From 324d531dfe2edd6ef06736cfd8e20c10da43e710 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Tue, 7 Oct 2025 19:44:49 +0200
Subject: [PATCH] Circle_2 - Segment_2 intersection does now consider inclusion
 as non intersecting

---
 .../CGAL/Intersections_2/Circle_2_Segment_2.h | 88 +++++++++++++++++--
 .../Intersections_2/test_intersections_2.cpp  |  1 +
 2 files changed, 84 insertions(+), 5 deletions(-)

diff --git a/Intersections_2/include/CGAL/Intersections_2/Circle_2_Segment_2.h b/Intersections_2/include/CGAL/Intersections_2/Circle_2_Segment_2.h
index d884d520332..fa5558f32b1 100644
--- a/Intersections_2/include/CGAL/Intersections_2/Circle_2_Segment_2.h
+++ b/Intersections_2/include/CGAL/Intersections_2/Circle_2_Segment_2.h
@@ -13,8 +13,9 @@
 #ifndef CGAL_INTERSECTIONS_2_CIRCLE_2_SEGMENT_2_H
 #define CGAL_INTERSECTIONS_2_CIRCLE_2_SEGMENT_2_H
 
-#include <CGAL/Distance_2/Point_2_Segment_2.h>
+#include <CGAL/Distance_2/internal/squared_distance_utils_2.h>
 #include <CGAL/Intersection_traits_2.h>
+#include <CGAL/tags.h>
 
 #include <CGAL/Circle_2.h>
 #include <CGAL/Segment_2.h>
@@ -22,23 +23,100 @@
 namespace CGAL {
 namespace Intersections {
 namespace internal {
+//
+
+template <class K>
+typename K::Boolean
+do_intersect(const typename K::Circle_2& circ,
+             const typename K::Segment_2& s,
+             const K& k,
+             const Homogeneous_tag&)
+{
+  typedef typename K::Vector_2 Vector_2;
+  typedef typename K::Point_2 Point_2;
+  typedef typename K::FT FT;
+
+  typename K::Construct_vector_2 vector = k.construct_vector_2_object();
+  typename K::Compute_squared_length_2 sq_length = k.compute_squared_length_2_object();
+  typename K::Compute_squared_distance_2 sq_dist = k.compute_squared_distance_2_object();
+
+  const Point_2 c = circ.center();
+  const FT sqrad = circ.squared_radius();
+  const Vector_2 diffsrc = vector(s.source(), c);
+  const Vector_2 difftgt = vector(s.target(), c);
+
+  FT lsrc = CGAL::internal::wdot(diffsrc, diffsrc, k);
+  FT lsrcw = square(diffsrc.hw());
+  FT ltgt = CGAL::internal::wdot(difftgt, difftgt, k);
+  FT ltgtw = square(difftgt.hw());
+
+  if (lsrc < sqrad * lsrcw) {
+    if (ltgt < sqrad * ltgtw)
+      return false;
+    else
+      return true;
+  }
+  else if (ltgt <= sqrad * ltgtw)
+    return true;
+
+  return sq_dist(c, s.supporting_line()) <= sqrad;
+}
+
+template <class K>
+typename K::Boolean
+do_intersect(const typename K::Circle_2& circ,
+             const typename K::Segment_2& s,
+             const K& k,
+             const Cartesian_tag&)
+{
+  typedef typename K::Vector_2 Vector_2;
+  typedef typename K::Point_2 Point_2;
+  typedef typename K::FT FT;
+
+  typename K::Construct_vector_2 vector = k.construct_vector_2_object();
+  typename K::Compute_squared_length_2 sq_length = k.compute_squared_length_2_object();
+  typename K::Compute_squared_distance_2 sq_dist = k.compute_squared_distance_2_object();
+
+  const Point_2 c = circ.center();
+  const FT sqrad = circ.squared_radius();
+  const Vector_2 diffsrc = vector(s.source(), c);
+  const Vector_2 difftgt = vector(s.target(), c);
+
+  FT lsrc = CGAL::internal::wdot(diffsrc, diffsrc, k);
+  FT ltgt = CGAL::internal::wdot(difftgt, difftgt, k);
+
+  if (lsrc < sqrad) {
+    if (ltgt < sqrad)
+      return false;
+    else
+      return true;
+  }
+  else if (ltgt <= sqrad)
+    return true;
+
+  return sq_dist(c, s.supporting_line()) <= sqrad;
+}
 
 template <class K>
 typename K::Boolean
 do_intersect(const typename K::Circle_2& c,
              const typename K::Segment_2& s,
-             const K&)
+             const K& k)
 {
-  return squared_distance(c.center(), s) <= c.squared_radius();
+  typedef typename K::Kernel_tag Tag;
+  Tag tag;
+  return do_intersect(c, s, k, tag);
 }
 
 template <class K>
 typename K::Boolean
 do_intersect(const typename K::Segment_2& s,
              const typename K::Circle_2& c,
-             const K&)
+             const K& k)
 {
-  return squared_distance(c.center(), s) <= c.squared_radius();
+  typedef typename K::Kernel_tag Tag;
+  Tag tag;
+  return do_intersect(c, s, k, tag);
 }
 
 } // namespace internal
diff --git a/Intersections_2/test/Intersections_2/test_intersections_2.cpp b/Intersections_2/test/Intersections_2/test_intersections_2.cpp
index 8219881120d..368fbd7d37c 100644
--- a/Intersections_2/test/Intersections_2/test_intersections_2.cpp
+++ b/Intersections_2/test/Intersections_2/test_intersections_2.cpp
@@ -341,6 +341,7 @@ struct Test
     check_no_do_intersect  (C(p( 2, 8), 6), S(p(-3, -2), p( 2,  -4)));
     check_no_do_intersect  (C(p( 2, 8), 6), S(p(-3, 22), p( 2, 34)));
     check_no_do_intersect  (C(p( 4, 16), 18), S(p(5, 7), p(6, 8)));
+    check_no_do_intersect  (C(p( 0, 0), 25), S(p(-2, -2), p(2, 2)));
 
     check_do_intersect     (C(p( 3, 4), 0), S(p(-3,  8), p( 6,  2)));
     check_do_intersect     (C(p( 4, 3), 4), S(p( 6, -7), p( 5, 2)));