diff --git a/primitive_process/interface/subface/simple/cylinder_face.hpp b/primitive_process/interface/subface/simple/cylinder_face.hpp
index db04f78..5d86b1f 100644
--- a/primitive_process/interface/subface/simple/cylinder_face.hpp
+++ b/primitive_process/interface/subface/simple/cylinder_face.hpp
@@ -34,8 +34,20 @@ template <>
 struct hasher<internal::cylinder_paired_model_matrix> {
     size_t operator()(const internal::cylinder_paired_model_matrix &block) const
     {
-        Eigen::Matrix<double, 2, 4> character_rows = block.data->local_to_world.matrix().topRows<2>();
-        return XXH3_64bits(character_rows.data(), sizeof(decltype(character_rows)));
+        const auto& mat = block.data->local_to_world.matrix(); // 3x4
+        Eigen::Matrix3d A = mat.block<3,3>(0,0);               
+        Eigen::Vector3d b = mat.col(3);
+
+        Eigen::Matrix3d B = A.inverse();
+        Eigen::Matrix<double, 2, 3> R = B.topRows<2>();
+
+        Eigen::Matrix3d G = R.transpose() * R;
+        Eigen::Vector2d zero_proj = R * b;
+
+        size_t h = XXH3_64bits(G.data(), sizeof(Eigen::Matrix3d));
+        h ^= XXH3_64bits(zero_proj.data(), sizeof(Eigen::Vector2d));
+
+        return h;
     }
 };