diff --git a/skeletor/skeletonize/__init__.py b/skeletor/skeletonize/__init__.py
index 43fb9a4..9bfaec5 100644
--- a/skeletor/skeletonize/__init__.py
+++ b/skeletor/skeletonize/__init__.py
@@ -28,7 +28,8 @@
 
 | function                                    | speed | robust | radii [^2] | mesh map [^3] | description                                        |
 | ------------------------------------------- | :---: | :----: | :--------: | :-----------: | ---------------------------------------------------|
-| `skeletor.skeletonize.by_wavefront()`       | +++   | ++     | yes        | yes           | works well for tubular meshes                      |
+| `skeletor.skeletonize.by_wavefront()`       | ++++  | ++     | yes        | yes           | works well for tubular meshes                      |
+| `skeletor.skeletonize.by_wavefront_exact()` | +++   | ++     | yes        | no            | works well for tubular meshes                      |
 | `skeletor.skeletonize.by_vertex_clusters()` | ++    | +      | no         | yes           | best with contracted meshes [^1]                   |
 | `skeletor.skeletonize.by_teasar()`          | +     | ++     | no         | yes           | works on mesh surface                              |
 | `skeletor.skeletonize.by_tangent_ball()`    | ++    | 0      | yes        | yes           | works with mesh normals                            |
@@ -47,9 +48,10 @@
 from .edge_collapse import *
 from .vertex_cluster import *
 from .wave import *
+from .wave2 import *
 from .teasar import *
 from .tangent_ball import *
 
 __docformat__ = "numpy"
-__all__ = ['by_teasar', 'by_wavefront', 'by_vertex_clusters',
+__all__ = ['by_teasar', 'by_wavefront', 'by_wavefront_exact', 'by_vertex_clusters',
            'by_edge_collapse', 'by_tangent_ball']
diff --git a/skeletor/skeletonize/teasar.py b/skeletor/skeletonize/teasar.py
index 4842c3c..0d4f647 100644
--- a/skeletor/skeletonize/teasar.py
+++ b/skeletor/skeletonize/teasar.py
@@ -98,7 +98,7 @@ def by_teasar(mesh, inv_dist, min_length=None, root=None, progress=True):
 
     with tqdm(desc='Invalidating', total=len(G.vs),
               disable=not progress, leave=False) as pbar:
-        for cc in sorted(G.clusters(), key=len, reverse=True):
+        for cc in sorted(G.connected_components(), key=len, reverse=True):
             # Make a subgraph for this connected component
             SG = G.subgraph(cc)
             cc = np.array(cc)
diff --git a/skeletor/skeletonize/wave.py b/skeletor/skeletonize/wave.py
index 7c1bbb7..5c4df9c 100644
--- a/skeletor/skeletonize/wave.py
+++ b/skeletor/skeletonize/wave.py
@@ -142,6 +142,7 @@ def by_wavefront(mesh,
 
     else:
         weights = np.linalg.norm(node_centers[el[:, 0]] - node_centers[el[:, 1]], axis=1)
+
     tree = G.spanning_tree(weights=1 / weights)
 
     # Create a directed acyclic and hierarchical graph
@@ -195,7 +196,7 @@ def _cast_waves(mesh, waves=1, origins=None, step_size=1,
 
     # Go over each connected component
     with tqdm(desc='Skeletonizing', total=len(G.vs), disable=not progress) as pbar:
-        for cc in G.clusters():
+        for cc in G.connected_components():
             # Make a subgraph for this connected component
             SG = G.subgraph(cc)
             cc = np.array(cc)
@@ -241,7 +242,7 @@ def _cast_waves(mesh, waves=1, origins=None, step_size=1,
                     this_dist = this_wave == i
                     ix = np.where(this_dist)[0]
                     SG2 = SG.subgraph(ix)
-                    for cc2 in SG2.clusters():
+                    for cc2 in SG2.connected_components():
                         this_verts = cc[ix[cc2]]
                         this_center = mesh.vertices[this_verts].mean(axis=0)
                         this_radius = cdist(this_center.reshape(1, -1), mesh.vertices[this_verts])
diff --git a/skeletor/skeletonize/wave2.py b/skeletor/skeletonize/wave2.py
new file mode 100644
index 0000000..eeb9e41
--- /dev/null
+++ b/skeletor/skeletonize/wave2.py
@@ -0,0 +1,290 @@
+#    This script is part of skeletor (http://www.github.com/navis-org/skeletor).
+#    Copyright (C) 2018 Philipp Schlegel
+#
+#    This program is free software: you can redistribute it and/or modify
+#    it under the terms of the GNU General Public License as published by
+#    the Free Software Foundation, either version 3 of the License, or
+#    (at your option) any later version.
+#
+#    This program is distributed in the hope that it will be useful,
+#    but WITHOUT ANY WARRANTY without even the implied warranty of
+#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+#    GNU General Public License for more details.
+#
+#    You should have received a copy of the GNU General Public License
+#    along with this program.
+
+import igraph as ig
+import numpy as np
+import pandas as pd
+
+from tqdm.auto import tqdm, trange
+
+from ..utilities import make_trimesh
+from .base import Skeleton
+
+
+def by_wavefront_exact(mesh, step_size, origins=None, radius_agg="mean", progress=True):
+    """Skeletonize a mesh using wave fronts.
+
+    This is the _exact_ version of the `by_wavefront` function meaning
+    that each wave front moves exactly the given distance (see `step_size`)
+    along the mesh, instead of hoping from vertex to vertex. This is
+    computationally more expensive but also more accurate.
+
+    Parameters
+    ----------
+    mesh :          mesh obj
+                    The mesh to be skeletonize. Can an object that has
+                    ``.vertices`` and ``.faces`` properties  (e.g. a
+                    trimesh.Trimesh) or a tuple ``(vertices, faces)`` or a
+                    dictionary ``{'vertices': vertices, 'faces': faces}``.
+    step_size :     float | int (>0)
+                    The distance each the wave fronts move along the mesh
+                    in each step.
+    origins :       int | list of ints, optional
+                    Vertex ID(s) where the wave(s) are initialized. If there
+                    is no origin for a given connected component, will fall
+                    back to semi-random origin.
+    radius_agg :    "mean" | "median" | "max" | "min" | "percentile75" | "percentile25"
+                    Function used to aggregate radii over sample (i.e. the
+                    vertices forming a ring that we collapse to its center).
+    progress :      bool
+                    If True, will show progress bar.
+
+    Returns
+    -------
+    skeletor.Skeleton
+                    Holds results of the skeletonization and enables quick
+                    visualization.
+
+    """
+    agg_map = {
+        "mean": np.mean,
+        "max": np.max,
+        "min": np.min,
+        "median": np.median,
+        "percentile75": lambda x: np.percentile(x, 75),
+        "percentile25": lambda x: np.percentile(x, 25),
+    }
+    assert radius_agg in agg_map, f'Unknown `radius_agg`: "{radius_agg}"'
+    rad_agg_func = agg_map[radius_agg]
+
+    mesh = make_trimesh(mesh, validate=False)
+
+    centers_final, radii_final, parents = _cast_waves(
+        mesh,
+        step_size=step_size,
+        origins=origins,
+        rad_agg_func=rad_agg_func,
+        progress=progress,
+    )
+
+    # Map radii for individual vertices to the collapsed nodes
+    # Using pandas is the fastest way here
+    swc = pd.DataFrame()
+    swc["node_id"] = np.arange(0, len(centers_final))
+    swc["parent_id"] = parents
+    swc["x"] = centers_final[:, 0]
+    swc["y"] = centers_final[:, 1]
+    swc["z"] = centers_final[:, 2]
+    swc["radius"] = radii_final
+
+    return Skeleton(swc=swc, mesh=mesh, method="wavefront_exact")
+
+
+def _cast_waves(mesh, step_size, origins=None, rad_agg_func=np.mean, progress=True):
+    """Cast waves across mesh."""
+    if not isinstance(origins, type(None)):
+        if isinstance(origins, int):
+            origins = [origins]
+        elif not isinstance(origins, (set, list)):
+            raise TypeError(
+                "`origins` must be vertex ID (int) or list "
+                f'thereof, got "{type(origins)}"'
+            )
+        origins = np.asarray(origins).astype(int)
+    else:
+        origins = np.array([])
+
+    # Step size must be positive
+    if step_size < 0:
+        raise ValueError("`step_size` must be > 0")
+
+    # Generate Graph (must be undirected)
+    G = ig.Graph(edges=mesh.edges_unique, directed=False)
+    G.es["weight"] = mesh.edges_unique_length
+
+    # Prepare empty array to fill with centers
+    centers = []
+    radii = []
+    data = []
+
+    # Go over each connected component
+    with tqdm(
+        desc="Skeletonizing", total=len(G.vs), disable=not progress, leave=False
+    ) as pbar:
+        for k, cc in enumerate(G.connected_components()):
+            # Make a subgraph for this connected component
+            SG = G.subgraph(cc)
+            cc = np.array(cc)
+
+            # Select seeds according to the number of waves
+            pot_seeds = np.arange(len(cc))
+            np.random.seed(1985)  # make seeds predictable
+            # See if we can use any origins
+            if len(origins):
+                # Get those origins in this cc
+                in_cc = np.isin(origins, cc)
+                if any(in_cc):
+                    # Map origins into cc
+                    cc_map = dict(zip(cc, np.arange(0, len(cc))))
+                    seed = np.array([cc_map[o] for o in origins[in_cc]])[0]
+                else:
+                    seed = np.random.choice(pot_seeds)
+            else:
+                seed = np.random.choice(pot_seeds)
+
+            # Get the distance between the seed and all other nodes
+            dist = np.array(
+                SG.distances(source=seed, target=None, mode="all", weights="weight")
+            )[0]
+
+            # What's the max distance we can reach?
+            mx = dist[dist < float("inf")].max()
+
+            # To keep track of which vertices we have already processed and can be
+            # safely ignored
+            is_inside_vert = np.zeros(len(dist)).astype(bool)
+
+            # Collect groups
+            for i, d in enumerate(np.arange(0, mx, step_size)):
+                # Inner verts are all vertices that are within the current distance
+                # (minus those that we have already processed)
+                inside_verts = np.where((dist <= d) & ~is_inside_vert)[0]
+
+                # To get the outer edge, we need to (1) find the neighbors of the inner edge
+                neighbors = [
+                    np.array(nn) for nn in SG.neighborhood(vertices=inside_verts)
+                ]
+                # (2) only keep those whose distance is above the current distance (i.e. those going outwards)
+                outer_verts = [nn[dist[nn] > d] for nn in neighbors]
+
+                # Inside vertices that are not part of the inner ring(s) have no neighbors outside
+                is_inside_edge = np.array([len(ov) > 0 for ov in outer_verts])
+                inner_verts = inside_verts[is_inside_edge]
+                outer_verts = [
+                    ov for ov, is_iv in zip(outer_verts, is_inside_edge) if is_iv
+                ]
+
+                # To avoid doing the same work twice, we will mark inner vertices
+                is_inside_vert[inside_verts[~is_inside_edge]] = True
+
+                # For each edge between inner-vertices and their outer neighbors calculate the
+                # exact position for the exact step_size distance
+                in_out_edges = np.array(
+                    [
+                        [iv, ov]
+                        for iv, ovs in zip(inner_verts, outer_verts)
+                        for ov in ovs
+                    ]
+                )
+                in_pos = mesh.vertices[cc[in_out_edges[:, 0]]]
+                out_pos = mesh.vertices[cc[in_out_edges[:, 1]]]
+
+                # The distance between the inner and outer vertices
+                in_out_dist = in_out_dist = np.sqrt(
+                    ((in_pos - out_pos) ** 2).sum(axis=1)
+                )
+
+                # For each in_out_edge the remaining distance
+                d_left = d - dist[in_out_edges[:, 0]]
+
+                # Move along the edges until we hit the target distance
+                new_verts = (
+                    in_pos + (out_pos - in_pos) * (d_left / in_out_dist)[:, None]
+                )
+
+                # To group vertices into rings we need to first determine which vertices
+                # are part of the same ring. We do this by checking which outer vertices
+                # are in connected components
+                outer_verts_unique = np.unique(np.concatenate(outer_verts))
+                for cc2 in SG.subgraph(outer_verts_unique).connected_components():
+                    # Translate this connected components back to the vertex IDs in SG
+                    outer_verts_cc2 = outer_verts_unique[cc2]
+
+                    # Get the new vertices that are part of this connected component
+                    this_new_verts = new_verts[
+                        np.isin(in_out_edges[:, 1], outer_verts_cc2)
+                    ]
+
+                    # Get the center of this connected component
+                    this_center = this_new_verts.mean(axis=0)
+
+                    # Calculate the radius of this connected component
+                    this_radius = rad_agg_func(
+                        np.sqrt((this_new_verts - this_center) ** 2).sum(axis=1)
+                    )
+
+                    centers.append(this_center)  # Store the center
+                    radii.append(this_radius)  # Store the radius
+                    data.append(
+                        (k, i, cc[outer_verts_cc2[0]])
+                    )  # Track the connected component, the step and a vertex from the outer ring for this center
+
+                # pbar.update(len(cc))
+                # Update progress bar based on the number of vertices we have invalidated
+                pbar.update((~is_inside_edge).sum())
+
+    centers = np.vstack(centers)
+    radii = np.array(radii)
+    data = np.array(data)
+
+    # Next we have to reconstruct the parent-child relationships
+    # For each center, we know _a_ vertex that is part of the (outer) ring
+    # With that information we can ask, for each center, which center in the
+    # previous step is closest to it (as per distance along the mesh)
+    parents = np.full(len(centers), fill_value=-1, dtype=int)
+
+    # This maps the step and the vertex ID to the index in the centers array
+    step_id_map = {(step, id): i for i, (step, id) in enumerate(data[:, 1:])}
+
+    tree = G.spanning_tree()
+
+    for i in trange(
+        1, data[:, 1].max(), desc="Connecting", disable=not progress, leave=False
+    ):
+        is_this_step = data[:, 1] == i  # All centers in this step
+        is_prev_step = data[:, 1] == i - 1  # All centers in the previous step
+
+        # If there is only one center in the previous step, we can just go on and connect these
+        if is_prev_step.sum() == 1:
+            parents[is_this_step] = np.where(is_prev_step)[0][0]
+            continue
+
+        this_step_track_verts = np.unique(
+            data[is_this_step, 2]
+        )  # All track-vertices in this step
+        prev_step_track_verts = np.unique(
+            data[is_prev_step, 2]
+        )  # All track-vertices in the previous step
+
+        # Get distances between current and previous track vertices
+        # Note to self: this step takes up about 60% of the time at the moment
+        # There should be a way to speed this up.
+        d = np.array(
+            tree.distances(
+                source=this_step_track_verts,
+                target=prev_step_track_verts,
+                mode="all",
+                weights="weight",
+            )
+        )
+
+        # Get the closest previous track-vertex for each current track-vertex
+        closest_prev_track_verts = prev_step_track_verts[d.argmin(axis=1)]
+
+        for this, prev in zip(this_step_track_verts, closest_prev_track_verts):
+            parents[is_this_step & (data[:, 2] == this)] = step_id_map[(i - 1, prev)]
+
+    return centers, radii, parents