diff --git a/vespa/Algorithm/vtkCGALPolyDataAlgorithm.cxx b/vespa/Algorithm/vtkCGALPolyDataAlgorithm.cxx
index dec3f9b2e3f7f6f3aafccd9c30dbe621c09894fa..72da29460694b40326111443161bb9614aac790d 100644
--- a/vespa/Algorithm/vtkCGALPolyDataAlgorithm.cxx
+++ b/vespa/Algorithm/vtkCGALPolyDataAlgorithm.cxx
@@ -49,9 +49,7 @@ bool vtkCGALPolyDataAlgorithm::toCGAL(vtkPolyData* vtkMesh, Vespa_soup* cgalMesh
     vtkIdList* ids   = cit->GetPointIds();
     vtkIdType  nbIds = cit->GetNumberOfPoints();
 
-    cgalMesh->faces[cid].reserve(3); // mostly triangles
-
-    std::vector<Graph_Verts> cell(nbIds);
+    cgalMesh->faces[cid].reserve(ids->GetNumberOfIds());
     for (vtkIdType i = 0; i < nbIds; i++)
     {
       cgalMesh->faces[cid].emplace_back(ids->GetId(i));
diff --git a/vespa/PolygonMeshProcessing/Testing/TestPMPAlphaWrapping.cxx b/vespa/PolygonMeshProcessing/Testing/TestPMPAlphaWrapping.cxx
index 40a816b77ff43bcf99b074b3505a5df08863c661..a89c224d8fceaedc301fcc591361b5f8220eb851 100644
--- a/vespa/PolygonMeshProcessing/Testing/TestPMPAlphaWrapping.cxx
+++ b/vespa/PolygonMeshProcessing/Testing/TestPMPAlphaWrapping.cxx
@@ -1,5 +1,4 @@
-#include <iostream>
-
+#include <vtkConvertToPointCloud.h>
 #include <vtkNew.h>
 #include <vtkTestUtilities.h>
 #include <vtkXMLPolyDataReader.h>
@@ -16,15 +15,24 @@ int TestPMPAlphaWrapping(int, char* argv[])
   cfname += "/dragon.vtp";
   reader->SetFileName(cfname.c_str());
 
-  // Remesh
+  // Remesh surface
+  vtkNew<vtkCGALAlphaWrapping> aw1;
+  aw1->SetInputConnection(reader->GetOutputPort());
+
+  // Remesh point cloud
+  vtkNew<vtkConvertToPointCloud> toPC;
+  toPC->SetInputConnection(aw1->GetOutputPort());
+  toPC->SetCellGenerationMode(vtkConvertToPointCloud::VERTEX_CELLS); 
 
-  vtkNew<vtkCGALAlphaWrapping> aw;
-  aw->SetInputConnection(reader->GetOutputPort());
+  // Remesh point cloud
+  vtkNew<vtkCGALAlphaWrapping> aw2;
+  aw2->SetInputConnection(toPC->GetOutputPort());
+  aw2->SetAlpha(2);
 
   // Save result
 
   vtkNew<vtkXMLPolyDataWriter> writer;
-  writer->SetInputConnection(aw->GetOutputPort());
+  writer->SetInputConnection(aw2->GetOutputPort());
   writer->SetFileName("alpha_wrapping.vtp");
   writer->Write();
 
diff --git a/vespa/PolygonMeshProcessing/vtk.module b/vespa/PolygonMeshProcessing/vtk.module
index 84ab51499a32c17362adac829a3ee702d11a4ccf..b66b03218c2bbcd43f5c90161586514e64c62c01 100644
--- a/vespa/PolygonMeshProcessing/vtk.module
+++ b/vespa/PolygonMeshProcessing/vtk.module
@@ -9,6 +9,7 @@ DEPENDS
 TEST_DEPENDS
   VTK::CommonSystem
   VTK::FiltersSources
+  VTK::FiltersPoints
   VTK::IOInfovis
   VTK::IOXML
   VTK::TestingCore
diff --git a/vespa/PolygonMeshProcessing/vtkCGALAlphaWrapping.cxx b/vespa/PolygonMeshProcessing/vtkCGALAlphaWrapping.cxx
index 54048efa7b56929f41513949253c3932d7afb769..4fcb341f29571cb35319e4991d5ee04aafe9c2ed 100644
--- a/vespa/PolygonMeshProcessing/vtkCGALAlphaWrapping.cxx
+++ b/vespa/PolygonMeshProcessing/vtkCGALAlphaWrapping.cxx
@@ -57,7 +57,6 @@ int vtkCGALAlphaWrapping::RequestData(
   // Create the surface mesh for CGAL
   // --------------------------------
 
-  // TODO switch to soup ? (or shrink 1)
   std::unique_ptr<Vespa_soup> cgalMesh = std::make_unique<Vespa_soup>();
   this->toCGAL(input, cgalMesh.get());
 
@@ -68,7 +67,24 @@ int vtkCGALAlphaWrapping::RequestData(
 
   try
   {
-    CGAL::alpha_wrap_3(cgalMesh->points, cgalMesh->faces, alpha, offset, cgalOutput->surface);
+    bool isPointCloud = true;
+    for (auto& cell : cgalMesh->faces)
+    {
+      if (cell.size() > 1)
+      {
+        isPointCloud = false;
+      }
+    }
+
+    if (isPointCloud)
+    {
+      // Specific version when we have only points
+      CGAL::alpha_wrap_3(cgalMesh->points, alpha, offset, cgalOutput->surface);
+    }
+    else
+    {
+      CGAL::alpha_wrap_3(cgalMesh->points, cgalMesh->faces, alpha, offset, cgalOutput->surface);
+    }
   }
   catch (std::exception& e)
   {