Sorting vertices of a polygon in CCW or CW direction

Question

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.

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)