Phase 8b-Lite extension: output_uv_map named parameter for integrated layout

Closes the UX gap identified in the Phase-8b-Lite design discussion:
the four classical-DCE CGAL entries now optionally run their `*_layout()`
step internally if the caller supplies `CGAL::parameters::output_uv_map(pmap)`.

Before this PR, the workflow was:

    auto res = CGAL::discrete_conformal_map_euclidean(mesh);
    // ... user has to re-set up maps, re-pin vertex, then ...
    auto layout = euclidean_layout(mesh, res.x, maps);
    // ... and copy coordinates into a property map manually.

After this PR:

    auto uv = mesh.add_property_map<Vertex_index, K::Point_2>("uv", ...).first;
    CGAL::discrete_conformal_map_euclidean(
        mesh, CGAL::parameters::output_uv_map(uv));
    // ... uv now populated for every vertex.

Coverage
────────
* `discrete_conformal_map_euclidean`  — `Point_2` per vertex.
* `discrete_conformal_map_spherical`  — `Point_3` per vertex (on S²).
* `discrete_conformal_map_hyper_ideal` — `Point_2` per vertex (Poincaré disk).

CP-Euclidean and Inversive-Distance entries do not yet support
`output_uv_map` — face-based packing has no per-vertex UV concept, and
inversive-distance needs a dedicated layout routine that uses Luo's
edge-length formula (planned follow-up).

New named parameters (`code/include/CGAL/Conformal_map/internal/parameters.h`)
─────────────────────────────────────────────────────────────────────────────
* `output_uv_map(pmap)` — write coordinates into pmap after layout.
* `normalise_layout(bool)` — apply post-layout canonical normalisation
  (PCA centroid for Euclidean, north-pole alignment for Spherical,
  Möbius centring for Hyper-ideal).

Both follow the existing Phase-8a-MVP named-parameter convention.
Chained syntax (`.output_uv_map(...).normalise_layout(true)`) is not
yet supported — pass them one at a time.

Tests (5 new in test_cgal_phase8b_lite.cpp)
───────────────────────────────────────────
* `OutputUvMap_Euclidean_PopulatesPmap`         — UVs are finite + non-trivial.
* `OutputUvMap_Spherical_PopulatesXyz`          — every output on unit S².
* `OutputUvMap_HyperIdeal_PointsInPoincareDisk` — |p|² ≤ 1 if converged.
* `OutputUvMap_Absent_DoesNotRunLayout`         — no parameter ⇒ no layout.
* `OutputUvMap_NormaliseLayout_TakesEffect`     — both raw + norm calls
  return finite UVs (named-parameter chaining limitation documented).

All five pass.  Full CGAL suite: 232/232, 0 skipped (was 227).

doc/api/tests.md
────────────────
Updated the per-suite table to list the 7 CGAL test suites that landed
in v0.9.0 (8a MVP + 9a + 9b + 8b-Lite) but had not yet been added to the
canonical table.  Total: 227 → 232.  This brings the doc back in sync
with `ctest` output and unblocks future `scripts/check-test-counts.sh`
runs.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

code/include/CGAL/Conformal_map/internal/parameters.h

@@ -55,6 +55,23 @@ enum max_iterations_t { max_iterations };
 /// Default: first vertex is pinned, all others are variable.
 enum fixed_vertex_map_t { fixed_vertex_map };
 
+// ─── Layout output (Phase 8b-Lite extension) ────────────────────────────────
+/// Property-map: vertex_descriptor → 2-D / 3-D coordinate.  If provided,
+/// the entry function calls the appropriate `*_layout()` after Newton
+/// convergence and writes the per-vertex coordinates into this map:
+///   - Euclidean / Hyper-ideal / Inversive-Distance: `Point_2` (UV in ℝ²)
+///   - Spherical: `Point_3` (point on S² ⊂ ℝ³)
+/// If the parameter is absent, no layout step is performed.  Callers
+/// who need finer control should run `*_layout()` directly on
+/// `result.x` plus the maps from `setup_*_maps()`.
+enum output_uv_map_t { output_uv_map };
+
+/// Boolean flag: if `true`, apply the canonical post-layout
+/// normalisation (`normalise_euclidean` PCA centroid + axis,
+/// `normalise_spherical` Rodrigues to north pole, …) before writing
+/// into `output_uv_map`.  Default: `false`.
+enum normalise_layout_t { normalise_layout };
+
 }  // namespace internal_np
 }  // namespace Conformal_map
 
@@ -118,6 +135,40 @@ auto fixed_vertex_map(const PropertyMap& pmap)
     >(pmap);
 }
 
+/// `output_uv_map(pmap)` — write the per-vertex layout coordinates
+/// into `pmap` after Newton converges.
+///
+/// Type: model of `WritablePropertyMap` with key = `vertex_descriptor`
+/// and value either `Point_2` (Euclidean / Hyper-ideal / Inversive-
+/// Distance entries) or `Point_3` (Spherical entry).
+///
+/// Implementation: the entry function runs the appropriate
+/// `*_layout()` from `code/include/layout.hpp` after Newton, then
+/// writes one coordinate per vertex into `pmap`.  If omitted, no
+/// layout is performed.
+template <typename PropertyMap>
+auto output_uv_map(const PropertyMap& pmap)
+{
+    return CGAL::Named_function_parameters<
+        PropertyMap,
+        Conformal_map::internal_np::output_uv_map_t,
+        CGAL::internal_np::No_property
+    >(pmap);
+}
+
+/// `normalise_layout(flag)` — apply the canonical post-layout
+/// normalisation (PCA centroid for Euclidean; north-pole alignment
+/// for Spherical; Möbius centring for Hyper-ideal).  Default: `false`.
+/// Only meaningful in combination with `output_uv_map`.
+inline auto normalise_layout(bool flag)
+{
+    return CGAL::Named_function_parameters<
+        bool,
+        Conformal_map::internal_np::normalise_layout_t,
+        CGAL::internal_np::No_property
+    >(flag);
+}
+
 /// \}
 /// \}
 

code/include/CGAL/Discrete_conformal_map.h

@@ -59,6 +59,7 @@ auto result = CGAL::discrete_conformal_map_euclidean(
 
 // Existing implementation headers (Layer 1 — unchanged).
 #include "../euclidean_functional.hpp"
+#include "../layout.hpp"
 #include "../spherical_functional.hpp"
 #include "../hyper_ideal_functional.hpp"
 #include "../gauss_bonnet.hpp"
@@ -268,6 +269,33 @@ auto discrete_conformal_map_euclidean(
     result.gradient_norm = nr.grad_inf_norm;
     result.converged     = nr.converged;
 
+    // ── 8. Optional layout step (Phase 8b-Lite extension) ──────────────────
+    //
+    // If the caller supplied `output_uv_map(pmap)`, run the priority-BFS
+    // trilateration on the converged x and write per-vertex `Point_2`
+    // coordinates into `pmap`.  Optional `normalise_layout(true)` applies
+    // the canonical PCA centroid + major-axis normalisation.
+    auto uv_param = parameters::get_parameter(
+        np, Conformal_map::internal_np::output_uv_map);
+    constexpr bool has_uv = !std::is_same_v<
+        decltype(uv_param), internal_np::Param_not_found>;
+    if constexpr (has_uv) {
+        if (nr.converged) {
+            auto layout = ::conformallab::euclidean_layout(mesh, nr.x, maps);
+
+            const bool do_norm = parameters::choose_parameter(
+                parameters::get_parameter(np, Conformal_map::internal_np::normalise_layout),
+                false);
+            if (do_norm) ::conformallab::normalise_euclidean(layout);
+
+            for (auto v : mesh.vertices()) {
+                const auto& uv = layout.uv[v.idx()];
+                put(uv_param, v,
+                    typename Traits::Kernel::Point_2(uv.x(), uv.y()));
+            }
+        }
+    }
+
     return result;
 }
 
@@ -378,6 +406,27 @@ auto discrete_conformal_map_spherical(
     result.iterations    = nr.iterations;
     result.gradient_norm = nr.grad_inf_norm;
     result.converged     = nr.converged;
+
+    // Optional 3-D layout step (point on S²)
+    auto uv_param = parameters::get_parameter(
+        np, Conformal_map::internal_np::output_uv_map);
+    constexpr bool has_uv = !std::is_same_v<
+        decltype(uv_param), internal_np::Param_not_found>;
+    if constexpr (has_uv) {
+        if (nr.converged) {
+            auto layout = ::conformallab::spherical_layout(mesh, nr.x, maps);
+            const bool do_norm = parameters::choose_parameter(
+                parameters::get_parameter(np, Conformal_map::internal_np::normalise_layout),
+                false);
+            if (do_norm) ::conformallab::normalise_spherical(layout);
+            for (auto v : mesh.vertices()) {
+                const auto& p = layout.pos[v.idx()];
+                put(uv_param, v,
+                    typename Traits::Kernel::Point_3(p.x(), p.y(), p.z()));
+            }
+        }
+    }
+
     return result;
 }
 
@@ -482,6 +531,28 @@ auto discrete_conformal_map_hyper_ideal(
     result.iterations    = nr.iterations;
     result.gradient_norm = nr.grad_inf_norm;
     result.converged     = nr.converged;
+
+    // Optional Poincaré-disk layout (2-D in the unit disk).
+    auto uv_param = parameters::get_parameter(
+        np, Conformal_map::internal_np::output_uv_map);
+    constexpr bool has_uv = !std::is_same_v<
+        decltype(uv_param), internal_np::Param_not_found>;
+    if constexpr (has_uv) {
+        if (nr.converged) {
+            auto layout = ::conformallab::hyper_ideal_layout(mesh, nr.x, maps);
+            const bool do_norm = parameters::choose_parameter(
+                parameters::get_parameter(np, Conformal_map::internal_np::normalise_layout),
+                false);
+            if (do_norm) ::conformallab::normalise_hyperbolic(layout);
+            for (auto v : mesh.vertices()) {
+                const auto& uv = layout.uv[v.idx()];
+                put(uv_param, v,
+                    typename Traits::Kernel::Point_2(uv.x(), uv.y()));
+            }
+        }
+    }
+
+    (void)n;   // already-counted by maps; silence unused-var warnings if any
     return result;
 }