How can I sort vertex positions sequentially indices in a closed area?

Question

I need to sort the vertices sequentially to make an effect, something like this video. I know I should draw them by hand, but sometimes when I subdivide edges, vertex indexes will change.

The vertices in the below image are correct.

For example, vertices in the below image are sorted randomly. Can you sort them sequentially?

I tried to sort them along the x-axis or z-axis, but it didn't work.

Please consider that your solution should work for complex shapes:

Answer 1

Sorting vertex indices.

Answer here https://blender.stackexchange.com/a/36619/15543 shows how to sort vertex indices using bmesh.

Answer here How to order a list of vertices based upon position? goes some way to show how to walk the edges for an order.

To be sure to be sure would walk the edges as shown above until the first vert is re-encountered (since its a loop) and use this for the order. Will leave it up to you to piece together the script from what is here

As demonstrated in @Leander's answer

Shortest Path

Using the script from What is the bmesh equivalent to bpy.ops.mesh.shortest_path_select()? could select edge as link between first and last index vert, temporarily remove it, find the shortest remaining path (the only path) from edges two verts. Reinstate the edge.

Face winding order

Instead for a closed loop like above, contend can fill with an ngon, use the ngon face verts as order (the winding order) re-sort the verts and remove the ngon face created.

import bpy
import bmesh
ob = bpy.context.object
assert ob.type == "MESH"
me = ob.data
bm = bmesh.from_edit_mesh(me)
f = bmesh.ops.contextual_create(
        bm,
        geom=bm.verts[:] + bm.edges[:],
        )["faces"][0]
for i, v in enumerate(f.verts):
    v.index = i
bm.verts.sort()
bm.faces.remove(f)
bmesh.update_edit_mesh(me)

Select a first vert and clockwise or counter

To select the zeroth vert, and ensure anticlockwise (from top view) indexing

Run in edit mode, select the vert you wish to have index 0. Assumes the shape lies in the XY plane. If the normal of the created face points down the winding is flipped.

Random order, vert 22 selected, script below run

import bpy
import bmesh
from mathutils import Vector
ob = bpy.context.object
assert ob.type == "MESH"
me = ob.data
bm = bmesh.from_edit_mesh(me)
v0 = bm.select_history.active
f = bmesh.ops.contextual_create(
        bm,
        geom=bm.verts[:] + bm.edges[:],
        )["faces"][0]
fverts = f.verts[:]
if f.normal.dot((0, 0, 1)) < 0:
    fverts.reverse()
for i, v in enumerate(fverts):
    v.index = i
    if v is v0:
        iv0 = i
for v in fverts:
    v.index = (v.index - iv0) % len(fverts)
bm.verts.sort()
bm.faces.remove(f)
bmesh.update_edit_mesh(me) 

Answer 2

1. Add a shapekey.
2. In that shapekey, place the vertices which are to be first and last far away from each other on the x axis.
3. Select all other (inbetween vertices).
4. Choose W > Smooth Vertices and set a high iteration count. The vertices will be smoothed.
5. Sort them by x-axis. Mesh > Sort Elements > X Axis
6. Delete the shapekey.

Answer 3

Using Python, you can walk the edges and assign them a new index.

import bpy
import bmesh
me = bpy.context.object.data
bm = bmesh.from_edit_mesh(me)
index of the start vertex
initial = bm.verts[0]
vert = initial
prev = None
for i in range(len(bm.verts)):
    print(vert.index, i)
    vert.index = i
    next = None
    adjacent = []
    for v in [e.other_vert(vert) for e in vert.link_edges]:
        if (v != prev and v != initial):
            next = v
    if next == None: break
    prev, vert = vert, next
bm.verts.sort()
bmesh.update_edit_mesh(me)

Answer 4

Without a script:

1. V split the mesh at the vertex you want to be first, if it's not already.
2. Header > Object Menu > Convert the mesh to a curve
3. Edit mode, right-click menu, switch the direction of the spline, if necessary
4. Object mode, right-click menu, Convert back to a mesh.

I don't know why Convert isn't in the Object mode right-click menu for a mesh, that's kind of annoying.

Barring refinements, as supplied by @Seyed, the script would be:

import bpy
bpy.ops.object.convert(target='CURVE', keep_original= False)
bpy.ops.object.convert(target='MESH', keep_original= False)

---

Or, to split a cyclic mesh at a selection:

import bpy
in edit mode, select one vertex
bpy.ops.mesh.split() 
bpy.ops.object.editmode_toggle()
bpy.ops.object.convert(target='CURVE', keep_original= False)
bpy.ops.object.convert(target='MESH', keep_original= False)

Then merge the two loose ends.

Thanks to @Paul St George