// A "mesh" is a set of points ("anchors") connected through curves.
// An anchor is either
// -the end of a curve
// -an intersection of curves
// -or a randomly chosen point along a curve (type 3)

// A type 3 anchor can be necessary to define an "o" shape
// (because such a shape doesn't have an anchor point per se,
// so we just choose one point along the ring).

// Sometimes however, a type 3 anchor is an artifact of the mesh
// finding process and can be eliminated, reducing the anchor and
// curve count by 1.

srecord noeq G22SkeletonToMesh<Img extends WidthAndHeight>(IImageRegion<Img> region) is Steppable {
  new Map<Pt, Anchor> anchors; // in pseudo-random order (HashSet order)
  new L<Curve> curves; // also in no particular order
  
  sclass Curve {
    Anchor start, end;
    OnePathWithOrigin path; // origin = start.pt
    
    *(Anchor *start, Anchor *end, PtBuffer points) {
      path = new OnePathWithOrigin(points, false);
      start.outgoingCurves.add(this);
      end.incomingCurves.add(this);
    }
  }
  
  sclass Anchor {
    Pt pt;
    new L<Curve> outgoingCurves;
    new L<Curve> incomingCurves;
    
    *(Pt *pt) {}
  }
  
  // TEMPORARY DATA
  
  ItIt<Pt> regionIterator;
  new L<WorkItem> queue;
  new PtSet pointsSeen;
  
  // p is a point in 3x3 neighborhood of anchor
  srecord noeq WorkItem(Anchor anchor, Pt p) {}

  public bool step() {
    // first, initialize iterator
    if (regionIterator == null)
      regionIterator = region.pixelIterator();
    
    // then check queue for work
    if (nempty(queue)) {
      WorkItem work = popLast(queue);
      
      Pt p = work.p;
      if (pointsSeen.contains(p)) true;
      
      new PtBuffer curvePoints;
      curvePoints.add(work.anchor.start); // add anchor to path
      Anchor endAnchor = null;

      while ping (true) {
        curvePoints.add(p);
        
        // did we hit another anchor?
        Anchor anchor = anchors.get(p);
        
        pointsSeen.add(p);
        PtBuffer branches = unexploredPointsAround(p);
        
        // line ends or branches - same thing for us
        if (l(branches) != 1) {
          endAnchor = newAnchor(p);
          break;
        }
      }

      if (endAnchor != null) {
        Curve curve = new(work.anchor, endAnchor, curvePoints);
        curves.add(curve);
      }
      
      true;
    }
    
    // finally look for next point in region
    if (regionIterator.hasNext()) {
      Pt p = regionIterator.next();
      
      // check if point already seen, otherwise mark as seen
      if (!pointsSeen.add(p)) true;
      
      // new point - save as anchor
      newAnchor(p);
      true;
    }
      
    false;
  }

  Anchor newAnchor(Pt p) {  
    Anchor anchor = new(p);
    anchors.put(p, anchor);
      
    // explore in all directions
    for (Pt p2 : unexploredPointsAround(p))
      queue.add(new WorkItem(anchor, p2));
      
    ret anchor;
  }
  
  PtBuffer unexploredPointsAround(Pt p) {
    new PtBuffer out;
    for (int dir = 1; dir <= 8; dir++) {
      Pt p2 = onePathDirection(p, dir);
      if (region.contains(p2) && !pointsSeen.contains(p))
        out.add(p2);
    }
    ret out;
  }
}