdistance=4.4]
 "7oc" [radialangle="7oc"  radialdistance=4.4]
 "sw" [radialangle="sw"  radialdistance=3]
 "8oc" [radialangle="8oc"  radialdistance=4.4]
 "w" [radialangle="w"  radialdistance=3]
 "9oc" [radialangle="9oc"  radialdistance=4.4]
 "10oc" [radialangle="10oc"  radialdistance=4.4]
 "nw" [radialangle="nw"  radialdistance=3]
 "11oc" [radialangle="11oc"  radialdistance=4.4]
 node[shape=circle style=filled fillcolor=orange radialdistance="3" CenterOn="D"]
 "ene" [radialangle="ene"  radialdistance=3]
 "nne" [radialangle="nne"  radialdistance=3]
 "nnw" [radialangle="nnw"  radialdistance=3]
 "wnw" [radialangle="wnw"  radialdistance=3]
 "wsw" [radialangle="wsw"  radialdistance=3]
 "ssw" [radialangle="ssw"  radialdistance=3]
 "sse" [radialangle="sse"  radialdistance=3]
 "ese" [radialangle="ese"  radialdistance=3]

  {
  node[shape=circle  style=filled fillcolor=lightpink CenterOn="2oc" radialdistance="3.1"]
  AAA [ radialangle="ne"]
  node[shape=circle  style=filled fillcolor=lightpink CenterOn="AAA" radialdistance="2.1"]
  DD1 [ radialangle="n"]
  DD2 [ radialangle="ne"]
  DD3 [ radialangle="s"]
  DD4 [ radialangle="nw"]
  }
  AAA--"2oc"
  AAA--{DD1 DD2 DD3 DD4}
  {
  node[shape=circle  style=filled fillcolor=yellow CenterOn="6oc" radialdistance="3"]
  BBB [ radialangle="s"]
  node[shape=circle  style=filled fillcolor=yellow CenterOn="BBB" radialdistance="2"]
  EE1 [ radialangle="ne"]
  EE2 [ radialangle="se"]
  EE3 [ radialangle="s"]
  EE4 [ radialangle="w"]
  EE5 [ radialangle="wsw"]  
  }
  "6oc"--BBB
  BBB--{EE1 EE2 EE3 EE4 EE5}
 }
diff --git a/radialTestPos.png b/radialTestPos.png
	/********************************************************************************
	RadialLayout - a radial layout engine for Graphviz

	radialLayout.gvpr takes a super-subset of Graphviz input and creates an enhanced output with explicit positioning for all nodes. Positioning for each node is based either on new angle & distance attributes or on explicit "pos" value. This output can be fed into `neato -n` (see https://graphviz.org/faq/#FaqDotWithNodeCoords) to route all defined edges.

	New node attributes:
	- radialangle - angle from the origin line units:
	- radians
	- degrees
	- clock-face hour posiyion (4oc)
	- compass position (e.g. n, ne, nne, ...)
	- "fraction" (3/17) (divide 360 into 17 slices, position at 3rd).
	By default, angles are in counter-clockwise direction and are degrees. Compass-based and clock-face-based angles are absolute. Other angles are relative.
	- radialdistance - distance from 0,0 in direction/angle specified by radialangle units: inches or points (in or pt). No unit defaults to inches. (e.g. 72pt == 1in == 1)
	- CenterOn - resets the radial center to the "pos" of an already-defined node.

	New graph attributes:

	- radialclockwise used to request clockwise angle measurements (default is counterclockwise). Values: true or false, false is default
	- radialstart set origin line, where default origin line is a line heading from the center of the graph to the right or (a line from 0,0 toward 999999,0) or (a line going due East). Legal values: (clock points) 1oc, 2oc, ..., 12oc and (compass points) n, s, e, w, ne, ne, se, sw, ...

	Of note:

	All nodes must have both radialangle & radialdistance values or an explicit "pos" value
	clusters do not (easily) work - a neato issue
	there is a gvpr problem setting label="" (no label). Set a node or edge label to "" like this: `{node [label=""] X Y Z}`
	gvpr is documented here: https://graphviz.org/pdf/gvpr.1.pdf
	neato -n is documented here: https://graphviz.org/pdf/gvpr.1.pdf
	Only lightly tested!!

	How to use:
	`gvpr -c -f radialLayout.gvpr myfile.gv \| neato -n -Tpng >myfile.png`

	Which Graphviz attributes do not apply?
	- attributes that only apply to a subset of the Graphviz engines (e.g. neato only)
	- attributes that affect positioning (e.g. rank, nodesep, weight)
	- attribute applicability (early guess):
	- _background - yes
	- Damping - no
	- URL - yes
	- area - yes
	- arrowhead - yes
	- arrowsize - yes
	- arrowtail - yes
	- bgcolor - yes
	- center - yes
	- charset - yes
	- class - yes
	- clusterrank - no
	- color - yes
	- colorscheme - yes
	- comment - yes
	- compound - yes
	- concentrate - yes
	- constraint - no
	- defaultdist - yes
	- decorate - yes
	- dim - yes
	- dimen - yes
	- dir - yes
	- diredgeconstraints - yes
	- distortion - yes
	- dpi - yes
	- edgeURL - yes
	- edgehref - yes
	- edgetarget - yes
	- edgetooltip - yes
	- epsilon - no
	- esep - no
	- fillcolor - yes
	- fixedsize - yes
	- fontcolor - yes
	- fontnames - yes
	- fontname - yes
	- fontpath - yes
	- fontsize - yes
	- forcelabels - yes
	- gradientangle - yes
	- group - no
	- headURL - yes
	- headclip - yes
	- headhref - yes
	- headlabel - yes
	- headport - yes
	- headtarget - yes
	- headtooltip - yes
	- height - yes
	- href - yes
	- id - yes
	- image - yes
	- imagepath - yes
	- imagepos - yes
	- imagescale - yes
	- inputscale - yes
	- K - no
	- label - yes
	- labelURL - yes
	- labelangle - yes
	- labeldistance - yes
	- labelfloat - yes
	- labelfontcolor - yes
	- labelfontname - yes
	- labelfontsize - yes
	- labelhref - yes
	- labeljust - yes
	- labelloc - yes
	- labeltarget - yes
	- labeltooltip - yes
	- label_scheme - yes
	- landscape - yes
	- layer - yes
	- layers - yes
	- layerlistsep - yes
	- layerselect - yes
	- layersep - yes
	- layout - must be neato
	- len - no
	- levels - no
	- levelsgap - no
	- lhead - yes
	- ltail - yes
	- margin - yes
	- maxiter - no
	- mclimit - no
	- mindist - no
	- minlen - no
	- mode - no
	- model - no
	- mosek - no
	- newrank - no
	- nodesep - no
	- nojustify - yes
	- normalize - no
	- notranslate - yes
	- ordering - no
	- orientation - yes
	- outputorder - yes
	- overlap - no
	- overlap_scaling - no
	- overlap_shrink - no
	- pack - no
	- packmode - no
	- pad - no
	- pagedir - yes
	- pencolor - yes
	- penwidth - yes
	- peripheries - yes
	- pin - no
	- quadtree - no
	- quantum - no
	- rank - no
	- rankdir - no
	- ranksep - no
	- regular - yes
	- remincross - no
	- repulsiveforce - no
	- resolution - yes
	- root - no
	- rotate - yes
	- rotation - no
	- samehead - yes
	- sametail - yes
	- samplepoints - yes
	- searchsize - no
	- sep - yes
	- shape - yes
	- shapefile - yes
	- showboxes - yes
	- sides - yes
	- skew - yes
	- smoothing - yes
	- sortv - no
	- start - no
	- style - yes
	- stylesheet - yes
	- tailURL - yes
	- tailclip - yes
	- tailhref - yes
	- taillabel - yes
	- tailport - yes
	- tailtarget - yes
	- tailtooltip - yes
	- target - yes
	- tooltip - yes
	- truecolor - yes
	- xdotversion - yes
	- viewport - yes
	- voro_margin - no
	- weight - yno
	- width - yes
	- xlabel - yes
	- z - yes
	********************************************************************/
	BEGIN{
	int clockwise, absoluteAngle, noLabel[];
	float x, y, start, _CenterX, _CenterY;
	float theta, D, pi=3.14159265;
	float deg2rad=3.14159/180.;
	string numstr="?([+-])@(+([0-9])?(.*([0-9]))\|\.+([0-9]))";
	string wrkStr, errStr;
	node_t cNode;
	graph_t Root;

	////////////////////////////////////////////////////////////////////////////
	// do NOT call with direct output from sprintf
	// - there is a bug - string will be empty
	void doErrs(string eString) {
	printf(2, "(%s) Error: %s\n", $F, eString);
	}
	/////////////////////////////////////////////////////////////////////////
	// NOTE: returns string "" if invalid input (yuck)
	/////////////////////////////////////////////////////////////////////////
	string computeAngle(string Astr) {
	int Alen, Aerr;
	float Afloat;
	string Awrk, Atok[int], ASrslt;

	Aerr=0;
	Awrk=Astr;
	absoluteAngle=1;
	switch(Astr) {
	case "n":
	case "12oc":
	Afloat=90*deg2rad;
	break;
	case "1oc":
	Afloat=60*deg2rad;
	break;
	case "ne":
	Afloat=45*deg2rad;
	break;
	case "2oc":
	Afloat=30*deg2rad;
	break;
	case "e":
	case "3oc":
	Afloat=0;
	break;
	case "4oc":
	Afloat=330*deg2rad;
	break;
	case "se":
	Afloat=-45*deg2rad;
	break;
	case "5oc":
	Afloat=300*deg2rad;
	break;
	case "s":
	case "6oc":
	Afloat=270*deg2rad;
	break;
	case "7oc":
	Afloat=240*deg2rad;
	break;
	case "sw":
	Afloat=225*deg2rad;
	break;
	case "8oc":
	Afloat=210*deg2rad;
	break;
	case "w":
	case "9oc":
	Afloat=180*deg2rad;
	break;
	case "10oc":
	Afloat=150*deg2rad;
	break;
	case "nw":
	Afloat=135*deg2rad;
	break;
	case "11oc":
	Afloat=120*deg2rad;
	break;
	case "ene":
	Afloat=22.5*deg2rad;
	break;
	case "nne":
	Afloat=67.5*deg2rad;
	break;
	case "nnw":
	Afloat=112.5*deg2rad;
	break;
	case "wnw":
	Afloat=157.5*deg2rad;
	break;
	case "wsw":
	Afloat=202.5*deg2rad;
	break;
	case "ssw":
	Afloat=247.5*deg2rad;
	break;
	case "sse":
	Afloat=292.5*deg2rad;
	break;
	case "ese":
	Afloat=337.5*deg2rad;
	break;
	default:
	absoluteAngle=0;
	if (Astr=="*(?)@(r\|rad\|rads\|radians)") {
	//print("// RADIANs: ", Astr);
	Alen=index(Astr,"r");
	//print("// Alen: ", Alen);
	Awrk=substr(Astr,0,Alen);
	//print("// radians work: ", Awrk);
	if (Awrk==numstr)
	Afloat=(float)Awrk;
	else {
	Aerr=1;
	}
	} else if (Astr=="*(?)@(d\|deg\|degrees)") {
	//print("// DEGREES: ", Astr);
	Alen=index(Astr,"d");
	Awrk=substr(Astr,0,Alen);
	if (Awrk==numstr)
	Afloat=((float)Awrk)*deg2rad;
	else {
	Aerr=1;
	}
	} else if (Astr==numstr + "([/])" + numstr) {
	//print("// Nth: ", Astr);
	split(Astr,Atok,"/");
	if ((int)Atok[1]<=0) {
	Aerr=1;
	Afloat=0;
	print("// error bad denominator: ", Astr);
	} else {
	Afloat=2pi((float)Atok[0]/(float)Atok[1]);
	}
	} else if (Astr==numstr) {
	//print("// default (degrees): ", Astr);
	Afloat=(float)Astr*deg2rad;
	} else {
	Aerr=1;
	break;
	}
	}
	if (Aerr==1) {
	print ("// error !!");
	ASrslt="";
	} else {
	ASrslt=(string)Afloat;
	}
	//print("// returning: >", Afloat, "<");
	return ASrslt;
	}
	////////////////////////////////////////////////////////////////////////
	float computeStartAngle(string Astr) {
	string a1;
	a1=computeAngle(Astr);
	if (a1=="") {
	errStr=sprintf("Invalid value for \"radialstart\" %s", Root.radialstart);
	doErrs(errStr);
	} else
	return (float)a1;
	}
	/////////////////////////////////////////////////////////////////////////
	float computeNodeAngle(string Astr, node_t Anode) {
	string a2;
	a2=computeAngle(Astr);
	if (a2=="") {
	errStr=sprintf("Node \"%s\" has bad radialangle attribute: %s", Anode.name, Astr);
	doErrs(errStr);
	} else
	return (float)a2;
	}
	////////////////////////////////////////////////////////////////////////////
	// return points
	float computeDistance(string Dstr, node_t Dnode) {
	int Dlen;
	float Drslt;
	string Dwrk;

	//print("// RAW DISTANCE: ", Dstr);
	Dwrk=Dstr;
	Dlen=length(Dstr)-1;
	if (Dstr=="*(?)@(in\|inch\|inches)") {
	//print("// INCHES ", Dstr);
	Dlen=index(Dstr,"i");
	Dwrk=substr(Dstr,0,Dlen);
	//print("// work: ", Dwrk);
	if (Dwrk==numstr)
	Drslt=72.*(float)Dwrk; // return points
	else {
	errStr=sprintf("Node \"%s\" has bad radialdistance attribute: %s", Dnode.name, Dstr);
	doErrs(errStr);
	Drslt=0;
	}
	} else if (Dstr=="*(?)@(pt\|point\|points)") {
	//print("// POINTS: ", Dstr);
	Dlen=index(Dstr,"p");
	Dwrk=substr(Dstr,0,Dlen);
	if (Dwrk==numstr)
	Drslt=((float)Dwrk);
	else {
	errStr=sprintf("Node \"%s\" has bad radialdistance attribute: %s", Dnode.name, Dstr);
	doErrs(errStr);
	Drslt=0;
	}
	} else if (Dstr==numstr) {
	//print("// default (inches): ", Dstr);
	Drslt=72.*(float)Dstr;
	} else {
	errStr=sprintf("Node \"%s\" has bad radialdistance attribute: %s", Dnode.name, Dstr);
	doErrs(errStr);
	Drslt=0;
	}
	//print("// DISTANCE: returning: ", Drslt);
	return Drslt;
	}

	} // end BEGIN
	////////////////////////////////////////////////////////////////////////////
	BEG_G{
	Root=$G;
	$G.bb="";
	clockwise=0;
	_CenterX=0;
	_CenterY=0;
	// first, determine direction /////////////////////////////////////////
	if (hasAttr($, "radialclockwise"))
	if ($.radialclockwise=="@(1\|yes\|true)")
	clockwise=1;
	else if ($.radialclockwise=="@(0\|no\|false)")
	clockwise=0;
	else {
	errStr=sprintf("Invalid value for \"radialclockwise\" %s", $.radialclockwise);
	doErrs(errStr);
	}
	// next, determine starting angle
	start=0;
	if (hasAttr($, "radialstart")) {
	wrkStr=$.radialstart;
	start=computeStartAngle(wrkStr);
	}
	}
	////////////////////////////////////////////////////////////////////////////////
	N{
	//print("// NODE: ", $.name);
	if (hasAttr($, "label") && $.label=="") {
	print("// EMPTY label: ", $.name);
	noLabel[$]=1;
	}
	if (isAttr($G, "N", "label") && $.label=="") {
	print("// isAttr - EMPTY label: ", $.name);
	noLabel[$]=1;
	}
	if (hasAttr($, "radialangle") && $.radialangle!="") {
	theta=computeNodeAngle($.radialangle, $);
	} else if (hasAttr($, "pos") && $.pos!="") {
	continue; // ok
	} else {
	errStr=sprintf("Node \"%s\" is missing radialangle attribute", $.name);
	doErrs(errStr);
	}
	if (hasAttr($, "radialdistance") && $.radialdistance!="") {
	D=computeDistance($.radialdistance, $);
	} else if (hasAttr($, "pos") && $.pos!="") {
	// ok
	} else {
	errStr=sprintf("Node \"%s\" is missing radialdistance attribute", $.name);
	doErrs(errStr);
	}
	if (hasAttr($, "pos") && $.pos!="") {
	continue; // ok
	}
	if (hasAttr($, "CenterOn") && $.CenterOn!="") {
	if (isNode(Root, $.CenterOn)!=NULL) {
	cNode=node(Root, $.CenterOn);
	_CenterX=cNode.X;
	_CenterY=cNode.Y;
	}
	} else {
	// ERROR, no such node
	}
	if (absoluteAngle) {
	x=_CenterX+(D*cos(theta));
	y=_CenterY+(D*sin(theta));
	} else {
	if (clockwise==1)
	theta=-theta; // clockwise
	x=_CenterX+(D*cos(theta+start));
	y=_CenterY+(D*sin(theta+start));
	}
	$.pos=(string)x + "," + (string)y;
	}
	graph radialTest1 {

	graph [radialclockwise="true" radialstart="12oc"]

	label="my cool\nRadial Graph"

	Center[radialdistance=0 radialangle=0 label="''" style=filled fillcolor=red shape=circle fixedsize=true width=.15 height=.15]

	node[shape=point]
	b1 [radialdistance="3" radialangle="1/8"]
	b2 [radialdistance="3" radialangle="2/8" ]
	b3 [radialdistance="3" radialangle="3/8"]
	b4 [radialdistance="1.8" radialangle="4/8"]
	b5 [radialdistance="3" radialangle="5/8"]
	b6 [radialdistance="3.7" radialangle="6/8"]
	b7 [radialdistance="3" radialangle="7/8"]
	b8 [radialdistance="3" radialangle="8/8"]

	node [shape=plaintext]
	LBL1 [radialdistance="4" radialangle="1/8"]
	LBL2 [radialdistance="4" radialangle="2/8"]
	LBL3 [radialdistance="4" radialangle="3/8"]
	LBL4 [radialdistance="4" radialangle="4/8"]
	LBL5 [radialdistance="4" radialangle="5/8"]
	LBL6 [radialdistance="4" radialangle="6/8"]
	LBL7 [radialdistance="4" radialangle="7/8"]
	LBL8 [radialdistance="4" radialangle="8/8"]

	Center -- b1 [style=dashed]
	Center -- b2 [style=dashed]
	Center -- b3 [style=dotted color=green]
	Center -- b4 [style=dashed]
	Center -- b5 [color=blue]
	Center -- b6
	Center -- b7
	Center -- b8

	}
	// written by gawk script
	graph RR{
	label="Graphviz - New Radial Engine Tricks (103) (accidentally wacky)"
	node [shape=point colorscheme=set312]
	edge [colorscheme=set312]
	Center[radialdistance=0 radialangle=0 label="" style=filled shape=point]

	"n_3.69618_120" [radialdistance=3.69618 radialangle="120/23" color="#984e94"]
	"n_2.96053_135" [radialdistance=2.96053 radialangle="135/23" color="#c96f55"]
	"n_3.69618_120" -- "n_2.96053_135"[color="#c96f55"]
	"n_3.11552_150" [radialdistance=3.11552 radialangle="150/23" color="#19c8d5"]
	"n_2.96053_135" -- "n_3.11552_150"[color="#19c8d5"]
	"n_3.04484_165" [radialdistance=3.04484 radialangle="165/23" color="#7e6df2"]
	"n_3.11552_150" -- "n_3.04484_165"[color="#7e6df2"]
	"n_3.28721_180" [radialdistance=3.28721 radialangle="180/23" color="#b5281e"]
	"n_3.04484_165" -- "n_3.28721_180"[color="#b5281e"]
	"n_3.63874_195" [radialdistance=3.63874 radialangle="195/23" color="#de73b4"]
	"n_3.28721_180" -- "n_3.63874_195"[color="#de73b4"]
	"n_1.59875_210" [radialdistance=1.59875 radialangle="210/23" color="#a5b24c"]
	"n_3.63874_195" -- "n_1.59875_210"[color="#a5b24c"]
	"n_2.36666_225" [radialdistance=2.36666 radialangle="225/23" color="#f428cc"]
	"n_1.59875_210" -- "n_2.36666_225"[color="#f428cc"]
	"n_0.529552_240" [radialdistance=0.529552 radialangle="240/23" color="#8cfbd2"]
	"n_2.36666_225" -- "n_0.529552_240"[color="#8cfbd2"]
	"n_1.69194_255" [radialdistance=1.69194 radialangle="255/23" color="#f6cb2c"]
	"n_0.529552_240" -- "n_1.69194_255"[color="#f6cb2c"]
	"n_2.27526_270" [radialdistance=2.27526 radialangle="270/23" color="#ee3405"]
	"n_1.69194_255" -- "n_2.27526_270"[color="#ee3405"]
	"n_3.39672_285" [radialdistance=3.39672 radialangle="285/23" color="#b9c232"]
	"n_2.27526_270" -- "n_3.39672_285"[color="#b9c232"]
	"n_2.99436_300" [radialdistance=2.99436 radialangle="300/23" color="#6e77c8"]
	"n_3.39672_285" -- "n_2.99436_300"[color="#6e77c8"]
	"n_1.29514_315" [radialdistance=1.29514 radialangle="315/23" color="#18e2fa"]
	"n_2.99436_300" -- "n_1.29514_315"[color="#18e2fa"]
	"n_2.48285_330" [radialdistance=2.48285 radialangle="330/23" color="#2870fd"]
	"n_1.29514_315" -- "n_2.48285_330"[color="#2870fd"]
	"n_3.96094_345" [radialdistance=3.96094 radialangle="345/23" color="#776cb1"]
	"n_2.48285_330" -- "n_3.96094_345"[color="#776cb1"]
	"n_0.507738_360" [radialdistance=0.507738 radialangle="360/23" color="#493f92"]
	"n_3.96094_345" -- "n_0.507738_360"[color="#493f92"]
	"n_2.0822_375" [radialdistance=2.0822 radialangle="375/23" color="#468688"]
	"n_0.507738_360" -- "n_2.0822_375"[color="#468688"]
	"n_2.5562_390" [radialdistance=2.5562 radialangle="390/23" color="#d00308"]
	"n_2.0822_375" -- "n_2.5562_390"[color="#d00308"]
	"n_0.366654_405" [radialdistance=0.366654 radialangle="405/23" color="#725f29"]
	"n_2.5562_390" -- "n_0.366654_405"[color="#725f29"]
	"n_1.84317_420" [radialdistance=1.84317 radialangle="420/23" color="#618807"]
	"n_0.366654_405" -- "n_1.84317_420"[color="#618807"]
	"n_2.43624_435" [radialdistance=2.43624 radialangle="435/23" color="#52c76b"]
	"n_1.84317_420" -- "n_2.43624_435"[color="#52c76b"]
	"n_0.651511_450" [radialdistance=0.651511 radialangle="450/23" color="#f9362f"]
	"n_2.43624_435" -- "n_0.651511_450"[color="#f9362f"]
	"n_0.651511_450" -- "n_3.69618_120" [color="#f9362f"]
	}
	digraph radialTest11 {
	// set optional radial parameters
	graph [radialclockwise="true" radialstart="12oc"]


	label="another cool\nRadial Graph"

	// define Center, needed by this graph type as tail of edges
	Center[radialdistance=0 radialangle=0 label="" style=filled shape=point]

	{
	node [shape=plaintext label=<
	<table border="0" cellborder="1" cellspacing="0">
	<tr> <td><i>Input Foo</i></td><td> two </td> </tr>
	<tr> <td bgcolor="lightblue" port="1">one</td><td> two </td></tr>
	<tr> <td port="2">two</td><td> four </td></tr>
	</table>>]

	b1 [radialdistance="3" radialangle="1/9"]
	b2 [radialdistance="3" radialangle="2/9" ]
	b3 [radialdistance="3" radialangle="3/9"]
	b4 [radialdistance="1.8" radialangle="4/9"]
	node [shape=plaintext label=<
	<table border="0" cellborder="1" cellspacing="0">
	<tr> <td bgcolor="green1"><i>This</i></td><td>That</td> </tr>
	<tr> <td port="1">100</td><td>bagles</td></tr>
	<tr> <td port="2">333</td><td>tacos</td></tr>
	</table>>]
	b5 [radialdistance="3" radialangle="5/9"]
	b6 [radialdistance="3.6" radialangle="6/9"]
	b7 [radialdistance="3" radialangle="7/9"]
	b8 [radialdistance="1.1" radialangle="8/9"]
	node [shape=ellipse label="Over\nunder"]
	b9 [radialdistance="3" radialangle="9/9"]
	}

	edge [arrowhead=normal] //dir=forward headclip=false] // why is dir needed?
	Center -> b1 [style=dashed]
	Center -> b2 [style=dashed]
	Center -> b3 [style=dotted color=darkgreen]
	Center -> b4
	Center -> b5 [color=blue arrowhead=odot]
	Center -> b6 [penwidth=3 arrowhead=odot]
	Center -> b7 [headclip=false arrowhead=dot]
	Center -> b8
	Center -> b9 [style=dashed ]

	}
	graph radialAngles {

	label="Radial Angles"

	node[shape=circle style=filled fillcolor=cyan radialdistance="3"]

	"n" [radialangle="n" radialdistance=3]
	"12oc" [radialangle="12oc" radialdistance=4.4]
	"1oc" [radialangle="1oc" radialdistance=4.4]
	"ne" [radialangle="ne" radialdistance=3]
	"2oc" [radialangle="2oc" radialdistance=4.4]
	"e" [radialangle="e" radialdistance=3]
	"3oc" [radialangle="3oc" radialdistance=4.4]
	"4oc" [radialangle="4oc" radialdistance=4.4]
	"se" [radialangle="se" radialdistance=3]
	"5oc" [radialangle="5oc" radialdistance=4.4]
	"s" [radialangle="s" radialdistance=3]
	"6oc" [radialangle="6oc" radialdistance=4.4]
	"7oc" [radialangle="7oc" radialdistance=4.4]
	"sw" [radialangle="sw" radialdistance=3]
	"8oc" [radialangle="8oc" radialdistance=4.4]
	"w" [radialangle="w" radialdistance=3]
	"9oc" [radialangle="9oc" radialdistance=4.4]
	"10oc" [radialangle="10oc" radialdistance=4.4]
	"nw" [radialangle="nw" radialdistance=3]
	"11oc" [radialangle="11oc" radialdistance=4.4]
	"ene" [radialangle="ene" radialdistance=3]
	"nne" [radialangle="nne" radialdistance=3]
	"nnw" [radialangle="nnw" radialdistance=3]
	"wnw" [radialangle="wnw" radialdistance=3]
	"wsw" [radialangle="wsw" radialdistance=3]
	"ssw" [radialangle="ssw" radialdistance=3]
	"sse" [radialangle="sse" radialdistance=3]
	"ese" [radialangle="ese" radialdistance=3]

	{
	node[shape=circle style=filled fillcolor=lightpink CenterOn="2oc" radialdistance="3.1"]
	AAA [ radialangle="ne"]
	node[shape=circle style=filled fillcolor=lightpink CenterOn="AAA" radialdistance="2.1"]
	DD1 [ radialangle="n"]
	DD2 [ radialangle="ne"]
	DD3 [ radialangle="s"]
	DD4 [ radialangle="nw"]
	}
	AAA--"2oc"
	AAA--{DD1 DD2 DD3 DD4}
	{
	node[shape=circle style=filled fillcolor=yellow CenterOn="6oc" radialdistance="3"]
	BBB [ radialangle="s"]
	node[shape=circle style=filled fillcolor=yellow CenterOn="BBB" radialdistance="2"]
	EE1 [ radialangle="ne"]
	EE2 [ radialangle="se"]
	EE3 [ radialangle="s"]
	EE4 [ radialangle="w"]
	EE5 [ radialangle="wsw"]
	}
	"6oc"--BBB
	BBB--{EE1 EE2 EE3 EE4 EE5}
	}
	digraph radialTestClock {
	// set optional radial parameters
	graph [radialclockwise="true" radialstart="12oc"]

	label="Clock: 4:45"

	// define Center, needed by this graph type as tail of edges
	Center[radialdistance=0 radialangle=0 label="" style=filled shape=point]

	{
	node [shape=circle width=.6 radialdistance="4" ]
	1 [ radialangle="1/12"]
	2 [ radialangle="2/12"]
	3 [ radialangle="3/12"]
	4 [ radialangle="4/12"]
	5 [ radialangle="5/12"]
	6 [ radialangle="6/12"]
	7 [ radialangle="7/12"]
	8 [ radialangle="8/12"]
	9 [ radialangle="9/12"]
	10 [ radialangle="10/12"]
	11 [ radialangle="11/12"]
	12 [ radialangle="12/12"]

	node[shape=point style=invis xlabel="\N"]
	hr [radialdistance="2.1" radialangle="4.75/12"]
	min [radialdistance="3.5" radialangle="9/12" ]

	}


	Center -> hr //[style=dashed]
	Center -> min // [style=dashed]

	}
	graph radialTestClock {
	// set optional radial parameters
	graph [radialclockwise="false" radialstart="-60deg"]

	label="concentric"

	// define Center, needed by this graph type as tail of edges
	Center[radialdistance=0 radialangle=0 label="" style=invis shape=point]

	{
	node [shape=circle width=.6 radialdistance="2" ]
	Aa [ radialangle="1/6"]
	Ba [ radialangle="2/6"]
	Ca [ radialangle="3/6"]
	Da [ radialangle="4/6"]
	Ea [ radialangle="5/6"]
	Fa [ radialangle="6/6"]
	}
	{
	node [shape=circle width=.6 radialdistance="4" ]
	Ab [ radialangle="1/6"]
	Bb [ radialangle="2/6"]
	Cb [ radialangle="3/6"]
	Db [ radialangle="4/6"]
	Eb [ radialangle="5/6"]
	Fb [ radialangle="6/6"]
	}
	Aa -- Ba -- Ca -- Da -- Ea -- Fa -- Aa
	Ab -- Bb -- Cb -- Db -- Eb -- Fb -- Ab

	Aa -- Ab
	Ba -- Bb
	Ca -- Cb
	Da -- Db
	Ea -- Eb
	Fa -- Fb
	}
	graph radialAngles {

	label="Radial Angles"

	A [pos="100,100" shape=rect]
	B [pos="400,200" shape=rect]
	C [pos="700,300" shape=rect]
	D [pos="1000,400" shape=rect]

	node[shape=circle style=filled fillcolor=cyan radialdistance="3" CenterOn="A"]

	"n" [radialangle="n" radialdistance=3]
	"12oc" [radialangle="12oc" radialdistance=4.4]
	"1oc" [radialangle="1oc" radialdistance=4.4]
	"ne" [radialangle="ne" radialdistance=3]
	"2oc" [radialangle="2oc" radialdistance=4.4]
	"e" [radialangle="e" radialdistance=3]
	"3oc" [radialangle="3oc" radialdistance=4.4]
	"4oc" [radialangle="4oc" radialdistance=4.4]
	"se" [radialangle="se" radialdistance=3]
	"5oc" [radialangle="5oc" radialdistance=4.4]
	"s" [radialangle="s" radialdistance=3]
	"6oc" [radialangle="6oc" radialdistance=4.4]
	"7oc" [radialangle="7oc" radialdistance=4.4]
	"sw" [radialangle="sw" radialdistance=3]
	"8oc" [radialangle="8oc" radialdistance=4.4]
	"w" [radialangle="w" radialdistance=3]
	"9oc" [radialangle="9oc" radialdistance=4.4]
	"10oc" [radialangle="10oc" radialdistance=4.4]
	"nw" [radialangle="nw" radialdistance=3]
	"11oc" [radialangle="11oc" radialdistance=4.4]
	node[shape=circle style=filled fillcolor=orange radialdistance="3" CenterOn="D"]
	"ene" [radialangle="ene" radialdistance=3]
	"nne" [radialangle="nne" radialdistance=3]
	"nnw" [radialangle="nnw" radialdistance=3]
	"wnw" [radialangle="wnw" radialdistance=3]
	"wsw" [radialangle="wsw" radialdistance=3]
	"ssw" [radialangle="ssw" radialdistance=3]
	"sse" [radialangle="sse" radialdistance=3]
	"ese" [radialangle="ese" radialdistance=3]

	{
	node[shape=circle style=filled fillcolor=lightpink CenterOn="2oc" radialdistance="3.1"]
	AAA [ radialangle="ne"]
	node[shape=circle style=filled fillcolor=lightpink CenterOn="AAA" radialdistance="2.1"]
	DD1 [ radialangle="n"]
	DD2 [ radialangle="ne"]
	DD3 [ radialangle="s"]
	DD4 [ radialangle="nw"]
	}
	AAA--"2oc"
	AAA--{DD1 DD2 DD3 DD4}
	{
	node[shape=circle style=filled fillcolor=yellow CenterOn="6oc" radialdistance="3"]
	BBB [ radialangle="s"]
	node[shape=circle style=filled fillcolor=yellow CenterOn="BBB" radialdistance="2"]
	EE1 [ radialangle="ne"]
	EE2 [ radialangle="se"]
	EE3 [ radialangle="s"]
	EE4 [ radialangle="w"]
	EE5 [ radialangle="wsw"]
	}
	"6oc"--BBB
	BBB--{EE1 EE2 EE3 EE4 EE5}
	}