code: public void placeRing(IRing ring, Point2d ringCenter, double bondLength, Map<Integer, Double> startAngles) {
          double radius = this.getNativeRingRadius(ring, bondLength);
          double addAngle = 2 * Math.PI / ring.getRingSize();
  
          IAtom startAtom = ring.getAtom(0);
          Point2d p = new Point2d(ringCenter.x + radius, ringCenter.y);
          startAtom.setPoint2d(p);
          double startAngle = Math.PI * 0.5;
  
          /*
           * Different ring sizes get different start angles to have visually
           * correct placement
           */
          int ringSize = ring.getRingSize();
          if (startAngles.get(ringSize) != null) startAngle = startAngles.get(ringSize);
  
          List<IBond> bonds = ring.getConnectedBondsList(startAtom);
          /*
           * Store all atoms to draw in consecutive order relative to the chosen
           * bond.
           */
          Vector<IAtom> atomsToDraw = new Vector<IAtom>();
          IAtom currentAtom = startAtom;
          IBond currentBond = (IBond) bonds.get(0);
          for (int i = 0; i < ring.getBondCount(); i++) {
              currentBond = ring.getNextBond(currentBond, currentAtom);
              currentAtom = currentBond.getOther(currentAtom);
              atomsToDraw.addElement(currentAtom);
          }
          atomPlacer.populatePolygonCorners(atomsToDraw, ringCenter, startAngle, addAngle, radius);
      }
docs: Place ring with user provided angles.
  
  @param ring the ring to place.
  @param ringCenter center coordinates of the ring.
  @param bondLength given bond length.
  @param startAngles a map with start angles when drawing the ring.