Add Origin based constructor to sphere_point and avoid conditional constructor

Nef_3/include/CGAL/Nef_3/SNC_constructor.h

@@ -2037,7 +2037,7 @@ class SNC_constructor<SNC_indexed_items, SNC_structure_>
         D.link_as_isolated_vertex(v2, f2);
         D.link_as_loop(l,f1);
         D.link_as_loop(l->twin(),f2);
-        l->circle() = Sphere_circle(faces_p->plane());
+        l->circle() = Sphere_circle(CGAL::ORIGIN,faces_p->plane());
         l->twin()->circle() = l->circle().opposite();
         f2->mark() = mf2;
         l->mark() = l->twin()->mark() = ml;
@@ -2053,7 +2053,7 @@ class SNC_constructor<SNC_indexed_items, SNC_structure_>
       SHalfedge_handle se1;
       SHalfedge_handle se2;
       SFace_handle sf;
-      Sphere_circle c(f->plane());
+      Sphere_circle c(CGAL::ORIGIN,f->plane());
 
       SHalfedge_handle next_edge;
       SHalfedge_around_svertex_const_circulator ec(E.out_edges(e)), ee(ec);
@@ -2104,7 +2104,7 @@ class SNC_constructor<SNC_indexed_items, SNC_structure_>
         se1 = D.new_shalfedge_pair(ec2->twin(), en->twin(), -1, 1);
         CGAL_NEF_TRACEN("new edge pair " << ec2->twin()->source()->vector() <<
                         " -> " << en->twin()->source()->vector());
-        se1->circle() = Sphere_circle(faces_p->plane());
+        se1->circle() = Sphere_circle(CGAL::ORIGIN,faces_p->plane());
         se1->twin()->circle() = se1->circle().opposite();
         se1->mark() = se1->twin()->mark() = BOP(mark_of_right_sface[ec2], faces_p->mark(), inv);
 

Nef_3/include/CGAL/Nef_3/polygon_mesh_to_nef_3.h

@@ -250,8 +250,7 @@ void polygon_mesh_to_nef_3(PolygonMesh& P, SNC_structure& S, FaceIndexMap fimap,
         with_border = true;
       else {
         std::size_t i = get(fimap,face(pe_prev,P));
-        Plane ss_plane( CGAL::ORIGIN, normals[i]);
-        Sphere_circle ss_circle(ss_plane);
+        Sphere_circle ss_circle(CGAL::ORIGIN, normals[i]);
         CGAL_assertion_code(if(num_edges[i] > 3) {
           CGAL_assertion(ss_circle.has_on(sp));
           CGAL_assertion(ss_circle.has_on(sv_prev->point()));
@@ -283,8 +282,7 @@ void polygon_mesh_to_nef_3(PolygonMesh& P, SNC_structure& S, FaceIndexMap fimap,
       e = sv_prev->out_sedge();
     } else {
       std::size_t i = get(fimap,face(pe_prev,P));
-      Plane ss_plane( CGAL::ORIGIN, normals[i]);
-      Sphere_circle ss_circle(ss_plane);
+      Sphere_circle ss_circle(CGAL::ORIGIN, normals[i]);
 
       CGAL_assertion_code(if(num_edges[i] > 3) {
         CGAL_assertion(ss_circle.has_on(sp_0));

Nef_S2/include/CGAL/Nef_S2/Sphere_circle.h

@@ -17,6 +17,7 @@
 
 
 #include <CGAL/basic.h>
+#include <CGAL/Nef_S2/Sphere_point.h>
 
 namespace CGAL {
 
@@ -47,6 +48,7 @@ typedef std::pair< Sphere_segment<R>,Sphere_segment<R> >
 typedef typename R_::Plane_3 Plane_3;
 typedef typename R_::Line_3 Line_3;
 typedef typename R_::Point_3 Point_3;
+typedef typename R_::Vector_3 Vector_3;
 typedef Sphere_circle<R_> Self;
 typedef typename R_::Plane_3 Base;
 
@@ -78,15 +80,20 @@ create any great circle that contains $p$ and $q$.}*/
   }
 }
 
- Sphere_circle(const Plane_3& h) : Base(h)
+Sphere_circle(const Plane_3& h) : Base(h)
 /*{\Mcreate creates the circle of $S_2$ corresponding to the plane
 |h|. If |h| does not contain the origin, then |\Mvar| becomes the
 circle parallel to |h| containing the origin.}*/
 {
-  if(h.d() != 0) *this = Plane_3(h.a(),h.b(),h.c(),RT(0));
+  if(h.d() != 0)
+    *this = Plane_3(h.a(),h.b(),h.c(),RT(0));
 }
 
-Sphere_circle(const RT& x, const RT& y, const RT& z): Base(x,y,z,0) {}
+Sphere_circle(const Origin& o, const Vector_3& v) : Base(o,v) {}
+
+Sphere_circle(const Origin&, const Plane_3& h) : Base(h.a(),h.b(),h.c(),RT(0)) {}
+
+Sphere_circle(const RT& x, const RT& y, const RT& z) : Base(x,y,z,0) {}
 
 /*{\Mcreate creates the circle orthogonal to the vector $(x,y,z)$.}*/
 
@@ -102,10 +109,9 @@ Sphere_circle(Sphere_circle<R> c, const Sphere_point<R>& p)
 }
 
 /*{\Moperations 4 2}*/
-
 Sphere_circle<R> opposite() const
 /*{\Mop returns the opposite of |\Mvar|.}*/
-{ return Base::opposite(); }
+{ return Sphere_circle<R>(Base::opposite(),Private_tag{}); }
 
 bool has_on(const Sphere_point<R>& p) const
 /*{\Mop returns true iff |\Mvar| contains |p|.}*/
@@ -117,7 +123,7 @@ Plane_3 plane() const { return Base(*this); }
 Plane_3 plane_through(const Point_3& p) const
 /*{\Mop returns the plane parallel to |\Mvar| that
 contains point |p|.}*/
-{ return Plane_3(p,((Base*) this)->orthogonal_direction()); }
+{ return Plane_3(p,((Base*) this)->orthogonal_vector()); }
 
 Sphere_point<R> orthogonal_pole() const
 /*{\Mop returns the point that is the pole of the
@@ -134,6 +140,10 @@ of splitting |\Mvar| at the $x$-$y$-coordinate plane if |\Mvar|
 is not part of it. Otherwise |\Mvar| is split at the
 $x$-$z$-coordinate plane.}*/
 
+private:
+struct Private_tag{};
+Sphere_circle(const Plane_3& h,Private_tag) : Base(h){}
+
 }; // Sphere_circle<R>
 
 /*{\Mtext\headerline{Global functions}}*/

Nef_S2/include/CGAL/Nef_S2/Sphere_segment.h

@@ -20,6 +20,7 @@
 #include <CGAL/Handle_for.h>
 #include <CGAL/Nef_S2/Sphere_point.h>
 #include <CGAL/Nef_S2/Sphere_circle.h>
+#include <CGAL/Kernel/global_functions.h>
 #include <vector>
 
 namespace CGAL {
@@ -37,7 +38,7 @@ Sphere_segment_rep() { ps_ = pt_ = Point(); c_ = Circle(); }
 
 Sphere_segment_rep(const Point& p1, const Point& p2,
                    bool shorter_arc=true) :
-  ps_(p1), pt_(p2), c_(Plane_3(p1,p2,Point_3(CGAL::ORIGIN)))
+  ps_(p1), pt_(p2), c_(CGAL::ORIGIN,CGAL::orthogonal_vector(p1,p2,Point_3(CGAL::ORIGIN)))
 { // warning stays as reminder that one gets an arbitrary plane equation
   // in this degenerate case
   CGAL_warning(p1 != p2.antipode());