diff --git a/core/include/detray/builders/detail/portal_accessor.hpp b/core/include/detray/builders/detail/portal_accessor.hpp
index b63f532b9..d757cf9d6 100644
--- a/core/include/detray/builders/detail/portal_accessor.hpp
+++ b/core/include/detray/builders/detail/portal_accessor.hpp
@@ -12,7 +12,7 @@
 #include "detray/definitions/detail/qualifiers.hpp"
 #include "detray/geometry/shapes/cylinder2D.hpp"
 #include "detray/geometry/shapes/ring2D.hpp"
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/geometry/tracking_volume.hpp"
 
 // System include(s).
@@ -37,7 +37,7 @@ auto get_cylinder_portals(const tracking_volume<detector_t> &vol) {
 
     // Loop over all portals
     for (const auto &pt_desc : vol.portals()) {
-        auto pt = tracking_surface{vol.detector(), pt_desc};
+        auto pt = geometry::surface{vol.detector(), pt_desc};
         const std::string name = pt.shape_name();
 
         if (name == "cylinder2D" || name == "concentric_cylinder2D") {
diff --git a/core/include/detray/builders/grid_builder.hpp b/core/include/detray/builders/grid_builder.hpp
index d7900fc8e..616a7041f 100644
--- a/core/include/detray/builders/grid_builder.hpp
+++ b/core/include/detray/builders/grid_builder.hpp
@@ -13,7 +13,6 @@
 #include "detray/builders/surface_factory_interface.hpp"
 #include "detray/builders/volume_builder.hpp"
 #include "detray/builders/volume_builder_interface.hpp"
-#include "detray/geometry/tracking_surface.hpp"
 #include "detray/geometry/tracking_volume.hpp"
 #include "detray/utils/grid/detail/concepts.hpp"
 
diff --git a/core/include/detray/builders/material_map_builder.hpp b/core/include/detray/builders/material_map_builder.hpp
index 39fca3928..0c8fbe660 100644
--- a/core/include/detray/builders/material_map_builder.hpp
+++ b/core/include/detray/builders/material_map_builder.hpp
@@ -13,7 +13,7 @@
 #include "detray/builders/material_map_generator.hpp"
 #include "detray/builders/surface_factory_interface.hpp"
 #include "detray/builders/volume_builder_interface.hpp"
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/materials/material_map.hpp"
 
 // System include(s)
@@ -125,7 +125,7 @@ class material_map_builder final : public volume_decorator<detector_t> {
             }
 
             // Construct and append the material map for a given surface shape
-            auto sf = tracking_surface{det, sf_desc};
+            auto sf = geometry::surface{det, sf_desc};
             [[maybe_unused]] auto [mat_id, mat_idx] = sf.template visit_mask<
                 detail::add_sf_material_map<materials_t>>(
                 m_factory, m_bin_data.at(sf_idx), m_n_bins.at(sf_idx),
diff --git a/core/include/detray/builders/volume_builder.hpp b/core/include/detray/builders/volume_builder.hpp
index 3c9521fff..88eeba4b3 100644
--- a/core/include/detray/builders/volume_builder.hpp
+++ b/core/include/detray/builders/volume_builder.hpp
@@ -11,7 +11,7 @@
 #include "detray/builders/surface_factory_interface.hpp"
 #include "detray/builders/volume_builder_interface.hpp"
 #include "detray/definitions/geometry.hpp"
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/utils/grid/detail/concepts.hpp"
 
 // System include(s)
@@ -210,7 +210,7 @@ class volume_builder : public volume_builder_interface<detector_t> {
         std::size_t n_portals{0u};
         for (auto& sf_desc : m_surfaces) {
 
-            const auto sf = tracking_surface{det, sf_desc};
+            const auto sf = geometry::surface{det, sf_desc};
 
             sf.template visit_mask<detail::mask_index_update>(sf_desc);
             sf_desc.set_volume(m_volume.index());
diff --git a/core/include/detray/geometry/detail/shape_utils.hpp b/core/include/detray/geometry/detail/shape_utils.hpp
index 5fa52d421..23cd46b28 100644
--- a/core/include/detray/geometry/detail/shape_utils.hpp
+++ b/core/include/detray/geometry/detail/shape_utils.hpp
@@ -17,7 +17,7 @@ namespace detray::detail {
 /// @return the opening angle of a chord the size of tol (= 2*arcsin(c/(2r)))
 /// using a small angle approximation
 template <typename scalar_t>
-inline constexpr scalar_t phi_tolerance(scalar_t tol, scalar_t radius) {
+constexpr scalar_t phi_tolerance(scalar_t tol, scalar_t radius) {
     return tol / radius;
 }
 
diff --git a/core/include/detray/geometry/detail/surface_kernels.hpp b/core/include/detray/geometry/detail/surface_kernels.hpp
index 695b9384d..48f67bfb7 100644
--- a/core/include/detray/geometry/detail/surface_kernels.hpp
+++ b/core/include/detray/geometry/detail/surface_kernels.hpp
@@ -8,14 +8,12 @@
 #pragma once
 
 // Project include(s)
+#include "detray/definitions/detail/algebra.hpp"
 #include "detray/definitions/detail/indexing.hpp"
 #include "detray/definitions/detail/qualifiers.hpp"
 #include "detray/materials/detail/concepts.hpp"
 #include "detray/materials/detail/material_accessor.hpp"
 #include "detray/materials/material.hpp"
-#include "detray/propagator/detail/jacobian_engine.hpp"
-#include "detray/tracks/detail/transform_track_parameters.hpp"
-#include "detray/tracks/tracks.hpp"
 
 // System include(s)
 #include <limits>
@@ -33,9 +31,6 @@ struct surface_kernels {
     using point3_type = dpoint3D<algebra_t>;
     using vector3_type = dvector3D<algebra_t>;
     using transform3_type = dtransform3D<algebra_t>;
-    using bound_param_vector_type = bound_parameters_vector<algebra_t>;
-    using free_param_vector_type = free_parameters_vector<algebra_t>;
-    using free_matrix_type = free_matrix<algebra_t>;
 
     /// A functor to retrieve the masks shape name
     struct get_shape_name {
@@ -211,111 +206,6 @@ struct surface_kernels {
         }
     };
 
-    /// A functor to get from a free to a bound vector
-    struct free_to_bound_vector {
-
-        // Visitor to the detector mask store that is called on the mask
-        // collection that contains the mask (shape) type of the surface
-        template <typename mask_group_t, typename index_t>
-        DETRAY_HOST_DEVICE inline bound_param_vector_type operator()(
-            const mask_group_t& /*mask_group*/, const index_t& /*index*/,
-            const transform3_type& trf3,
-            const free_param_vector_type& free_vec) const {
-
-            using frame_t = typename mask_group_t::value_type::local_frame;
-
-            return detail::free_to_bound_vector<frame_t>(trf3, free_vec);
-        }
-    };
-
-    /// A functor to get from a bound to a free vector
-    struct bound_to_free_vector {
-
-        template <typename mask_group_t, typename index_t>
-        DETRAY_HOST_DEVICE inline free_param_vector_type operator()(
-            const mask_group_t& mask_group, const index_t& index,
-            const transform3_type& trf3,
-            const bound_param_vector_type& bound_vec) const {
-
-            return detail::bound_to_free_vector(trf3, mask_group[index],
-                                                bound_vec);
-        }
-    };
-
-    /// A functor to get the free-to-bound Jacobian
-    struct free_to_bound_jacobian {
-
-        template <typename mask_group_t, typename index_t>
-        DETRAY_HOST_DEVICE inline auto operator()(
-            const mask_group_t& /*mask_group*/, const index_t& /*index*/,
-            const transform3_type& trf3,
-            const free_param_vector_type& free_vec) const {
-
-            using frame_t = typename mask_group_t::value_type::local_frame;
-
-            return detail::jacobian_engine<frame_t>::free_to_bound_jacobian(
-                trf3, free_vec);
-        }
-    };
-
-    /// A functor to get the bound-to-free Jacobian
-    struct bound_to_free_jacobian {
-
-        template <typename mask_group_t, typename index_t>
-        DETRAY_HOST_DEVICE inline auto operator()(
-            const mask_group_t& mask_group, const index_t& index,
-            const transform3_type& trf3,
-            const bound_param_vector_type& bound_vec) const {
-
-            using frame_t = typename mask_group_t::value_type::local_frame;
-
-            return detail::jacobian_engine<frame_t>::bound_to_free_jacobian(
-                trf3, mask_group[index], bound_vec);
-        }
-    };
-
-    /// A functor to get the path correction
-    struct path_correction {
-
-        template <typename mask_group_t, typename index_t, typename scalar_t>
-        DETRAY_HOST_DEVICE inline free_matrix_type operator()(
-            const mask_group_t& /*mask_group*/, const index_t& /*index*/,
-            const transform3_type& trf3, const vector3_type& pos,
-            const vector3_type& dir, const vector3_type& dtds,
-            const scalar_t dqopds) const {
-
-            using frame_t = typename mask_group_t::value_type::local_frame;
-
-            return detail::jacobian_engine<frame_t>::path_correction(
-                pos, dir, dtds, dqopds, trf3);
-        }
-    };
-
-    /// A functor to get the local min bounds.
-    struct local_min_bounds {
-
-        template <typename mask_group_t, typename index_t, typename scalar_t>
-        DETRAY_HOST_DEVICE inline auto operator()(
-            const mask_group_t& mask_group, const index_t& index,
-            const scalar_t env =
-                std::numeric_limits<scalar_t>::epsilon()) const {
-
-            return mask_group[index].local_min_bounds(env);
-        }
-    };
-
-    /// A functor to get the minimum distance to any surface boundary.
-    struct min_dist_to_boundary {
-
-        template <typename mask_group_t, typename index_t, typename point_t>
-        DETRAY_HOST_DEVICE inline auto operator()(
-            const mask_group_t& mask_group, const index_t& index,
-            const point_t& loc_p) const {
-
-            return mask_group[index].min_dist_to_boundary(loc_p);
-        }
-    };
-
     /// A functor to get the vertices in local coordinates.
     struct local_vertices {
 
diff --git a/core/include/detray/geometry/tracking_surface.hpp b/core/include/detray/geometry/surface.hpp
similarity index 71%
rename from core/include/detray/geometry/tracking_surface.hpp
rename to core/include/detray/geometry/surface.hpp
index 932991f8d..a55cdc263 100644
--- a/core/include/detray/geometry/tracking_surface.hpp
+++ b/core/include/detray/geometry/surface.hpp
@@ -21,7 +21,7 @@
 #include <ostream>
 #include <type_traits>
 
-namespace detray {
+namespace detray::geometry {
 
 /// @brief Facade for a detray detector surface.
 ///
@@ -31,16 +31,12 @@ namespace detray {
 /// that contains the indices into the detector data containers for the
 /// specific surface instance.
 template <typename detector_t>  // @TODO: This needs a concept
-class tracking_surface {
+class surface {
 
     /// Surface descriptor type
     using descr_t = typename detector_t::surface_type;
-
+    /// Implementation
     using kernels = detail::surface_kernels<typename detector_t::algebra_type>;
-    /// Vector type for track parameters in global coordinates
-    using free_param_vector_type = typename kernels::free_param_vector_type;
-    /// Vector type for track parameters in local (bound) coordinates
-    using bound_param_vector_type = typename kernels::bound_param_vector_type;
 
     public:
     using algebra_type = typename detector_t::algebra_type;
@@ -52,39 +48,37 @@ class tracking_surface {
     using context = typename detector_t::geometry_context;
 
     /// Not allowed: always needs a detector and a descriptor.
-    tracking_surface() = delete;
+    surface() = delete;
 
     /// Constructor from detector @param det and surface descriptor
     /// @param desc from that detector.
     DETRAY_HOST_DEVICE
-    constexpr tracking_surface(const detector_t &det, const descr_t &desc)
+    constexpr surface(const detector_t &det, const descr_t &desc)
         : m_detector{det}, m_desc{desc} {}
 
     /// Constructor from detector @param det and barcode @param bcd in
     /// that detector.
     DETRAY_HOST_DEVICE
-    constexpr tracking_surface(const detector_t &det,
-                               const geometry::barcode bcd)
-        : tracking_surface(det, det.surface(bcd)) {}
+    constexpr surface(const detector_t &det, const geometry::barcode bcd)
+        : surface(det, det.surface(bcd)) {}
 
     /// Constructor from detector @param det and surface index @param sf_idx
     DETRAY_HOST_DEVICE
-    constexpr tracking_surface(const detector_t &det, const dindex sf_idx)
-        : tracking_surface(det, det.surface(sf_idx)) {}
+    constexpr surface(const detector_t &det, const dindex sf_idx)
+        : surface(det, det.surface(sf_idx)) {}
 
     /// Conversion to surface interface around constant detector type
     template <typename detector_type = detector_t>
     requires(!std::is_const_v<detector_type>) DETRAY_HOST_DEVICE constexpr
-    operator tracking_surface<const detector_type>() const {
-        return tracking_surface<const detector_type>{this->m_detector,
-                                                     this->m_desc};
+    operator surface<const detector_type>() const {
+        return surface<const detector_type>{this->m_detector, this->m_desc};
     }
 
     /// Equality operator
     ///
     /// @param rhs is the right hand side to be compared to
     DETRAY_HOST_DEVICE
-    constexpr auto operator==(const tracking_surface &rhs) const -> bool {
+    constexpr auto operator==(const surface &rhs) const -> bool {
         return (&m_detector == &(rhs.m_detector) && m_desc == rhs.m_desc);
     }
 
@@ -203,17 +197,6 @@ class tracking_surface {
         return visit_mask<typename kernels::normal>(transform(ctx), p);
     }
 
-    /// @returns the cosine of the incidence angle given a local/bound position
-    /// @param p and a global direction @param dir
-    /// @note The direction has to be normalized
-    template <typename point_t = point2_type>
-        requires std::is_same_v<point_t, point3_type> ||
-        std::is_same_v<point_t, point2_type> DETRAY_HOST_DEVICE constexpr auto
-        cos_angle(const context &ctx, const vector3_type &dir,
-                  const point_t &p) const -> scalar_type {
-        return math::fabs(vector::dot(dir, normal(ctx, p)));
-    }
-
     /// @returns a pointer to the material parameters at the local position
     /// @param loc_p
     DETRAY_HOST_DEVICE constexpr const material<scalar_type>
@@ -243,104 +226,28 @@ class tracking_surface {
 
     /// @returns the global position to the given local position @param local
     /// for a given geometry context @param ctx
-    DETRAY_HOST_DEVICE constexpr point3_type local_to_global(
-        const context &ctx, const point3_type &local,
-        const vector3_type &dir) const {
+    template <typename point_t = point2_type>
+        requires std::is_same_v<point_t, point3_type> ||
+        std::is_same_v<point_t, point2_type>
+            DETRAY_HOST_DEVICE constexpr point3_type local_to_global(
+                const context &ctx, const point_t &local,
+                const vector3_type &dir) const {
         return visit_mask<typename kernels::local_to_global>(transform(ctx),
                                                              local, dir);
     }
 
-    /// @returns the global position to the given bound position @param bound
-    /// for a given geometry context @param ctx
-    DETRAY_HOST_DEVICE constexpr point3_type bound_to_global(
-        const context &ctx, const point2_type &bound,
-        const vector3_type &dir) const {
-        return visit_mask<typename kernels::local_to_global>(transform(ctx),
-                                                             bound, dir);
-    }
-
-    /// @returns the track parametrization projected onto the surface (bound)
-    DETRAY_HOST_DEVICE
-    constexpr auto free_to_bound_vector(
-        const context &ctx, const free_param_vector_type &free_vec) const {
-        return visit_mask<typename kernels::free_to_bound_vector>(
-            transform(ctx), free_vec);
-    }
-
-    /// @returns the global track parametrization from a bound representation
-    DETRAY_HOST_DEVICE
-    constexpr auto bound_to_free_vector(
-        const context &ctx, const bound_param_vector_type &bound_vec) const {
-        return visit_mask<typename kernels::bound_to_free_vector>(
-            transform(ctx), bound_vec);
-    }
-
-    /// @returns the jacobian to go from a free to a bound track parametrization
-    DETRAY_HOST_DEVICE
-    constexpr auto free_to_bound_jacobian(
-        const context &ctx, const free_param_vector_type &free_vec) const {
-        return this
-            ->template visit_mask<typename kernels::free_to_bound_jacobian>(
-                transform(ctx), free_vec);
-    }
-
-    /// @returns the jacobian to go from a bound to a free track parametrization
-    DETRAY_HOST_DEVICE
-    constexpr auto bound_to_free_jacobian(
-        const context &ctx, const bound_param_vector_type &bound_vec) const {
-        return this
-            ->template visit_mask<typename kernels::bound_to_free_jacobian>(
-                transform(ctx), bound_vec);
-    }
-
-    /// @returns the path correction term
-    DETRAY_HOST_DEVICE
-    constexpr auto path_correction(const context &ctx, const vector3_type &pos,
-                                   const vector3_type &dir,
-                                   const vector3_type &dtds,
-                                   const scalar_type dqopds) const {
-        return visit_mask<typename kernels::path_correction>(
-            transform(ctx), pos, dir, dtds, dqopds);
-    }
-
-    /// @returns the vertices in local frame with @param n_seg the number of
-    /// segments used along acrs
-    DETRAY_HOST
-    constexpr auto local_vertices(const dindex n_seg) const {
-        return visit_mask<typename kernels::vertices>(n_seg);
-    }
-
     /// @returns the vertices in global frame with @param n_seg the number of
     /// segments used along acrs
     DETRAY_HOST
     constexpr auto global_vertices(const context &ctx,
                                    const dindex n_seg) const {
-        auto vertices = local_vertices(n_seg);
+        auto vertices = visit_mask<typename kernels::vertices>(n_seg);
         for (std::size_t i = 0u; i < vertices.size(); ++i) {
             vertices[i] = transform(ctx).point_to_global(vertices[i]);
         }
         return vertices;
     }
 
-    /// @returns the vertices in local frame with @param n_seg the number of
-    /// segments used along acrs
-    /// @note the point has to be inside the surface mask
-    template <typename point_t>
-    DETRAY_HOST constexpr auto min_dist_to_boundary(
-        const point_t &loc_p) const {
-        return visit_mask<typename kernels::min_dist_to_boundary>(loc_p);
-    }
-
-    /// @brief Lower and upper point for minimal axis aligned bounding box.
-    ///
-    /// Computes the min and max vertices in a local cartesian frame.
-    DETRAY_HOST
-    constexpr auto local_min_bounds(
-        const scalar_type env =
-            std::numeric_limits<scalar_type>::epsilon()) const {
-        return visit_mask<typename kernels::local_min_bounds>(env);
-    }
-
     /// Call a functor on the surfaces mask with additional arguments.
     ///
     /// @tparam functor_t the prescription to be applied to the mask
@@ -431,14 +338,22 @@ class tracking_surface {
         return true;
     }
 
+    protected:
     /// @returns a string stream that prints the surface details
     DETRAY_HOST
-    friend std::ostream &operator<<(std::ostream &os,
-                                    const tracking_surface &sf) {
+    friend std::ostream &operator<<(std::ostream &os, const surface &sf) {
         os << sf.m_desc;
         return os;
     }
 
+    /// @returns access to the underlying detector object
+    DETRAY_HOST_DEVICE
+    const detector_t &detector() const { return m_detector; }
+
+    /// @returns access to the underlying surface descriptor object
+    DETRAY_HOST_DEVICE
+    descr_t descriptor() const { return m_desc; }
+
     private:
     /// Access to the detector stores
     const detector_t &m_detector;
@@ -447,11 +362,11 @@ class tracking_surface {
 };
 
 template <typename detector_t, typename descr_t>
-DETRAY_HOST_DEVICE tracking_surface(const detector_t &, const descr_t &)
-    ->tracking_surface<detector_t>;
+DETRAY_HOST_DEVICE surface(const detector_t &, const descr_t &)
+    ->surface<detector_t>;
 
 template <typename detector_t>
-DETRAY_HOST_DEVICE tracking_surface(const detector_t &, const geometry::barcode)
-    ->tracking_surface<detector_t>;
+DETRAY_HOST_DEVICE surface(const detector_t &, const geometry::barcode)
+    ->surface<detector_t>;
 
-}  // namespace detray
+}  // namespace detray::geometry
diff --git a/core/include/detray/materials/detail/material_utils.hpp b/core/include/detray/materials/detail/material_utils.hpp
new file mode 100644
index 000000000..2cefd1d4d
--- /dev/null
+++ b/core/include/detray/materials/detail/material_utils.hpp
@@ -0,0 +1,37 @@
+/** Detray library, part of the ACTS project (R&D line)
+ *
+ * (c) 2024 CERN for the benefit of the ACTS project
+ *
+ * Mozilla Public License Version 2.0
+ */
+
+#pragma once
+
+// Project include(s)
+#include "detray/definitions/detail/algebra.hpp"
+#include "detray/definitions/detail/math.hpp"
+#include "detray/geometry/surface.hpp"
+
+namespace detray::detail {
+
+/// Helper function to calculate the incidence angle of a track on a surface
+///
+/// @param ctx the geometric context
+/// @param sf the geometric surface
+/// @param track_dir normalized direction vector of the track
+/// @param loc the local/bound position of the track on the surface
+///
+/// @returns the cosine of the incidence angle given a local/bound position
+template <typename detector_t, typename point_t>
+    requires std::is_same_v<point_t,
+                            dpoint3D<typename detector_t::algebra_type>> ||
+    std::is_same_v<point_t, dpoint2D<typename detector_t::algebra_type>>
+        DETRAY_HOST_DEVICE constexpr dscalar<typename detector_t::algebra_type>
+        cos_angle(const typename detector_t::geometry_context &ctx,
+                  geometry::surface<detector_t> sf,
+                  const dvector3D<typename detector_t::algebra_type> &track_dir,
+                  const point_t &loc) {
+    return math::fabs(vector::dot(track_dir, sf.normal(ctx, loc)));
+}
+
+}  // namespace detray::detail
diff --git a/core/include/detray/navigation/detail/ray.hpp b/core/include/detray/navigation/detail/ray.hpp
index dc7eea49c..7d6649470 100644
--- a/core/include/detray/navigation/detail/ray.hpp
+++ b/core/include/detray/navigation/detail/ray.hpp
@@ -25,9 +25,6 @@ class ray {
     using vector3_type = dvector3D<algebra_type>;
     using transform3_type = dtransform3D<algebra_type>;
 
-    using free_track_parameters_type = free_track_parameters<algebra_t>;
-    using free_vector_type = typename free_track_parameters_type::vector_type;
-
     ray() = default;
 
     /// Parametrized constructor that complies with track interface
@@ -41,7 +38,8 @@ class ray {
     /// Parametrized constructor that complies with track interface
     ///
     /// @param track the track state that should be approximated
-    DETRAY_HOST_DEVICE explicit ray(const free_track_parameters_type &track)
+    DETRAY_HOST_DEVICE explicit ray(
+        const free_track_parameters<algebra_t> &track)
         : ray(track.pos(), 0.f, track.dir(), 0.f) {}
 
     /// @returns position on the ray (compatible with tracks/intersectors)
diff --git a/core/include/detray/navigation/navigator.hpp b/core/include/detray/navigation/navigator.hpp
index e0d5e53d9..0f29e0353 100644
--- a/core/include/detray/navigation/navigator.hpp
+++ b/core/include/detray/navigation/navigator.hpp
@@ -15,6 +15,7 @@
 #include "detray/definitions/detail/qualifiers.hpp"
 #include "detray/definitions/units.hpp"
 #include "detray/geometry/barcode.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/navigation/detail/ray.hpp"
 #include "detray/navigation/intersection/intersection.hpp"
 #include "detray/navigation/intersection/ray_intersector.hpp"
@@ -256,8 +257,8 @@ class navigator {
         /// @returns the next surface the navigator intends to reach
         DETRAY_HOST_DEVICE
         inline auto next_surface() const {
-            return tracking_surface<detector_type>{*m_detector,
-                                                   target().sf_desc};
+            return geometry::surface<detector_type>{*m_detector,
+                                                    target().sf_desc};
         }
 
         /// @returns current detector surface the navigator is on
@@ -265,8 +266,8 @@ class navigator {
         DETRAY_HOST_DEVICE
         inline auto get_surface() const {
             assert(is_on_module() || is_on_portal());
-            return tracking_surface<detector_type>{*m_detector,
-                                                   current().sf_desc};
+            return geometry::surface<detector_type>{*m_detector,
+                                                    current().sf_desc};
         }
 
         /// @returns current detector volume of the navigation stream
@@ -598,7 +599,7 @@ class navigator {
             const scalar_type mask_tol_scalor,
             const scalar_type overstep_tol) const {
 
-            const auto sf = tracking_surface{det, sf_descr};
+            const auto sf = geometry::surface{det, sf_descr};
 
             sf.template visit_mask<intersection_initialize<ray_intersector>>(
                 nav_state, detail::ray(track), sf_descr, det.transform_store(),
@@ -886,7 +887,7 @@ class navigator {
             return false;
         }
 
-        const auto sf = tracking_surface{det, candidate.sf_desc};
+        const auto sf = geometry::surface{det, candidate.sf_desc};
 
         // Check whether this candidate is reachable by the track
         return sf.template visit_mask<intersection_update<ray_intersector>>(
diff --git a/core/include/detray/propagator/actors/parameter_resetter.hpp b/core/include/detray/propagator/actors/parameter_resetter.hpp
index 9aeeeb71e..d3b1a04cf 100644
--- a/core/include/detray/propagator/actors/parameter_resetter.hpp
+++ b/core/include/detray/propagator/actors/parameter_resetter.hpp
@@ -10,7 +10,6 @@
 // Project include(s).
 #include "detray/definitions/detail/qualifiers.hpp"
 #include "detray/definitions/track_parametrization.hpp"
-#include "detray/geometry/tracking_surface.hpp"
 #include "detray/propagator/base_actor.hpp"
 #include "detray/propagator/detail/jacobian_engine.hpp"
 
diff --git a/core/include/detray/propagator/actors/parameter_transporter.hpp b/core/include/detray/propagator/actors/parameter_transporter.hpp
index 94e1c41d5..3856828bf 100644
--- a/core/include/detray/propagator/actors/parameter_transporter.hpp
+++ b/core/include/detray/propagator/actors/parameter_transporter.hpp
@@ -10,9 +10,9 @@
 // Project include(s).
 #include "detray/definitions/detail/qualifiers.hpp"
 #include "detray/definitions/track_parametrization.hpp"
-#include "detray/geometry/tracking_surface.hpp"
 #include "detray/propagator/base_actor.hpp"
 #include "detray/propagator/detail/jacobian_engine.hpp"
+#include "detray/propagator/tracking_surface.hpp"
 
 namespace detray {
 
@@ -102,7 +102,7 @@ struct parameter_transporter : actor {
         const geo_cxt_t ctx{};
 
         // Current Surface
-        const auto sf = navigation.get_surface();
+        const auto sf = tracking_surface{navigation.get_surface()};
 
         // Covariance is transported only when the previous surface is an
         // actual tracking surface. (i.e. This disables the covariance transport
diff --git a/core/include/detray/propagator/actors/pointwise_material_interactor.hpp b/core/include/detray/propagator/actors/pointwise_material_interactor.hpp
index d1d973b08..21edbee54 100644
--- a/core/include/detray/propagator/actors/pointwise_material_interactor.hpp
+++ b/core/include/detray/propagator/actors/pointwise_material_interactor.hpp
@@ -10,14 +10,12 @@
 // Project include(s).
 #include "detray/definitions/detail/qualifiers.hpp"
 #include "detray/definitions/track_parametrization.hpp"
-#include "detray/geometry/tracking_surface.hpp"
 #include "detray/materials/detail/concepts.hpp"
 #include "detray/materials/detail/material_accessor.hpp"
+#include "detray/materials/detail/material_utils.hpp"
 #include "detray/materials/interaction.hpp"
 #include "detray/propagator/base_actor.hpp"
 #include "detray/tracks/bound_track_parameters.hpp"
-#include "detray/utils/ranges.hpp"
-#include "detray/utils/type_traits.hpp"
 
 namespace detray {
 
@@ -165,8 +163,8 @@ struct pointwise_material_interactor : actor {
         // Closest approach of the track to a line surface. Otherwise this is
         // ignored.
         const auto approach{bound_params[e_bound_loc0]};
-        const scalar_type cos_inc_angle{math::fabs(sf.cos_angle(
-            gctx, bound_params.dir(), bound_params.bound_local()))};
+        const scalar_type cos_inc_angle{detail::cos_angle(
+            gctx, sf, bound_params.dir(), bound_params.bound_local())};
 
         const bool succeed = sf.template visit_material<kernel>(
             interactor_state, ptc, bound_params, cos_inc_angle, approach);
diff --git a/core/include/detray/propagator/base_stepper.hpp b/core/include/detray/propagator/base_stepper.hpp
index 749340daa..9eea5943b 100644
--- a/core/include/detray/propagator/base_stepper.hpp
+++ b/core/include/detray/propagator/base_stepper.hpp
@@ -12,7 +12,7 @@
 #include "detray/definitions/pdg_particle.hpp"
 #include "detray/definitions/units.hpp"
 #include "detray/geometry/barcode.hpp"
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/propagator/actors/parameter_resetter.hpp"
 #include "detray/propagator/constrained_step.hpp"
 #include "detray/propagator/stepping_config.hpp"
@@ -95,7 +95,7 @@ class base_stepper {
             : _bound_params(bound_params) {
 
             // Surface
-            const auto sf = tracking_surface{det, bound_params.surface_link()};
+            const auto sf = geometry::surface{det, bound_params.surface_link()};
 
             const typename detector_t::geometry_context ctx{};
             sf.template visit_mask<
diff --git a/core/include/detray/propagator/detail/tracking_surface_kernels.hpp b/core/include/detray/propagator/detail/tracking_surface_kernels.hpp
new file mode 100644
index 000000000..4fca0a9bc
--- /dev/null
+++ b/core/include/detray/propagator/detail/tracking_surface_kernels.hpp
@@ -0,0 +1,112 @@
+/** Detray library, part of the ACTS project (R&D line)
+ *
+ * (c) 2023-2024 CERN for the benefit of the ACTS project
+ *
+ * Mozilla Public License Version 2.0
+ */
+
+#pragma once
+
+// Project include(s)
+#include "detray/definitions/detail/qualifiers.hpp"
+#include "detray/propagator/detail/jacobian_engine.hpp"
+#include "detray/tracks/detail/transform_track_parameters.hpp"
+#include "detray/tracks/tracks.hpp"
+
+// System include(s)
+#include <ostream>
+
+namespace detray::detail {
+
+/// Functors to be used in the @c tracking_surface class
+template <typename algebra_t>
+struct tracking_surface_kernels : public surface_kernels<algebra_t> {
+
+    using vector3_type = dvector3D<algebra_t>;
+    using transform3_type = dtransform3D<algebra_t>;
+    using bound_param_vector_type = bound_parameters_vector<algebra_t>;
+    using free_param_vector_type = free_parameters_vector<algebra_t>;
+    using free_matrix_type = free_matrix<algebra_t>;
+
+    /// A functor to get from a free to a bound vector
+    struct free_to_bound_vector {
+
+        // Visitor to the detector mask store that is called on the mask
+        // collection that contains the mask (shape) type of the surface
+        template <typename mask_group_t, typename index_t>
+        DETRAY_HOST_DEVICE inline bound_param_vector_type operator()(
+            const mask_group_t& /*mask_group*/, const index_t& /*index*/,
+            const transform3_type& trf3,
+            const free_param_vector_type& free_vec) const {
+
+            using frame_t = typename mask_group_t::value_type::local_frame;
+
+            return detail::free_to_bound_vector<frame_t>(trf3, free_vec);
+        }
+    };
+
+    /// A functor to get from a bound to a free vector
+    struct bound_to_free_vector {
+
+        template <typename mask_group_t, typename index_t>
+        DETRAY_HOST_DEVICE inline free_param_vector_type operator()(
+            const mask_group_t& mask_group, const index_t& index,
+            const transform3_type& trf3,
+            const bound_param_vector_type& bound_vec) const {
+
+            return detail::bound_to_free_vector(trf3, mask_group[index],
+                                                bound_vec);
+        }
+    };
+
+    /// A functor to get the free-to-bound Jacobian
+    struct free_to_bound_jacobian {
+
+        template <typename mask_group_t, typename index_t>
+        DETRAY_HOST_DEVICE inline auto operator()(
+            const mask_group_t& /*mask_group*/, const index_t& /*index*/,
+            const transform3_type& trf3,
+            const free_param_vector_type& free_vec) const {
+
+            using frame_t = typename mask_group_t::value_type::local_frame;
+
+            return detail::jacobian_engine<frame_t>::free_to_bound_jacobian(
+                trf3, free_vec);
+        }
+    };
+
+    /// A functor to get the bound-to-free Jacobian
+    struct bound_to_free_jacobian {
+
+        template <typename mask_group_t, typename index_t>
+        DETRAY_HOST_DEVICE inline auto operator()(
+            const mask_group_t& mask_group, const index_t& index,
+            const transform3_type& trf3,
+            const bound_param_vector_type& bound_vec) const {
+
+            using frame_t = typename mask_group_t::value_type::local_frame;
+
+            return detail::jacobian_engine<frame_t>::bound_to_free_jacobian(
+                trf3, mask_group[index], bound_vec);
+        }
+    };
+
+    /// A functor to get the path correction
+    struct path_correction {
+
+        template <typename mask_group_t, typename index_t, typename scalar_t>
+        DETRAY_HOST_DEVICE inline free_matrix_type operator()(
+            const mask_group_t& /*mask_group*/, const index_t& /*index*/,
+            const transform3_type& trf3, const vector3_type& pos,
+            const vector3_type& dir, const vector3_type& dtds,
+            const scalar_t dqopds) const {
+
+            using frame_t = typename mask_group_t::value_type::local_frame;
+
+            return detail::jacobian_engine<frame_t>::path_correction(
+                pos, dir, dtds, dqopds, trf3);
+        }
+    };
+};
+
+}  // namespace detray::detail
diff --git a/core/include/detray/propagator/tracking_surface.hpp b/core/include/detray/propagator/tracking_surface.hpp
new file mode 100644
index 000000000..6613a9e22
--- /dev/null
+++ b/core/include/detray/propagator/tracking_surface.hpp
@@ -0,0 +1,118 @@
+
+/** Detray library, part of the ACTS project (R&D line)
+ *
+ * (c) 2024 CERN for the benefit of the ACTS project
+ *
+ * Mozilla Public License Version 2.0
+ */
+
+#pragma once
+
+// Project include(s)
+#include "detray/definitions/detail/qualifiers.hpp"
+#include "detray/geometry/surface.hpp"
+#include "detray/propagator/detail/tracking_surface_kernels.hpp"
+
+// System include(s)
+#include <ostream>
+
+namespace detray {
+
+/// @brief Facade for a detray detector surface with tracking capabilities.
+template <typename detector_t>  // @TODO: This needs a concept
+class tracking_surface : public geometry::surface<detector_t> {
+
+    using base_surface_t = geometry::surface<detector_t>;
+
+    /// Implementation of tracking functionality
+    using kernels =
+        detail::tracking_surface_kernels<typename detector_t::algebra_type>;
+    /// Vector type for track parameters in global coordinates
+    using free_param_vector_type = typename kernels::free_param_vector_type;
+    /// Vector type for track parameters in local (bound) coordinates
+    using bound_param_vector_type = typename kernels::bound_param_vector_type;
+
+    public:
+    using algebra_type = typename base_surface_t::algebra_type;
+    using scalar_type = typename base_surface_t::scalar_type;
+    using point2_type = typename base_surface_t::point2_type;
+    using point3_type = typename base_surface_t::point3_type;
+    using vector3_type = typename base_surface_t::vector3_type;
+    using transform3_type = typename base_surface_t::transform3_type;
+    using context = typename base_surface_t::context;
+
+    /// Use base class constructors
+    using base_surface_t::base_surface_t;
+
+    /// Decorate a geometric surface with tracking functionality
+    DETRAY_HOST_DEVICE
+    explicit tracking_surface(const base_surface_t sf) : base_surface_t(sf) {}
+
+    /// Conversion to surface interface around constant detector type
+    template <typename detector_type = detector_t>
+    requires(!std::is_const_v<detector_type>) DETRAY_HOST_DEVICE constexpr
+    operator tracking_surface<const detector_type>() const {
+        return tracking_surface<const detector_type>{this->m_detector,
+                                                     this->m_desc};
+    }
+
+    /// @returns the track parametrization projected onto the surface (bound)
+    DETRAY_HOST_DEVICE
+    constexpr auto free_to_bound_vector(
+        const context &ctx, const free_param_vector_type &free_vec) const {
+        return this
+            ->template visit_mask<typename kernels::free_to_bound_vector>(
+                this->transform(ctx), free_vec);
+    }
+
+    /// @returns the global track parametrization from a bound representation
+    DETRAY_HOST_DEVICE
+    constexpr auto bound_to_free_vector(
+        const context &ctx, const bound_param_vector_type &bound_vec) const {
+        return this
+            ->template visit_mask<typename kernels::bound_to_free_vector>(
+                this->transform(ctx), bound_vec);
+    }
+
+    /// @returns the jacobian to go from a free to a bound track parametrization
+    DETRAY_HOST_DEVICE
+    constexpr auto free_to_bound_jacobian(
+        const context &ctx, const free_param_vector_type &free_vec) const {
+        return this
+            ->template visit_mask<typename kernels::free_to_bound_jacobian>(
+                this->transform(ctx), free_vec);
+    }
+
+    /// @returns the jacobian to go from a bound to a free track parametrization
+    DETRAY_HOST_DEVICE
+    constexpr auto bound_to_free_jacobian(
+        const context &ctx, const bound_param_vector_type &bound_vec) const {
+        return this
+            ->template visit_mask<typename kernels::bound_to_free_jacobian>(
+                this->transform(ctx), bound_vec);
+    }
+
+    /// @returns the path correction term
+    DETRAY_HOST_DEVICE
+    constexpr auto path_correction(const context &ctx, const vector3_type &pos,
+                                   const vector3_type &dir,
+                                   const vector3_type &dtds,
+                                   const scalar_type dqopds) const {
+        return this->template visit_mask<typename kernels::path_correction>(
+            this->transform(ctx), pos, dir, dtds, dqopds);
+    }
+};
+
+template <typename detector_t, typename descr_t>
+DETRAY_HOST_DEVICE tracking_surface(const detector_t &, const descr_t &)
+    ->tracking_surface<detector_t>;
+
+template <typename detector_t>
+DETRAY_HOST_DEVICE tracking_surface(const detector_t &, const geometry::barcode)
+    ->tracking_surface<detector_t>;
+
+template <typename detector_t>
+DETRAY_HOST_DEVICE tracking_surface(const geometry::surface<detector_t>)
+    ->tracking_surface<detector_t>;
+
+}  // namespace detray
diff --git a/core/include/detray/utils/consistency_checker.hpp b/core/include/detray/utils/consistency_checker.hpp
index cb0f589c3..f8eec2790 100644
--- a/core/include/detray/utils/consistency_checker.hpp
+++ b/core/include/detray/utils/consistency_checker.hpp
@@ -8,7 +8,7 @@
 #pragma once
 
 // Project include(s)
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/geometry/tracking_volume.hpp"
 #include "detray/materials/detail/concepts.hpp"
 #include "detray/materials/predefined_materials.hpp"
@@ -56,7 +56,7 @@ struct surface_checker {
         const detector_t &det, const dindex vol_idx,
         const typename detector_t::name_map &names) const {
 
-        const auto sf = tracking_surface{det, sf_descr};
+        const auto sf = geometry::surface{det, sf_descr};
         const auto vol = tracking_volume{det, vol_idx};
         std::stringstream err_stream{};
         err_stream << "VOLUME \"" << print_volume_name(vol, names) << "\":\n";
@@ -93,7 +93,7 @@ struct surface_checker {
         // Check that the same surface is registered in the detector surface
         // lookup
         const auto sf_from_lkp =
-            tracking_surface{det, det.surface(sf.barcode())};
+            geometry::surface{det, det.surface(sf.barcode())};
         if (sf_from_lkp != sf) {
             err_stream << "ERROR: Surfaces in volume and detector lookups "
                        << "differ:\n In volume acceleration data structure: "
@@ -121,7 +121,7 @@ struct surface_checker {
         if (ref_descr.volume() != check_descr.volume()) {
             std::stringstream err_stream{};
             err_stream << "Incorrect volume index on surface: "
-                       << tracking_surface{det, check_descr};
+                       << geometry::surface{det, check_descr};
 
             throw std::invalid_argument(err_stream.str());
         }
@@ -330,7 +330,7 @@ inline bool check_consistency(const detector_t &det, const bool verbose = false,
     // Check the surfaces in the detector's surface lookup
     for (const auto &[idx, sf_desc] :
          detray::views::enumerate(det.surfaces())) {
-        const auto sf = tracking_surface{det, sf_desc};
+        const auto sf = geometry::surface{det, sf_desc};
         const auto vol = tracking_volume{det, sf.volume()};
         err_stream << "VOLUME \"" << print_volume_name(vol, names) << "\":\n";
 
diff --git a/io/include/detray/io/common/geometry_writer.hpp b/io/include/detray/io/common/geometry_writer.hpp
index 0b290a495..6c5935a4b 100644
--- a/io/include/detray/io/common/geometry_writer.hpp
+++ b/io/include/detray/io/common/geometry_writer.hpp
@@ -10,7 +10,7 @@
 // Project include(s)
 #include "detray/definitions/detail/indexing.hpp"
 #include "detray/geometry/mask.hpp"
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/io/common/detail/basic_converter.hpp"
 #include "detray/io/common/detail/type_info.hpp"
 #include "detray/io/frontend/payloads.hpp"
@@ -103,7 +103,7 @@ class geometry_writer {
 
     /// Convert a detector surface @param sf into its io payload
     template <typename detector_t>
-    static surface_payload convert(const tracking_surface<detector_t>& sf,
+    static surface_payload convert(const geometry::surface<detector_t>& sf,
                                    std::size_t sf_idx) {
         surface_payload sf_data;
 
@@ -137,7 +137,7 @@ class geometry_writer {
         for (const auto& sf_desc : det.surfaces()) {
             if (sf_desc.volume() == vol_desc.index()) {
                 vol_data.surfaces.push_back(
-                    convert(tracking_surface{det, sf_desc}, sf_idx++));
+                    convert(geometry::surface{det, sf_desc}, sf_idx++));
             }
         }
 
diff --git a/io/include/detray/io/common/homogeneous_material_writer.hpp b/io/include/detray/io/common/homogeneous_material_writer.hpp
index 23fa943d0..98801a72d 100644
--- a/io/include/detray/io/common/homogeneous_material_writer.hpp
+++ b/io/include/detray/io/common/homogeneous_material_writer.hpp
@@ -8,7 +8,7 @@
 #pragma once
 
 // Project include(s)
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/geometry/tracking_volume.hpp"
 #include "detray/io/common/detail/basic_converter.hpp"
 #include "detray/io/common/detail/type_info.hpp"
@@ -104,7 +104,7 @@ class homogeneous_material_writer {
         for (const auto& sf_desc : vol.surfaces()) {
 
             // Convert material slabs and rods
-            const auto sf = tracking_surface{det, sf_desc};
+            const auto sf = geometry::surface{det, sf_desc};
             material_slab_payload mslp =
                 sf.template visit_material<get_material_payload>(sf_idx);
 
diff --git a/plugins/svgtools/include/detray/plugins/svgtools/conversion/information_section.hpp b/plugins/svgtools/include/detray/plugins/svgtools/conversion/information_section.hpp
index 988b218bf..fec1b2daa 100644
--- a/plugins/svgtools/include/detray/plugins/svgtools/conversion/information_section.hpp
+++ b/plugins/svgtools/include/detray/plugins/svgtools/conversion/information_section.hpp
@@ -8,7 +8,7 @@
 #pragma once
 
 // Project include(s)
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/plugins/svgtools/meta/proto/information_section.hpp"
 
 // Actsvg include(s)
@@ -37,7 +37,7 @@ inline std::string point_to_string(point3_t point) {
 template <typename detector_t>
 inline auto information_section(
     const typename detector_t::geometry_context& context,
-    const detray::tracking_surface<detector_t>& d_surface) {
+    const detray::geometry::surface<detector_t>& d_surface) {
 
     using point3_t = typename detector_t::point3_type;
 
diff --git a/plugins/svgtools/include/detray/plugins/svgtools/conversion/intersection.hpp b/plugins/svgtools/include/detray/plugins/svgtools/conversion/intersection.hpp
index 95444a53c..9c3dc54c2 100644
--- a/plugins/svgtools/include/detray/plugins/svgtools/conversion/intersection.hpp
+++ b/plugins/svgtools/include/detray/plugins/svgtools/conversion/intersection.hpp
@@ -8,6 +8,9 @@
 #pragma once
 
 // Project include(s)
+#include "detray/geometry/surface.hpp"
+
+// Plugin include(s)
 #include "detray/plugins/svgtools/conversion/landmark.hpp"
 #include "detray/plugins/svgtools/meta/proto/intersection.hpp"
 
@@ -32,13 +35,13 @@ inline auto intersection(const detector_t& detector,
 
     for (const auto& intr : intersections) {
 
-        const detray::tracking_surface<detector_t> sf{detector, intr.sf_desc};
+        const detray::geometry::surface<detector_t> sf{detector, intr.sf_desc};
         if (sf.barcode().is_invalid()) {
             continue;
         }
 
         const point2_t bound{intr.local[0], intr.local[1]};
-        const auto position = sf.bound_to_global(gctx, bound, dir);
+        const auto position = sf.local_to_global(gctx, bound, dir);
         const auto p_lm = svgtools::conversion::landmark(position, style);
 
         p_ir._landmarks.push_back(p_lm);
diff --git a/plugins/svgtools/include/detray/plugins/svgtools/conversion/link.hpp b/plugins/svgtools/include/detray/plugins/svgtools/conversion/link.hpp
index ac1dae9ec..d5a402d6c 100644
--- a/plugins/svgtools/include/detray/plugins/svgtools/conversion/link.hpp
+++ b/plugins/svgtools/include/detray/plugins/svgtools/conversion/link.hpp
@@ -8,7 +8,9 @@
 #pragma once
 
 // Project include(s)
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
+
+// Plugin include(s)
 #include "detray/plugins/svgtools/utils/link_utils.hpp"
 #include "detray/plugins/svgtools/utils/surface_kernels.hpp"
 
@@ -21,7 +23,7 @@ namespace detray::svgtools::conversion {
 template <typename detector_t>
 inline auto link(const typename detector_t::geometry_context& context,
                  const detector_t& detector,
-                 const detray::tracking_surface<detector_t>& d_portal) {
+                 const detray::geometry::surface<detector_t>& d_portal) {
 
     using point3_container_t = std::vector<typename detector_t::point3_type>;
     using p_link_t = typename actsvg::proto::portal<point3_container_t>::link;
diff --git a/plugins/svgtools/include/detray/plugins/svgtools/conversion/portal.hpp b/plugins/svgtools/include/detray/plugins/svgtools/conversion/portal.hpp
index 1a04b8b18..0217c1ff2 100644
--- a/plugins/svgtools/include/detray/plugins/svgtools/conversion/portal.hpp
+++ b/plugins/svgtools/include/detray/plugins/svgtools/conversion/portal.hpp
@@ -8,7 +8,9 @@
 #pragma once
 
 // Project include(s)
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
+
+// Plugin include(s)
 #include "detray/plugins/svgtools/conversion/link.hpp"
 #include "detray/plugins/svgtools/conversion/surface.hpp"
 #include "detray/plugins/svgtools/styling/styling.hpp"
@@ -24,7 +26,7 @@ namespace detray::svgtools::conversion {
 template <typename detector_t, typename view_t>
 auto portal(const typename detector_t::geometry_context& context,
             const detector_t& detector,
-            const detray::tracking_surface<detector_t>& d_portal,
+            const detray::geometry::surface<detector_t>& d_portal,
             const view_t& view,
             const styling::portal_style& style =
                 styling::tableau_colorblind::portal_style,
diff --git a/plugins/svgtools/include/detray/plugins/svgtools/conversion/surface.hpp b/plugins/svgtools/include/detray/plugins/svgtools/conversion/surface.hpp
index bc2aed36e..d54c4a234 100644
--- a/plugins/svgtools/include/detray/plugins/svgtools/conversion/surface.hpp
+++ b/plugins/svgtools/include/detray/plugins/svgtools/conversion/surface.hpp
@@ -10,7 +10,9 @@
 // Project include(s)
 #include "detray/geometry/mask.hpp"
 #include "detray/geometry/shapes.hpp"
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
+
+// Plugin include(s)
 #include "detray/plugins/svgtools/conversion/surface_material.hpp"
 #include "detray/plugins/svgtools/styling/styling.hpp"
 
@@ -207,7 +209,7 @@ struct surface_converter {
 template <typename detector_t, typename view_t>
 auto surface(const typename detector_t::geometry_context& context,
              const detector_t& detector,
-             const detray::tracking_surface<detector_t>& d_surface,
+             const detray::geometry::surface<detector_t>& d_surface,
              const view_t& view,
              const styling::surface_style& style =
                  styling::tableau_colorblind::surface_style_sensitive,
diff --git a/plugins/svgtools/include/detray/plugins/svgtools/conversion/surface_material.hpp b/plugins/svgtools/include/detray/plugins/svgtools/conversion/surface_material.hpp
index 97489d34d..0a497c78f 100644
--- a/plugins/svgtools/include/detray/plugins/svgtools/conversion/surface_material.hpp
+++ b/plugins/svgtools/include/detray/plugins/svgtools/conversion/surface_material.hpp
@@ -8,7 +8,7 @@
 #pragma once
 
 // Project include(s)
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/utils/grid/detail/concepts.hpp"
 
 // Plugin include(s)
@@ -143,7 +143,7 @@ struct material_converter {
 /// @returns An actsvg proto surface material the material map.
 template <typename detector_t, typename view_t>
 auto surface_material(const detector_t& detector,
-                      const detray::tracking_surface<detector_t>& d_surface,
+                      const detray::geometry::surface<detector_t>& d_surface,
                       const view_t& view,
                       const styling::surface_material_style& style =
                           styling::tableau_colorblind::material_style) {
diff --git a/plugins/svgtools/include/detray/plugins/svgtools/conversion/volume.hpp b/plugins/svgtools/include/detray/plugins/svgtools/conversion/volume.hpp
index bac3ab988..ab8924f56 100644
--- a/plugins/svgtools/include/detray/plugins/svgtools/conversion/volume.hpp
+++ b/plugins/svgtools/include/detray/plugins/svgtools/conversion/volume.hpp
@@ -8,8 +8,10 @@
 #pragma once
 
 // Project include(s)
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/geometry/tracking_volume.hpp"
+
+// Plugin include(s)
 #include "detray/plugins/svgtools/conversion/portal.hpp"
 #include "detray/plugins/svgtools/conversion/surface.hpp"
 #include "detray/plugins/svgtools/conversion/surface_grid.hpp"
@@ -65,7 +67,7 @@ auto volume(const typename detector_t::geometry_context& context,
 
     for (const auto& desc : d_volume.surfaces()) {
 
-        const auto sf = detray::tracking_surface<detector_t>{detector, desc};
+        const auto sf = detray::geometry::surface<detector_t>{detector, desc};
 
         if (sf.is_portal()) {
             if (!hide_portals) {
diff --git a/plugins/svgtools/include/detray/plugins/svgtools/illustrator.hpp b/plugins/svgtools/include/detray/plugins/svgtools/illustrator.hpp
index 12ebca55d..e1de19abd 100644
--- a/plugins/svgtools/include/detray/plugins/svgtools/illustrator.hpp
+++ b/plugins/svgtools/include/detray/plugins/svgtools/illustrator.hpp
@@ -8,7 +8,7 @@
 #pragma once
 
 // Project include(s)
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/plugins/svgtools/conversion/detector.hpp"
 #include "detray/plugins/svgtools/conversion/grid.hpp"
 #include "detray/plugins/svgtools/conversion/information_section.hpp"
@@ -107,7 +107,7 @@ class illustrator {
         const typename detector_t::geometry_context& gctx = {}) const {
 
         const auto surface =
-            detray::tracking_surface<detector_t>{_detector, index};
+            detray::geometry::surface<detector_t>{_detector, index};
 
         actsvg::svg::object ret, material;
         const auto& style = _style._detector_style._volume_style;
@@ -206,7 +206,7 @@ class illustrator {
                                       const view_t& view) const {
 
         const auto surface =
-            detray::tracking_surface<detector_t>{_detector, index};
+            detray::geometry::surface<detector_t>{_detector, index};
 
         if (_hide_material) {
             return actsvg::svg::object{};
@@ -523,7 +523,7 @@ class illustrator {
                 prefix + "_record", p_ir, view));
 
             // The intersection record is always sorted by path length
-            const auto sf{detray::tracking_surface{
+            const auto sf{detray::geometry::surface{
                 _detector, intersections.back().sf_desc}};
             const auto final_pos = sf.local_to_global(
                 gctx, intersections.back().local, trajectory.dir(0.f));
diff --git a/plugins/svgtools/include/detray/plugins/svgtools/utils/link_utils.hpp b/plugins/svgtools/include/detray/plugins/svgtools/utils/link_utils.hpp
index a1c03e6ca..4f4873dde 100644
--- a/plugins/svgtools/include/detray/plugins/svgtools/utils/link_utils.hpp
+++ b/plugins/svgtools/include/detray/plugins/svgtools/utils/link_utils.hpp
@@ -8,10 +8,12 @@
 #pragma once
 
 // Project include(s)
-#include "detray/geometry/tracking_surface.hpp"
-#include "detray/plugins/svgtools/utils/surface_kernels.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/utils/invalid_values.hpp"
 
+// Plugin include(s)
+#include "detray/plugins/svgtools/utils/surface_kernels.hpp"
+
 // System include(s)
 #include <cassert>
 #include <tuple>
@@ -21,7 +23,7 @@ namespace detray::svgtools::utils {
 /// @brief Checks if the detray surface has a volume link.
 template <typename detector_t>
 inline auto is_not_world_portal(
-    const detray::tracking_surface<detector_t>& d_portal) {
+    const detray::geometry::surface<detector_t>& d_portal) {
     const auto d_link_idx = d_portal.template visit_mask<link_getter>();
     return !detail::is_invalid_value(d_link_idx);
 }
@@ -31,7 +33,7 @@ inline auto is_not_world_portal(
 template <typename detector_t>
 inline auto get_linked_volume(
     const detector_t& detector,
-    const detray::tracking_surface<detector_t>& d_portal) {
+    const detray::geometry::surface<detector_t>& d_portal) {
     assert(is_not_world_portal(d_portal));
     const auto d_link_idx = d_portal.template visit_mask<link_getter>();
     return tracking_volume{detector, d_link_idx};
@@ -43,7 +45,7 @@ inline auto get_linked_volume(
 template <typename detector_t>
 inline auto link_points(const typename detector_t::geometry_context& context,
                         const detector_t& detector,
-                        const detray::tracking_surface<detector_t>& d_portal,
+                        const detray::geometry::surface<detector_t>& d_portal,
                         typename detector_t::vector3_type dir,
                         const double link_length) {
     assert(is_not_world_portal(d_portal));
diff --git a/plugins/svgtools/include/detray/plugins/svgtools/utils/surface_kernels.hpp b/plugins/svgtools/include/detray/plugins/svgtools/utils/surface_kernels.hpp
index 12b769697..2f72dfdb3 100644
--- a/plugins/svgtools/include/detray/plugins/svgtools/utils/surface_kernels.hpp
+++ b/plugins/svgtools/include/detray/plugins/svgtools/utils/surface_kernels.hpp
@@ -11,7 +11,7 @@
 #include "detray/definitions/units.hpp"
 #include "detray/geometry/mask.hpp"
 #include "detray/geometry/shapes.hpp"
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/geometry/tracking_volume.hpp"
 
 // System include(s)
@@ -231,7 +231,7 @@ struct link_end_getter {
             const vector3_t& surface_normal) const {
         for (const auto& desc : volume.portals()) {
 
-            const detray::tracking_surface surface{detector, desc};
+            const detray::geometry::surface surface{detector, desc};
 
             if (auto r = surface.template visit_mask<outer_radius_getter>()) {
                 if (*r > mask[shape_t::e_r]) {
diff --git a/tests/benchmarks/cpu/intersect_all.cpp b/tests/benchmarks/cpu/intersect_all.cpp
index 0aa7b3cf2..44b88071e 100644
--- a/tests/benchmarks/cpu/intersect_all.cpp
+++ b/tests/benchmarks/cpu/intersect_all.cpp
@@ -8,7 +8,7 @@
 // Project include(s)
 #include "detray/core/detector.hpp"
 #include "detray/definitions/units.hpp"
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/navigation/detail/ray.hpp"
 #include "detray/navigation/intersection/ray_intersector.hpp"
 #include "detray/navigation/intersection_kernel.hpp"
@@ -77,7 +77,7 @@ void BM_INTERSECT_ALL(benchmark::State &state) {
 
             // Loop over all surfaces in detector
             for (const sf_desc_t &sf_desc : d.surfaces()) {
-                const auto sf = tracking_surface{d, sf_desc};
+                const auto sf = geometry::surface{d, sf_desc};
                 sf.template visit_mask<
                     intersection_initialize<ray_intersector>>(
                     intersections, detail::ray(track), sf_desc, transforms,
diff --git a/tests/include/detray/test/cpu/detector_scan.hpp b/tests/include/detray/test/cpu/detector_scan.hpp
index 869e408ff..abc967ed3 100644
--- a/tests/include/detray/test/cpu/detector_scan.hpp
+++ b/tests/include/detray/test/cpu/detector_scan.hpp
@@ -8,7 +8,6 @@
 #pragma once
 
 // Project include(s)
-#include "detray/geometry/tracking_surface.hpp"
 #include "detray/navigation/detail/ray.hpp"
 #include "detray/navigation/volume_graph.hpp"
 
diff --git a/tests/include/detray/test/cpu/material_scan.hpp b/tests/include/detray/test/cpu/material_scan.hpp
index 59a34e65e..ffc3141c4 100644
--- a/tests/include/detray/test/cpu/material_scan.hpp
+++ b/tests/include/detray/test/cpu/material_scan.hpp
@@ -8,6 +8,7 @@
 #pragma once
 
 // Project include(s)
+#include "detray/geometry/surface.hpp"
 #include "detray/navigation/detail/ray.hpp"
 
 // Detray IO include(s)
@@ -151,7 +152,7 @@ class material_scan : public test::fixture_base<> {
                 }
 
                 const auto sf =
-                    tracking_surface{m_det, record.intersection.sf_desc};
+                    geometry::surface{m_det, record.intersection.sf_desc};
 
                 if (!sf.has_material()) {
                     continue;
@@ -160,7 +161,8 @@ class material_scan : public test::fixture_base<> {
                 const auto &p = record.intersection.local;
                 const auto mat_params = sf.template visit_material<
                     material_validator::get_material_params>(
-                    point2_t{p[0], p[1]}, sf.cos_angle(m_gctx, ray.dir(), p));
+                    point2_t{p[0], p[1]},
+                    detail::cos_angle(m_gctx, sf, ray.dir(), p));
 
                 const scalar_t seg{mat_params.path};
                 const scalar_t t{mat_params.thickness};
diff --git a/tests/include/detray/test/utils/detectors/build_toy_detector.hpp b/tests/include/detray/test/utils/detectors/build_toy_detector.hpp
index cee8e27d6..7fae8ae07 100644
--- a/tests/include/detray/test/utils/detectors/build_toy_detector.hpp
+++ b/tests/include/detray/test/utils/detectors/build_toy_detector.hpp
@@ -21,7 +21,6 @@
 #include "detray/definitions/detail/indexing.hpp"
 #include "detray/definitions/units.hpp"
 #include "detray/detectors/toy_metadata.hpp"
-#include "detray/geometry/tracking_surface.hpp"
 #include "detray/geometry/tracking_volume.hpp"
 #include "detray/materials/mixture.hpp"
 #include "detray/materials/predefined_materials.hpp"
diff --git a/tests/include/detray/test/utils/inspectors.hpp b/tests/include/detray/test/utils/inspectors.hpp
index a286fff7a..d0fd73736 100644
--- a/tests/include/detray/test/utils/inspectors.hpp
+++ b/tests/include/detray/test/utils/inspectors.hpp
@@ -13,7 +13,7 @@
 #endif
 
 // Project include(s)
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/navigation/detail/ray.hpp"
 #include "detray/navigation/navigation_config.hpp"
 #include "detray/navigation/navigator.hpp"
@@ -277,7 +277,7 @@ struct print_inspector {
         for (const auto &sf_cand : state) {
             const auto &local = sf_cand.local;
             const auto pos =
-                tracking_surface{state.detector(), sf_cand.sf_desc}
+                geometry::surface{state.detector(), sf_cand.sf_desc}
                     .local_to_global(geo_ctx_t{}, local, track_dir);
 
             debug_stream << sf_cand;
diff --git a/tests/include/detray/test/utils/simulation/random_scatterer.hpp b/tests/include/detray/test/utils/simulation/random_scatterer.hpp
index 45aaec7b1..25c1f621b 100644
--- a/tests/include/detray/test/utils/simulation/random_scatterer.hpp
+++ b/tests/include/detray/test/utils/simulation/random_scatterer.hpp
@@ -12,13 +12,13 @@
 #include "detray/definitions/pdg_particle.hpp"
 #include "detray/definitions/track_parametrization.hpp"
 #include "detray/definitions/units.hpp"
-#include "detray/geometry/tracking_surface.hpp"
 #include "detray/materials/detail/concepts.hpp"
+#include "detray/materials/detail/material_accessor.hpp"
+#include "detray/materials/detail/material_utils.hpp"
 #include "detray/materials/interaction.hpp"
 #include "detray/propagator/base_actor.hpp"
 #include "detray/tracks/bound_track_parameters.hpp"
 #include "detray/utils/axis_rotation.hpp"
-#include "detray/utils/ranges.hpp"
 #include "detray/utils/unit_vectors.hpp"
 
 // Detray test include(s)
@@ -148,8 +148,8 @@ struct random_scatterer : actor {
         auto& bound_params = stepping._bound_params;
         const auto sf = navigation.get_surface();
         const scalar_type cos_inc_angle{
-            sf.cos_angle(geo_context_type{}, bound_params.dir(),
-                         bound_params.bound_local())};
+            detail::cos_angle(geo_context_type{}, sf, bound_params.dir(),
+                              bound_params.bound_local())};
 
         sf.template visit_material<kernel>(simulator_state, ptc, bound_params,
                                            cos_inc_angle,
diff --git a/tests/include/detray/test/validation/detector_scanner.hpp b/tests/include/detray/test/validation/detector_scanner.hpp
index 1f9977fe8..a164dd7e3 100644
--- a/tests/include/detray/test/validation/detector_scanner.hpp
+++ b/tests/include/detray/test/validation/detector_scanner.hpp
@@ -8,7 +8,7 @@
 #pragma once
 
 // Project include(s)
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 #include "detray/navigation/detail/trajectories.hpp"
 #include "detray/navigation/intersection/intersection.hpp"
 #include "detray/navigation/intersection_kernel.hpp"
@@ -87,7 +87,7 @@ struct brute_force_scan {
         // Loop over all surfaces in the detector
         for (const sf_desc_t &sf_desc : detector.surfaces()) {
             // Retrieve candidate(s) from the surface
-            const auto sf = tracking_surface{detector, sf_desc};
+            const auto sf = geometry::surface{detector, sf_desc};
             sf.template visit_mask<intersection_kernel_t>(
                 intersections, traj, sf_desc, trf_store,
                 sf.is_portal() ? std::array<scalar_t, 2>{0.f, 0.f}
diff --git a/tests/include/detray/test/validation/material_validation_utils.hpp b/tests/include/detray/test/validation/material_validation_utils.hpp
index 1e38fd0c3..08a278913 100644
--- a/tests/include/detray/test/validation/material_validation_utils.hpp
+++ b/tests/include/detray/test/validation/material_validation_utils.hpp
@@ -201,7 +201,7 @@ struct material_tracer : detray::actor {
 
         // Fetch the material parameters and pathlength through the material
         const auto mat_params = sf.template visit_material<get_material_params>(
-            loc_pos, sf.cos_angle(gctx, glob_dir, loc_pos));
+            loc_pos, detail::cos_angle(gctx, sf, glob_dir, loc_pos));
 
         const scalar_t seg{mat_params.path};
         const scalar_t t{mat_params.thickness};
diff --git a/tests/include/detray/test/validation/navigation_validation_utils.hpp b/tests/include/detray/test/validation/navigation_validation_utils.hpp
index 2c0171720..d566139c3 100644
--- a/tests/include/detray/test/validation/navigation_validation_utils.hpp
+++ b/tests/include/detray/test/validation/navigation_validation_utils.hpp
@@ -8,6 +8,7 @@
 #pragma once
 
 // Project include(s)
+#include "detray/geometry/surface.hpp"
 #include "detray/navigation/navigator.hpp"
 #include "detray/propagator/actor_chain.hpp"
 #include "detray/propagator/actors/aborters.hpp"
@@ -31,6 +32,18 @@
 
 namespace detray::navigation_validator {
 
+/// A functor to get the minimum distance to any surface boundary.
+struct min_dist_to_boundary {
+
+    template <typename mask_group_t, typename index_t, typename point_t>
+    DETRAY_HOST_DEVICE inline auto operator()(const mask_group_t &mask_group,
+                                              const index_t &index,
+                                              const point_t &loc_p) const {
+
+        return mask_group[index].min_dist_to_boundary(loc_p);
+    }
+};
+
 /// B-field placeholder for straight-line navigation
 struct empty_bfield {};
 
@@ -386,10 +399,12 @@ auto write_dist_to_boundary(
         for (const auto &missed_sfi : missed_inters_vec) {
 
             const auto &track = entry.first;
-            const auto sf = tracking_surface{det, missed_sfi.sf_desc.barcode()};
+            const auto sf =
+                geometry::surface{det, missed_sfi.sf_desc.barcode()};
             const auto vol = tracking_volume{det, sf.volume()};
 
-            const auto dist = sf.min_dist_to_boundary(missed_sfi.local);
+            const auto dist =
+                sf.template visit_mask<min_dist_to_boundary>(missed_sfi.local);
             const auto glob_pos = sf.local_to_global(
                 gctx, missed_sfi.local, track.dir(missed_sfi.path));
 
diff --git a/tests/integration_tests/cpu/propagator/jacobian_validation.cpp b/tests/integration_tests/cpu/propagator/jacobian_validation.cpp
index 0fb3adf26..137ba679b 100644
--- a/tests/integration_tests/cpu/propagator/jacobian_validation.cpp
+++ b/tests/integration_tests/cpu/propagator/jacobian_validation.cpp
@@ -14,6 +14,7 @@
 #include "detray/propagator/actors/parameter_transporter.hpp"
 #include "detray/propagator/propagator.hpp"
 #include "detray/propagator/rk_stepper.hpp"
+#include "detray/propagator/tracking_surface.hpp"
 
 // Detray test include(s)
 #include "detray/test/utils/detectors/build_telescope_detector.hpp"
diff --git a/tests/integration_tests/cpu/propagator/propagator.cpp b/tests/integration_tests/cpu/propagator/propagator.cpp
index 9ac31f746..3c3bd62ff 100644
--- a/tests/integration_tests/cpu/propagator/propagator.cpp
+++ b/tests/integration_tests/cpu/propagator/propagator.cpp
@@ -10,7 +10,6 @@
 
 #include "detray/definitions/units.hpp"
 #include "detray/detectors/bfield.hpp"
-#include "detray/geometry/tracking_surface.hpp"
 #include "detray/navigation/detail/trajectories.hpp"
 #include "detray/navigation/navigator.hpp"
 #include "detray/propagator/actor_chain.hpp"
@@ -21,6 +20,7 @@
 #include "detray/propagator/base_actor.hpp"
 #include "detray/propagator/line_stepper.hpp"
 #include "detray/propagator/rk_stepper.hpp"
+#include "detray/propagator/tracking_surface.hpp"
 #include "detray/tracks/tracks.hpp"
 
 // Detray test include(s)
diff --git a/tests/unit_tests/cpu/CMakeLists.txt b/tests/unit_tests/cpu/CMakeLists.txt
index 07c9e4eaa..13a9c9eab 100644
--- a/tests/unit_tests/cpu/CMakeLists.txt
+++ b/tests/unit_tests/cpu/CMakeLists.txt
@@ -52,7 +52,7 @@ macro(detray_add_cpu_test algebra)
       "geometry/masks/trapezoid2D.cpp"
       "geometry/masks/unbounded.cpp"
       "geometry/masks/unmasked.cpp"
-      "geometry/tracking_surface.cpp"
+      "geometry/surface.cpp"
       "geometry/tracking_volume.cpp"
       "grid2/axis.cpp"
       "grid2/grid2.cpp"
diff --git a/tests/unit_tests/cpu/geometry/tracking_surface.cpp b/tests/unit_tests/cpu/geometry/surface.cpp
similarity index 80%
rename from tests/unit_tests/cpu/geometry/tracking_surface.cpp
rename to tests/unit_tests/cpu/geometry/surface.cpp
index 25bed70a6..211f48b6e 100644
--- a/tests/unit_tests/cpu/geometry/tracking_surface.cpp
+++ b/tests/unit_tests/cpu/geometry/surface.cpp
@@ -6,9 +6,10 @@
  */
 
 // Project include(s)
-#include "detray/geometry/tracking_surface.hpp"
+#include "detray/geometry/surface.hpp"
 
 #include "detray/definitions/detail/indexing.hpp"
+#include "detray/materials/detail/material_utils.hpp"  //< cos incidence angle
 
 // Detray test include(s)
 #include "detray/test/utils/detectors/build_toy_detector.hpp"
@@ -90,10 +91,10 @@ GTEST_TEST(detray_geometry, surface_toy_detector) {
 
     using detector_t = detector<toy_metadata>;
 
-    using scalar_t = tracking_surface<detector_t>::scalar_type;
-    using point2_t = tracking_surface<detector_t>::point2_type;
-    using point3_t = tracking_surface<detector_t>::point3_type;
-    using vector3_t = tracking_surface<detector_t>::vector3_type;
+    using scalar_t = geometry::surface<detector_t>::scalar_type;
+    using point2_t = geometry::surface<detector_t>::point2_type;
+    using point3_t = geometry::surface<detector_t>::point3_type;
+    using vector3_t = geometry::surface<detector_t>::vector3_type;
 
     vecmem::host_memory_resource host_mr;
     toy_det_config toy_cfg{};
@@ -106,7 +107,7 @@ GTEST_TEST(detray_geometry, surface_toy_detector) {
     // Disc
     //
     const auto disc_descr = toy_det.surfaces()[1u];
-    const auto disc = tracking_surface{toy_det, disc_descr};
+    const auto disc = geometry::surface{toy_det, disc_descr};
 
     // IDs
     ASSERT_EQ(disc.barcode(), disc_descr.barcode());
@@ -138,23 +139,25 @@ GTEST_TEST(detray_geometry, surface_toy_detector) {
 
     // Cos incidence angle
     auto dir = vector::normalize(vector3_t{1.f, 0.f, 1.f});
-    ASSERT_NEAR(disc.cos_angle(ctx, dir, point3_t{0.f, 0.f, 0.f}),
+    ASSERT_NEAR(detail::cos_angle(ctx, disc, dir, point3_t{0.f, 0.f, 0.f}),
                 constant<scalar_t>::inv_sqrt2, tol);
-    ASSERT_NEAR(disc.cos_angle(ctx, dir, point2_t{0.f, 0.f}),
+    ASSERT_NEAR(detail::cos_angle(ctx, disc, dir, point2_t{0.f, 0.f}),
                 constant<scalar_t>::inv_sqrt2, tol);
 
     dir = vector::normalize(vector3_t{1.f, 1.f, 0.f});
-    ASSERT_NEAR(disc.cos_angle(ctx, dir, point3_t{1.f, 0.5f, 0.f}), 0.f, tol);
-    ASSERT_NEAR(disc.cos_angle(ctx, dir, point2_t{1.f, 0.5f}), 0.f, tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, disc, dir, point3_t{1.f, 0.5f, 0.f}),
+                0.f, tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, disc, dir, point2_t{1.f, 0.5f}), 0.f,
+                tol);
 
     dir = vector::normalize(vector3_t{1.f, 0.f, constant<scalar_t>::pi});
     scalar_t cos_inc_angle{
         constant<scalar_t>::pi /
         std::sqrt(1.f + std::pow(constant<scalar_t>::pi, 2.f))};
-    ASSERT_NEAR(disc.cos_angle(ctx, dir, point3_t{2.f, 1.f, 0.f}),
+    ASSERT_NEAR(detail::cos_angle(ctx, disc, dir, point3_t{2.f, 1.f, 0.f}),
+                cos_inc_angle, tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, disc, dir, point2_t{2.f, 1.f}),
                 cos_inc_angle, tol);
-    ASSERT_NEAR(disc.cos_angle(ctx, dir, point2_t{2.f, 1.f}), cos_inc_angle,
-                tol);
 
     // Coordinate transformations
     point3_t glob_pos = {4.f, 7.f, 4.f};
@@ -168,7 +171,7 @@ GTEST_TEST(detray_geometry, surface_toy_detector) {
 
     // Roundtrip
     point3_t global = disc.local_to_global(ctx, local, {});
-    point3_t global2 = disc.bound_to_global(ctx, bound, {});
+    point3_t global2 = disc.local_to_global(ctx, bound, {});
 
     ASSERT_NEAR(glob_pos[0], global[0], tol);
     ASSERT_NEAR(glob_pos[1], global[1], tol);
@@ -189,7 +192,7 @@ GTEST_TEST(detray_geometry, surface_toy_detector) {
     // Rectangle
     //
     const auto rec_descr = toy_det.surfaces()[604u];
-    const auto rec = tracking_surface{toy_det, rec_descr};
+    const auto rec = geometry::surface{toy_det, rec_descr};
 
     // IDs
     ASSERT_EQ(rec.barcode(), rec_descr.barcode());
@@ -219,19 +222,22 @@ GTEST_TEST(detray_geometry, surface_toy_detector) {
 
     // Incidence angle
     dir = vector::normalize(global);
-    ASSERT_NEAR(rec.cos_angle(ctx, dir, point3_t{0.f, 0.f, 0.f}), 1.f, tol);
-    ASSERT_NEAR(rec.cos_angle(ctx, dir, point2_t{0.f, 0.f}), 1.f, tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, rec, dir, point3_t{0.f, 0.f, 0.f}), 1.f,
+                tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, rec, dir, point2_t{0.f, 0.f}), 1.f, tol);
 
     dir = vector::normalize(vector3_t{0.f, -global[2], global[1]});
-    ASSERT_NEAR(rec.cos_angle(ctx, dir, point3_t{1.f, 0.5f, 0.f}), 0.f, tol);
-    ASSERT_NEAR(rec.cos_angle(ctx, dir, point2_t{1.f, 0.5f}), 0.f, tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, rec, dir, point3_t{1.f, 0.5f, 0.f}), 0.f,
+                tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, rec, dir, point2_t{1.f, 0.5f}), 0.f,
+                tol);
 
     dir = vector::normalize(vector3_t{1.f, 0.f, constant<scalar_t>::pi});
     cos_inc_angle = std::fabs(vector::dot(dir, global));
-    ASSERT_NEAR(rec.cos_angle(ctx, dir, point3_t{2.f, 1.f, 0.f}), cos_inc_angle,
-                tol);
-    ASSERT_NEAR(rec.cos_angle(ctx, dir, point2_t{2.f, 1.f}), cos_inc_angle,
-                tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, rec, dir, point3_t{2.f, 1.f, 0.f}),
+                cos_inc_angle, tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, rec, dir, point2_t{2.f, 1.f}),
+                cos_inc_angle, tol);
 
     // Coordinate transformation roundtrip
     glob_pos = {4.f, 7.f, 4.f};
@@ -251,7 +257,7 @@ GTEST_TEST(detray_geometry, surface_toy_detector) {
     ASSERT_NEAR(glob_pos[2], global[2], tol);
 
     bound = rec.global_to_bound(ctx, glob_pos, {});
-    global = rec.bound_to_global(ctx, bound, {});
+    global = rec.local_to_global(ctx, bound, {});
     ASSERT_NEAR(global[0], glob_pos[0], tol);
     ASSERT_NEAR(global[1], glob_pos[1], tol);
     ASSERT_NEAR(global[2], glob_pos[2], tol);
@@ -265,7 +271,7 @@ GTEST_TEST(detray_geometry, surface_toy_detector) {
     // Concentric Cylinder
     //
     const auto cyl_descr = toy_det.surfaces()[8u];
-    const auto cyl = tracking_surface{toy_det, cyl_descr};
+    const auto cyl = geometry::surface{toy_det, cyl_descr};
 
     // IDs
     ASSERT_EQ(cyl.barcode(), cyl_descr.barcode());
@@ -318,24 +324,25 @@ GTEST_TEST(detray_geometry, surface_toy_detector) {
         0.f, tol);
 
     // Incidence angle
-    ASSERT_NEAR(cyl.cos_angle(ctx, x_axis,
-                              point3_t{r * constant<scalar_t>::pi, 0.f, r}),
+    ASSERT_NEAR(detail::cos_angle(ctx, cyl, x_axis,
+                                  point3_t{r * constant<scalar_t>::pi, 0.f, r}),
+                1.f, tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, cyl, x_axis,
+                                  point2_t{r * constant<scalar_t>::pi, 0.f}),
                 1.f, tol);
-    ASSERT_NEAR(
-        cyl.cos_angle(ctx, x_axis, point2_t{r * constant<scalar_t>::pi, 0.f}),
-        1.f, tol);
 
-    ASSERT_NEAR(cyl.cos_angle(ctx, z_axis,
-                              point3_t{r * constant<scalar_t>::pi_2, 0.f, r}),
-                0.f, tol);
     ASSERT_NEAR(
-        cyl.cos_angle(ctx, z_axis, point2_t{r * constant<scalar_t>::pi_2, 0.f}),
+        detail::cos_angle(ctx, cyl, z_axis,
+                          point3_t{r * constant<scalar_t>::pi_2, 0.f, r}),
         0.f, tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, cyl, z_axis,
+                                  point2_t{r * constant<scalar_t>::pi_2, 0.f}),
+                0.f, tol);
 
     dir = vector::normalize(vector3_t{1.f, 1.f, 0.f});
-    ASSERT_NEAR(cyl.cos_angle(ctx, dir, point3_t{0.f, 1.f, r}),
+    ASSERT_NEAR(detail::cos_angle(ctx, cyl, dir, point3_t{0.f, 1.f, r}),
                 constant<scalar_t>::inv_sqrt2, tol);
-    ASSERT_NEAR(cyl.cos_angle(ctx, dir, point2_t{0.f, 1.f}),
+    ASSERT_NEAR(detail::cos_angle(ctx, cyl, dir, point2_t{0.f, 1.f}),
                 constant<scalar_t>::inv_sqrt2, tol);
 
     // Coordinate transformation roundtrip
@@ -357,7 +364,7 @@ GTEST_TEST(detray_geometry, surface_toy_detector) {
     ASSERT_NEAR(glob_pos[2], global[2], tol);
 
     bound = cyl.global_to_bound(ctx, glob_pos, {});
-    global = cyl.bound_to_global(ctx, bound, {});
+    global = cyl.local_to_global(ctx, bound, {});
     ASSERT_NEAR(global[0], glob_pos[0], tol);
     ASSERT_NEAR(global[1], glob_pos[1], tol);
     ASSERT_NEAR(global[2], glob_pos[2], tol);
@@ -377,10 +384,10 @@ GTEST_TEST(detray_geometry, surface_wire_chamber) {
 
     using detector_t = detector<default_metadata>;
 
-    using scalar_t = tracking_surface<detector_t>::scalar_type;
-    using point2_t = tracking_surface<detector_t>::point2_type;
-    using point3_t = tracking_surface<detector_t>::point3_type;
-    using vector3_t = tracking_surface<detector_t>::vector3_type;
+    using scalar_t = geometry::surface<detector_t>::scalar_type;
+    using point2_t = geometry::surface<detector_t>::point2_type;
+    using point3_t = geometry::surface<detector_t>::point3_type;
+    using vector3_t = geometry::surface<detector_t>::vector3_type;
 
     vecmem::host_memory_resource host_mr;
     wire_chamber_config<> cfg{};
@@ -392,7 +399,7 @@ GTEST_TEST(detray_geometry, surface_wire_chamber) {
     // Line
     //
     const auto line_descr = wire_chmbr.surfaces()[23u];
-    const auto line = tracking_surface{wire_chmbr, line_descr};
+    const auto line = geometry::surface{wire_chmbr, line_descr};
 
     // IDs
     ASSERT_EQ(line.barcode(), line_descr.barcode());
@@ -425,17 +432,21 @@ GTEST_TEST(detray_geometry, surface_wire_chamber) {
 
     // Cos incidence angle
     auto dir = vector::normalize(global);
-    ASSERT_NEAR(line.cos_angle(ctx, dir, point3_t{1.f, 0.f, 0.f}), 1.f, tol);
-    ASSERT_NEAR(line.cos_angle(ctx, dir, point2_t{1.f, 0.f}), 1.f, tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, line, dir, point3_t{1.f, 0.f, 0.f}), 1.f,
+                tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, line, dir, point2_t{1.f, 0.f}), 1.f,
+                tol);
 
     dir = vector::normalize(vector3_t{0.f, -global[2], global[1]});
-    ASSERT_NEAR(line.cos_angle(ctx, dir, point3_t{1.f, 100.f, 0.f}), 0.f, tol);
-    ASSERT_NEAR(line.cos_angle(ctx, dir, point2_t{1.f, 100.f}), 0.f, tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, line, dir, point3_t{1.f, 100.f, 0.f}),
+                0.f, tol);
+    ASSERT_NEAR(detail::cos_angle(ctx, line, dir, point2_t{1.f, 100.f}), 0.f,
+                tol);
 
     dir = vector3_t{-0.685475f, -0.0404595f, 0.726971f};
-    ASSERT_NEAR(line.cos_angle(ctx, dir, point3_t{2.f, 1.f, 0.f}),
+    ASSERT_NEAR(detail::cos_angle(ctx, line, dir, point3_t{2.f, 1.f, 0.f}),
                 constant<scalar_t>::inv_sqrt2, 0.0005);
-    ASSERT_NEAR(line.cos_angle(ctx, dir, point2_t{2.f, 1.f}),
+    ASSERT_NEAR(detail::cos_angle(ctx, line, dir, point2_t{2.f, 1.f}),
                 constant<scalar_t>::inv_sqrt2, 0.0005);
 
     // Coordinate transformation roundtrip
@@ -460,7 +471,7 @@ GTEST_TEST(detray_geometry, surface_wire_chamber) {
     ASSERT_NEAR(glob_pos[2], global[2], red_tol);
 
     point2_t bound = line.global_to_bound(ctx, glob_pos, dir);
-    global = line.bound_to_global(ctx, bound, dir);
+    global = line.local_to_global(ctx, bound, dir);
     ASSERT_NEAR(global[0], glob_pos[0], red_tol);
     ASSERT_NEAR(global[1], glob_pos[1], red_tol);
     ASSERT_NEAR(global[2], glob_pos[2], red_tol);
diff --git a/tests/unit_tests/cpu/propagator/rk_stepper.cpp b/tests/unit_tests/cpu/propagator/rk_stepper.cpp
index 8f13e616f..641181d6e 100644
--- a/tests/unit_tests/cpu/propagator/rk_stepper.cpp
+++ b/tests/unit_tests/cpu/propagator/rk_stepper.cpp
@@ -12,7 +12,6 @@
 #include "detray/core/detector.hpp"
 #include "detray/definitions/units.hpp"
 #include "detray/detectors/bfield.hpp"
-#include "detray/geometry/tracking_surface.hpp"
 #include "detray/io/utils/file_handle.hpp"
 #include "detray/navigation/detail/trajectories.hpp"
 #include "detray/propagator/line_stepper.hpp"