From af7b223c2561abc94ce1f3de0a93213fcf393d56 Mon Sep 17 00:00:00 2001
From: Laurent Rineau <laurent.rineau@cgal.org>
Date: Mon, 10 Nov 2025 15:58:55 +0100
Subject: [PATCH] better use of .exact()

---
 .../CGAL/Conforming_Delaunay_triangulation_3.h    | 15 ++++++++-------
 .../cdt_3_from_off.cpp                            |  8 ++++++--
 2 files changed, 14 insertions(+), 9 deletions(-)

diff --git a/Constrained_triangulation_3/include/CGAL/Conforming_Delaunay_triangulation_3.h b/Constrained_triangulation_3/include/CGAL/Conforming_Delaunay_triangulation_3.h
index 06a445b0b90..40982b2068d 100644
--- a/Constrained_triangulation_3/include/CGAL/Conforming_Delaunay_triangulation_3.h
+++ b/Constrained_triangulation_3/include/CGAL/Conforming_Delaunay_triangulation_3.h
@@ -1008,10 +1008,11 @@ protected:
   static constexpr bool has_exact_member_function_v<T, std::void_t<decltype(std::declval<T>().exact())>> = true;
 
   template <typename T>
-  static void exact(T&& obj) {
+  static decltype(auto) exact(T&& obj) {
     if constexpr (has_exact_member_function_v<T>) {
-      std::forward<T>(obj).exact();
+      return std::forward<T>(obj).exact();
     }
+    return std::forward<T>(obj);
   }
 
   // Helper to compute a projected point with optional exact kernel and custom threshold check
@@ -1079,14 +1080,14 @@ protected:
 
     // Check threshold before computing projection
     if(use_midpoint_check(lambda, std::nullopt)) {
-      return midpoint_functor(midpoint_start, midpoint_end);
+      return exact(midpoint_functor(midpoint_start, midpoint_end));
     }
 
     const auto vector_ab = vector_functor(start_pt, end_pt);
     const auto projected_pt = translate_functor(start_pt, scaled_vector_functor(vector_ab, lambda));
 
     // Second threshold check with actual projected point if needed
-    return use_midpoint_check(lambda, projected_pt) ? midpoint_functor(midpoint_start, midpoint_end) : projected_pt;
+    return exact(use_midpoint_check(lambda, projected_pt) ? midpoint_functor(midpoint_start, midpoint_end) : projected_pt);
   }
 
   // Convenience wrapper for simple lambda-based threshold (lambda < 0.2 || lambda > 0.8)
@@ -1122,7 +1123,7 @@ protected:
 
     if(this->dimension() < 2) {
       std::cerr << "dim < 2: midpoint\n";
-      return {midpoint_functor(pa, pb), va->cell(), va};
+      return {exact(midpoint_functor(pa, pb)), va->cell(), va};
     }
 
     if(debug().encroaching_vertices()) {
@@ -1184,7 +1185,7 @@ protected:
 #if CGAL_CDT_3_DEBUG_CONFORMING
         std::cerr << "  -> Steiner point: " << result_point << '\n';
 #endif // CGAL_CDT_3_DEBUG_CONFORMING
-        return {result_point, reference_vertex->cell(), reference_vertex};
+        return {exact(result_point), reference_vertex->cell(), reference_vertex};
       };
 
       const auto length_orig_ab = CGAL::approximate_sqrt(sq_length_functor(vector_orig_ab));
@@ -1236,7 +1237,7 @@ protected:
     std::cerr << "  lambda = " << lambda << '\n';
     std::cerr << "  -> Steiner point: " << result_point << '\n';
 #endif // CGAL_CDT_3_DEBUG_CONFORMING
-    return {result_point, reference_vertex->cell(), reference_vertex};
+    return {exact(result_point), reference_vertex->cell(), reference_vertex};
   }
 
 protected:
diff --git a/Constrained_triangulation_3/test/Constrained_triangulation_3/cdt_3_from_off.cpp b/Constrained_triangulation_3/test/Constrained_triangulation_3/cdt_3_from_off.cpp
index 6752c673fae..ca1920d78b1 100644
--- a/Constrained_triangulation_3/test/Constrained_triangulation_3/cdt_3_from_off.cpp
+++ b/Constrained_triangulation_3/test/Constrained_triangulation_3/cdt_3_from_off.cpp
@@ -123,8 +123,8 @@ Usage: cdt_3_from_off [options] input.off output.off
   --debug-geometric-errors: debug geometric error handling
   --debug-polygon-insertion: debug polygon insertion process
   --use-finite-edges-map: use a hash map for finite edges (default: false)
-  --use-epeck-for-normals: use exact kernel for normal computations (default: false)
-  --use-epeck-for-Steiner-points: use exact kernel for Steiner point computations (default: false)
+  --use-epeck-for-normals/--no-use-epeck-for-normals: use exact kernel for normal computations (default: true)
+  --use-epeck-for-Steiner-points/--no-use-epeck-for-Steiner-points: use exact kernel for Steiner point computations (default: true)
 
   --verbose/-V: verbose (can be used several times)
   --quiet: do not print anything
@@ -261,6 +261,10 @@ CDT_options::CDT_options(int argc, char* argv[]) {
       debug_polygon_insertion             = true;
     } else if(arg == "--use-finite-edges-map"sv) {
       use_finite_edges_map                = true;
+    } else if(arg == "--no-use-epeck-for-normals"sv) {
+      use_epeck_for_normals               = false;
+    } else if(arg == "--no-use-epeck-for-Steiner-points"sv) {
+      use_epeck_for_Steiner_points        = false;
     } else if(arg == "--use-epeck-for-normals"sv) {
       use_epeck_for_normals               = true;
     } else if(arg == "--use-epeck-for-Steiner-points"sv) {