diff --git a/src/Model/Geometry/Point.py b/src/Model/Geometry/Point.py
index 24c96137..5de3b058 100644
--- a/src/Model/Geometry/Point.py
+++ b/src/Model/Geometry/Point.py
@@ -58,7 +58,7 @@ class Point(SQLSubModel):
         self._name = name
         self.modified()
 
-    def point_is_named(self):
+    def is_named(self):
         """
         Returns:
             True if the point is named.
diff --git a/src/Model/Geometry/PointXYZ.py b/src/Model/Geometry/PointXYZ.py
index ad6b92f1..2cc5936e 100644
--- a/src/Model/Geometry/PointXYZ.py
+++ b/src/Model/Geometry/PointXYZ.py
@@ -368,5 +368,10 @@ class PointXYZ(Point):
         a = PointXYZ.distance(p1, p2)
         b = PointXYZ.distance(p2, p3)
         c = PointXYZ.distance(p3, p1)
-        s = (a + b + c) / 2
-        return (s*(s-a) * (s-b)*(s-c)) ** 0.5
+
+        s = float((a + b + c) / 2)
+        res = (
+            s * abs(s - a) * abs(s - b) * abs(s - c)
+        ) ** 0.5
+
+        return res
diff --git a/src/Model/Geometry/Profile.py b/src/Model/Geometry/Profile.py
index 45685caa..af1e8f5e 100644
--- a/src/Model/Geometry/Profile.py
+++ b/src/Model/Geometry/Profile.py
@@ -187,7 +187,7 @@ class Profile(object):
             The list of named point
         """
         return [point for point in self.points
-                if point.point_is_named()]
+                if point.is_named()]
 
     def insert_point(self, index: int, point: Point):
         """Insert point at index.
diff --git a/src/Model/Geometry/ProfileXYZ.py b/src/Model/Geometry/ProfileXYZ.py
index b6c98cec..6dd2d7d5 100644
--- a/src/Model/Geometry/ProfileXYZ.py
+++ b/src/Model/Geometry/ProfileXYZ.py
@@ -16,6 +16,8 @@
 
 # -*- coding: utf-8 -*-
 
+import queue
+import random
 import logging
 import numpy as np
 from typing import List
@@ -929,13 +931,13 @@ class ProfileXYZ(Profile, SQLSubModel):
         last_point_not_nan = self._last_point_not_nan(points)
 
         for index, point in enumerate(points):
-            if point.point_is_named():
+            if point.is_named():
                 index_first_named_point = index
                 first_named_point = point
                 break
 
         for point in reversed(points):
-            if point.point_is_named():
+            if point.is_named():
                 last_named_point = point
                 break
 
@@ -1009,46 +1011,47 @@ class ProfileXYZ(Profile, SQLSubModel):
         if (self.nb_points <= np_purge):
             return
 
-        nb_named = 2   # we consider the first and last point as named
-        area = [0.0]
+        q_area = queue.PriorityQueue()
+        deleted = []
 
-        for i in range(1, self.nb_points-1):
-            if self.point(i).point_is_named():
-                area.append(9999999.999)
-                nb_named += 1
-            else:
-                area.append(
+        for ind, point in enumerate(self.points):
+            if (ind == 0) or (ind == self.nb_points - 1):
+                continue
+
+            if not point.is_named():
+                q_area.put((
                     PointXYZ.areatriangle3d(
-                        self.point(i-1),
-                        self.point(i),
-                        self.point(i+1))
-                )
+                        self.point(ind - 1),
+                        point,
+                        self.point(ind + 1)
+                    ),
+                    ind,
+                    point
+                ))
 
-        area.append(0.0)
+        while self.nb_points > np_purge and not q_area.empty():
+            area, ind, point = q_area.get()
 
-        while self.nb_points > max(np_purge, nb_named):
-            to_rm = np.argmin(area[1:self.nb_points - 1]) + 1
+            self.delete_points([point])
+            deleted.append(point)
 
-            self.delete_i([to_rm])
-            area.pop(to_rm)
-
-            for i in [to_rm-1, to_rm]:
-                if (i == 0):
+            # Recompute point neighbourhood
+            for i in [ind-1, ind]:
+                if (i <= 0) or (i >= self.nb_points - 1):
                     continue
 
-                if (i == self.nb_points - 1):
-                    continue
-
-                if self.point(i).point_is_named():
-                    area[i] = 9999999.999
-                else:
-                    area[i] = PointXYZ.areatriangle3d(
-                        self.point(i-1),
-                        self.point(i),
-                        self.point(i+1)
-                    )
+                point = self.point(i)
+                if not point.is_named():
+                      q_area.put((
+                          PointXYZ.areatriangle3d(
+                              self.point(i-1),
+                              point,
+                              self.point(i+1)
+                          ), i, point
+                      ))
 
         self.modified()
+        return deleted
 
     def shift(self, x, y, z):
         for p in self._points:
diff --git a/src/View/Geometry/Profile/UndoCommand.py b/src/View/Geometry/Profile/UndoCommand.py
index 30cc86c9..9a12e243 100644
--- a/src/View/Geometry/Profile/UndoCommand.py
+++ b/src/View/Geometry/Profile/UndoCommand.py
@@ -202,16 +202,17 @@ class PurgeCommand(QUndoCommand):
     def __init__(self, profile, np_purge):
         QUndoCommand.__init__(self)
 
+        self._deleted = []
         self._profile = profile
-        self._old = self._profile.points.copy()
         self._np_purge = np_purge
 
     def undo(self):
-        self._profile._points = self._old.copy()
+        for point in self._deleted:
+            point.set_as_not_deleted()
         self._profile.modified()
 
     def redo(self):
-        self._profile.purge(self._np_purge)
+        self._deleted = self._profile.purge(self._np_purge)
         self._profile.modified()
 
 
diff --git a/src/View/Geometry/UndoCommand.py b/src/View/Geometry/UndoCommand.py
index 562bd65d..c0c9a7fc 100644
--- a/src/View/Geometry/UndoCommand.py
+++ b/src/View/Geometry/UndoCommand.py
@@ -277,18 +277,17 @@ class PurgeCommand(QUndoCommand):
 
         self._reach = reach
         self._np_purge = np_purge
-
-        self._old = []
-        for profile in self._reach.profiles:
-            self._old.append(profile.points.copy())
+        self._deleted = {}
 
     def undo(self):
-        for i in range(self._reach.number_profiles):
-            self._reach.profiles[i]._points = self._old[i].copy()
+        for profile in self._deleted:
+            for point in self._deleted[profile]:
+                point.set_as_not_deleted()
+            profile.modified()
 
     def redo(self):
         for profile in self._reach._profiles:
-            profile.purge(self._np_purge)
+            self._deleted[profile] = profile.purge(self._np_purge)
 
 
 class ChangeReachCommand(QUndoCommand):