Sorting vertices of a polygon in CCW or CW direction

Question

I really need some urgent help with this problem.

I have a set of edges and vertices defining a polygon (not necessarily convex). The vertices and edges are in random order and I want to sort/order the vertices of this polygon in clockwise (or anti-clock wise) direction.

please see this page for more detailed description: http://www.dixittech.com/blog/2012/10/28/sorting-vertices-of-a-polygon-in-ccw-or-cw-direction/

Any idea how this can be achieved?

Answer 1

I think this is a simplified version of Königsberg Bridge Problem essentially.

if there's no any case that more than two edges are connected at a single node, you can build an adjacent list and "travel" through all the nodes.

If there's case that >2 edges are connected at a node, ... hum i think there will be more than one possible order. Just refer to the solution of Königsberg Bridge Problem.

for v,u in edges:
  adjacent[v].append(u)
  adjacent[u].append(v)

order=[]

start = v0 #start from an arbitrary node

def draw(now,last):
  if now==start and len(order)>0:
    return
  order.append(now)
  for i in adjacent[now]:
    if i != last:
      draw(i,now)

draw(start,NULL)

Answer 2

I'm assuming that CW/CCW direction is of no concern (guaranteeing one or the other is much more complex). This pseudo-code algorithm sort vertices either CW or CCW.

marked_edge <- any edge
first <- marked_edge.start
list <- [first]
current <- marked_edge.end
while current <> first
    list <- list + [current]
    new_edge <- find the edge that is not the marked_edge and has the vertex current as either start or end
    if new_edge.start=current then
        current <- new_edge.end
    else
        current <- new_edge.start
   endif
   marked_edge <- new_edge
endwhile