diff --git a/primitive_process/interface/base/primitive.hpp b/primitive_process/interface/base/primitive.hpp
index b0cf6e1..622b5e2 100644
--- a/primitive_process/interface/base/primitive.hpp
+++ b/primitive_process/interface/base/primitive.hpp
@@ -62,7 +62,9 @@ EXTERN_C struct PE_API primitive {
     // so we don't need to fetch aabb anymore
     // aabb fetch_aabb() const;
     // CAUTION: keep characteristics local_to_world as the first subface's part
-    const internal::transform_block &get_identity_local_to_world() const;
+    // why virtual? for special primitive like cylinder, it may have multiple parts, the part
+    // with index 0 may not be the identity transform. e.g., cylinder face has no z translation.
+    virtual const internal::transform_block &get_identity_local_to_world() const;
 
     void apply_transform(internal::transform_type, Eigen::Vector4d);
 
diff --git a/primitive_process/interface/primitive/simple/cylinder.hpp b/primitive_process/interface/primitive/simple/cylinder.hpp
index 0f42e37..20d6ac5 100644
--- a/primitive_process/interface/primitive/simple/cylinder.hpp
+++ b/primitive_process/interface/primitive/simple/cylinder.hpp
@@ -16,6 +16,15 @@ struct cylinder_t final : primitive {
     marked_subface_ptr_t<internal::plane_t>         bottom_plane{};
     marked_subface_ptr_t<internal::plane_t>         top_plane{};
 
+    // why virtual? For special primitives like cylinder, it may have multiple parts.
+    // The part with index 0 may not be the identity transform. 
+    // For example, the cylinder face has no z translation.
+    // Note: The AABB of a cylinder is defined by the side surface, and z-axis scaling does not affect the side surface's radius.
+    // The degeneracy (simplification) check for a cylinder only considers the first two rows of the transform matrix (x/y directions),
+    // because scaling along z does not change the essential geometry of the cylinder side surface.
+    // TODO: the better way is to redefine cylinder, make identity transform as the first part.
+    const internal::transform_block &get_identity_local_to_world() const override;
+
 protected:
     void initialize(primitive_data_center_t &, const std::vector<std::pair<internal::paired_model_matrix *, bool>> &) override;
 
diff --git a/primitive_process/src/primitive/simple/cylinder.cpp b/primitive_process/src/primitive/simple/cylinder.cpp
index 20623a6..593e02d 100644
--- a/primitive_process/src/primitive/simple/cylinder.cpp
+++ b/primitive_process/src/primitive/simple/cylinder.cpp
@@ -61,4 +61,9 @@ void cylinder_t::initialize(primitive_data_center_t
             data_center.planes.release(plane_paired_model_matrix{old_model_matrices[2]});
     }
 }
+
+const internal::transform_block &cylinder_t::get_identity_local_to_world() const
+{
+    return get_subface()[1].get_ptr()->raw_local_to_world();
+}
 } // namespace internal
\ No newline at end of file