code/include/CGAL/Discrete_conformal_map.h

@@ -52,8 +52,10 @@ auto result = CGAL::discrete_conformal_map_euclidean(
 
 #include <CGAL/Conformal_map_traits.h>
 #include <CGAL/Conformal_map/internal/parameters.h>
+#include <CGAL/Kernel_traits.h>
 #include <CGAL/Named_function_parameters.h>
 #include <CGAL/boost/graph/named_params_helper.h>
+#include <CGAL/property_map.h>
 
 // Existing implementation headers (Layer 1 — unchanged).
 #include "../euclidean_functional.hpp"
@@ -147,9 +149,21 @@ auto discrete_conformal_map_euclidean(
     TriangleMesh& mesh,
     const CGAL_NP_CLASS& np = parameters::default_values())
 {
-    using Traits  = Default_conformal_map_traits<TriangleMesh, Simple_cartesian<double>>;
-    using FT      = typename Traits::FT;
-    using Vertex_descriptor = typename Traits::Vertex_descriptor;
+    // ── Type plumbing ──────────────────────────────────────────────────────
+    //
+    // Deduce the kernel from the mesh's Point_3 type rather than hard-coding
+    // Simple_cartesian<double>.  This lets the wrapper work with any
+    // Surface_mesh<P> whose P is a CGAL kernel point.  The user can override
+    // the entire traits class via the `geom_traits(...)` named parameter
+    // (Phase 8b.2 extension; default below covers the common case).
+    using Point_type      = typename TriangleMesh::Point;
+    using Default_kernel  = typename CGAL::Kernel_traits<Point_type>::Kernel;
+    using Default_traits  = Default_conformal_map_traits<TriangleMesh, Default_kernel>;
+    using Traits          = typename internal_np::Lookup_named_param_def<
+                                internal_np::geom_traits_t,
+                                CGAL_NP_CLASS,
+                                Default_traits>::type;
+    using FT              = typename Traits::FT;
 
     Conformal_map_result<FT> result;
 

code/tests/cgal/test_cgal_traits_mvp.cpp

@@ -17,6 +17,7 @@
 
 #include <CGAL/Conformal_map_traits.h>
 #include <CGAL/Discrete_conformal_map.h>
+#include <CGAL/Kernel_traits.h>
 
 #include "mesh_builder.hpp"   // make_triangle, make_quad_strip, make_tetrahedron
 #include "euclidean_functional.hpp"
@@ -169,6 +170,36 @@ TEST(CGALDiscreteConformalMap, GradientToleranceTakesEffect)
 // match what newton_euclidean produces directly.
 // ════════════════════════════════════════════════════════════════════════════
 
+// ════════════════════════════════════════════════════════════════════════════
+// 6.  Kernel deduction: the wrapper must NOT hard-code Simple_cartesian
+//
+// Regression guard: the wrapper deduces its kernel from the mesh point type
+// via `CGAL::Kernel_traits`.  If anyone re-introduces a hard-coded
+// `Simple_cartesian<double>` in the wrapper, the static_asserts here still
+// pass (the legacy ConformalMesh uses that kernel) — but Phase 9a or any
+// user with a different kernel-backed Surface_mesh would fail to compile.
+// This test pins the deduction *contract* explicitly.
+// ════════════════════════════════════════════════════════════════════════════
+
+TEST(CGALDiscreteConformalMap, KernelIsDeducedFromMeshPointType)
+{
+    using Mesh = ConformalMesh;
+    using P    = typename Mesh::Point;
+
+    using DeducedKernel = typename CGAL::Kernel_traits<P>::Kernel;
+    using DeducedTraits = CGAL::Default_conformal_map_traits<Mesh, DeducedKernel>;
+
+    static_assert(std::is_same_v<DeducedKernel, CGAL::Simple_cartesian<double>>,
+                  "ConformalMesh point type must deduce to Simple_cartesian<double>");
+    static_assert(std::is_same_v<typename DeducedTraits::FT, double>);
+    static_assert(std::is_same_v<typename DeducedTraits::Triangle_mesh, Mesh>);
+
+    // Run-time sanity: the wrapper accepts the deduced-kernel mesh end-to-end.
+    auto mesh = make_quad_strip();
+    auto result = CGAL::discrete_conformal_map_euclidean(mesh);
+    EXPECT_TRUE(result.converged);
+}
+
 TEST(CGALDiscreteConformalMap, WrapperMatchesLegacyAPI)
 {
     auto mesh = make_quad_strip();