Fix #144610: Cycles: do not convert open volume mesh to sdf

because we can't determine the interior. Sample densities in the whole
bounding box instead.

Pull Request: https://projects.blender.org/blender/blender/pulls/144732

intern/cycles/bvh/octree.cpp

@@ -105,7 +105,7 @@ static bool vdb_voxel_intersect(const float3 p_min,
                                 const openvdb::tools::FindActiveValues<openvdb::BoolTree> &find)
 {
   if (grid->empty()) {
-    /* Non-mesh volume. */
+    /* Non-mesh volume or open mesh. */
     return true;
   }
 

intern/cycles/scene/volume.cpp

@@ -655,6 +655,50 @@ bool VolumeManager::is_homogeneous_volume(const Object *object, const Shader *sh
 }
 
 #ifdef WITH_OPENVDB
+/* Given a mesh, check if every edge has exactly two incident triangles, and if the two triangles
+ * have the same orientation. */
+static bool mesh_is_closed(const std::vector<openvdb::Vec3I> &triangles)
+{
+  const size_t num_triangles = triangles.size();
+  if (num_triangles % 2) {
+    return false;
+  }
+
+  /* Store the two vertices that forms an edge. */
+  std::multiset<std::pair<int, int>> edges;
+  int num_edges = 0;
+
+  for (const auto &tri : triangles) {
+    for (int i = 0; i < 3; i++) {
+      const std::pair<int, int> e = {tri[i], tri[(i + 1) % 3]};
+      if (edges.count(e)) {
+        /* Same edge exists. */
+        return false;
+      }
+
+      /* Check if an edge in the opposite order exists. */
+      const auto count = edges.count({e.second, e.first});
+      if (count > 1) {
+        /* Edge has more than 2 incident faces. */
+        return false;
+      }
+      if (count == 1) {
+        /* If an edge in the opposite order exists, increment the count. */
+        edges.insert({e.second, e.first});
+      }
+      else {
+        /* Insert a new edge. */
+        num_edges++;
+        edges.insert(e);
+      }
+    }
+  }
+
+  /* Until this point, the count of each element in the set is at most 2; to check if they are
+   * exactly 2, we just need to compare the total numbers. */
+  return num_triangles * 3 == num_edges * 2;
+}
+
 openvdb::BoolGrid::ConstPtr VolumeManager::mesh_to_sdf_grid(const Mesh *mesh,
                                                             const Shader *shader,
                                                             const float half_width)
@@ -679,6 +723,12 @@ openvdb::BoolGrid::ConstPtr VolumeManager::mesh_to_sdf_grid(const Mesh *mesh,
     }
   }
 
+  if (!mesh_is_closed(triangles)) {
+    /* `meshToLevelSet()` requires a closed mesh, otherwise we can not determine the interior of
+     * the mesh. Evaluate the whole bounding box in this case. */
+    return openvdb::BoolGrid::create();
+  }
+
   /* TODO(weizhen): Should consider object instead of mesh size. */
   const float3 mesh_size = mesh->bounds.size();
   const auto vdb_voxel_size = openvdb::Vec3d(mesh_size.x, mesh_size.y, mesh_size.z) /