fix(minor): all five MINOR findings — doc, accuracy, and DRY

MINOR-1 (spherical_functional.hpp:426)
  Wrong comment said "second derivative < 0 for a convex functional".
  The spherical energy is *concave* (NSD Hessian); the monotone-f argument
  applies to both convex and concave functionals equally.  Comment rewritten
  to explain the actual physics: increasing scale increases all angles and
  thus reduces Σ G_v.

MINOR-2 (spherical_functional.hpp:494-495)
  Forward finite difference O(ε) → central finite difference O(ε²):
    old: dft = (sum_Gv(t + fd_eps) - ft) / fd_eps
    new: dft = (sum_Gv(t + fd_eps) - sum_Gv(t - fd_eps)) / (2*fd_eps)
  Same cost when the extra sum_Gv(t - fd_eps) replaces the cached ft.

MINOR-3 (euclidean_functional.hpp, spherical_functional.hpp,
         inversive_distance_functional.hpp)
  New header gauss_legendre.hpp centralises the 10-point Gauss-Legendre
  nodes and weights (gl10_nodes() / gl10_weights()).  The three energy
  functions now use the shared accessors instead of duplicated local
  static arrays.

MINOR-4 (euclidean_functional.hpp, spherical_functional.hpp,
         hyper_ideal_functional.hpp, inversive_distance_functional.hpp)
  halfedge_to_index() centralised in conformal_mesh.hpp.  All four local
  aliases (eucl_hidx, spher_hidx, hidx, id_detail::hidx) now delegate to
  it as one-line wrappers; the aliases are kept for now to avoid a larger
  call-site churn, clearly documented as thin wrappers.

MINOR-5 (clausen.hpp:33-38)
  Added a comment above inits() explaining the intentional off-by-one
  return value and how it interacts with csevl() — matching the Java
  Clausen.inits() / csevl() contract.

277/277 CGAL + 26/26 pure-math tests pass, 0 failed.

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

code/include/euclidean_functional.hpp

@@ -41,6 +41,7 @@
 
 #include "conformal_mesh.hpp"
 #include "constants.hpp"
+#include "gauss_legendre.hpp"
 #include "euclidean_geometry.hpp"
 #include <CGAL/boost/graph/iterator.h>
 #include <vector>
@@ -173,11 +174,10 @@ static inline double eucl_dof_val(int idx, const std::vector<double>& x)
     return idx >= 0 ? x[static_cast<std::size_t>(idx)] : 0.0;
 }
 
-/// Convert a CGAL half-edge index to a plain `std::size_t` for vector indexing.
-static inline std::size_t eucl_hidx(Halfedge_index h)
-{
-    return static_cast<std::size_t>(static_cast<std::uint32_t>(h));
-}
+// halfedge_to_index is defined in conformal_mesh.hpp (included above).
+// The old local alias eucl_hidx is retained as a thin wrapper for now so
+// call-sites below do not need touching; a follow-up can remove it.
+static inline std::size_t eucl_hidx(Halfedge_index h) { return halfedge_to_index(h); }
 
 /// Compute the Euclidean-functional gradient G(x):
 ///   * `G_v = Θ_v − Σ_faces α_v(face)`
@@ -272,20 +272,8 @@ inline double euclidean_energy(
     const std::vector<double>& x,
     const EuclideanMaps&       m)
 {
-    static const double gl_s[10] = {
-        -0.9739065285171717,  -0.8650633666889845,
-        -0.6794095682990244,  -0.4333953941292472,
-        -0.1488743389816312,   0.1488743389816312,
-         0.4333953941292472,   0.6794095682990244,
-         0.8650633666889845,   0.9739065285171717
-    };
-    static const double gl_w[10] = {
-        0.0666713443086881,  0.1494513491505806,
-        0.2190863625159820,  0.2692667193099963,
-        0.2955242247147529,  0.2955242247147529,
-        0.2692667193099963,  0.2190863625159820,
-        0.1494513491505806,  0.0666713443086881
-    };
+    const double* gl_s = gl10_nodes();
+    const double* gl_w = gl10_weights();
 
     const std::size_t n = x.size();
     double E = 0.0;