First move the C2 and H2 pedicate and construction files operating on the RT

Cartesian_kernel/include/CGAL/constructions/kernel_ftC2.h

@@ -418,6 +418,65 @@ scaled_distance_to_lineC2( const FT &px, const FT &py,
   return determinant<FT>(px-rx, py-ry, qx-rx, qy-ry);
 }
 
+
+template < class RT >
+void
+weighted_circumcenter_translateC2(const RT &dqx, const RT &dqy, const RT &dqw,
+				  const RT &drx, const RT &dry, const RT &drw,
+				  RT &dcx,       RT &dcy)
+{
+  // Given 3 points P, Q, R, this function takes as input:
+  // qx-px, qy-py,qw-pw,  rx-px, ry-py, rw-pw.  And returns cx-px, cy-py,
+  // where (cx, cy) are the coordinates of the circumcenter C.
+
+  // What we do is intersect the radical axis
+  RT r2 = CGAL_NTS square(drx) + CGAL_NTS square(dry) - drw;
+  RT q2 = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - dqw;
+
+  RT den = RT(2) * determinant(dqx, dqy, drx, dry);
+
+  // The 3 points aren't collinear.
+  // Hopefully, this is already checked at the upper level.
+  CGAL_assertion ( den != RT(0) );
+
+  // One possible optimization here is to precompute 1/den, to avoid one
+  // division.  However, we loose precision, and it's maybe not worth it (?).
+  dcx =   determinant (dry, dqy, r2, q2) / den;
+  dcy = - determinant (drx, dqx, r2, q2) / den;
+}
+
+//template < class RT >
+template < class RT, class We>
+void
+weighted_circumcenterC2( const RT &px, const RT &py, const We &pw,
+			 const RT &qx, const RT &qy, const We &qw,
+			 const RT &rx, const RT &ry, const We &rw,
+			 RT &x, RT &y )
+{
+  RT dqw = RT(qw-pw);
+  RT drw = RT(rw-pw);
+ 
+  weighted_circumcenter_translateC2(qx-px, qy-py, dqw,rx-px, ry-py,drw,x, y);
+  x += px;
+  y += py;
+}
+
+
+template < class RT , class We>
+void
+radical_axisC2(const RT &px, const RT &py, const We &pw,
+	       const RT &qx, const RT &qy, const We &qw,
+	       RT &a, RT &b, RT& c )
+{
+  a =  RT(2)*(px - qx);
+  b =  RT(2)*(py - qy);
+  c = - CGAL_NTS square(px) - CGAL_NTS square(py) 
+      + CGAL_NTS square(qx) + CGAL_NTS square(qy) 
+       +RT(pw) - RT(qw);
+}
+
+
+
 } //namespace CGAL
 
 #endif // CGAL_CONSTRUCTIONS_KERNEL_FTC2_H

Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h

@@ -635,6 +635,71 @@ side_of_oriented_lineC2(const FT &a, const FT &b, const FT &c,
   return CGAL_NTS sign(a*x+b*y+c);
 }
 
+
+template <class FT>
+Comparison_result
+compare_power_distanceC2(const FT& px, const FT& py, const FT& pwt,
+			 const FT& qx, const FT& qy, const FT& qwt,
+			 const FT& rx, const FT& ry)
+{
+  // returns SMALLER if r is closer to p w.r.t. the power metric
+  FT d1 = CGAL_NTS square(rx - px) + CGAL_NTS square(ry - py) - pwt;
+  FT d2 = CGAL_NTS square(rx - qx) + CGAL_NTS square(ry - qy) - qwt;
+  return CGAL_NTS compare(d1, d2);
+}
+
+
+template <class FT>
+Oriented_side
+power_testC2( const FT &px, const FT &py, const FT &pwt,
+              const FT &qx, const FT &qy, const FT &qwt,
+              const FT &rx, const FT &ry, const FT &rwt,
+              const FT &tx, const FT &ty, const FT &twt)
+{
+    // Note: maybe this can be further optimized like the usual in_circle() ?
+
+    // We translate the 4 points so that T becomes the origin.
+    FT dpx = px - tx;
+    FT dpy = py - ty;
+    FT dpz = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) - pwt + twt;
+    FT dqx = qx - tx;
+    FT dqy = qy - ty;
+    FT dqz = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - qwt + twt;
+    FT drx = rx - tx;
+    FT dry = ry - ty;
+    FT drz = CGAL_NTS square(drx) + CGAL_NTS square(dry) - rwt + twt;
+
+    return sign_of_determinant(dpx, dpy, dpz,
+                                  dqx, dqy, dqz,
+                                  drx, dry, drz);
+}
+
+
+template <class FT>
+Oriented_side
+power_testC2( const FT &px, const FT &py, const FT &pwt,
+	      const FT &qx, const FT &qy, const FT &qwt,
+	      const FT &tx, const FT &ty, const FT &twt)
+{
+    // Same translation as above.
+    FT dpx = px - tx;
+    FT dpy = py - ty;
+    FT dpz = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) - pwt + twt;
+    FT dqx = qx - tx;
+    FT dqy = qy - ty;
+    FT dqz = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - qwt + twt;
+
+    // We do an orthogonal projection on the (x) axis, if possible.
+    Comparison_result cmpx = CGAL_NTS compare(px, qx);
+    if (cmpx != EQUAL)
+	return cmpx * sign_of_determinant(dpx, dpz, dqx, dqz);
+
+    // If not possible, then on the (y) axis.
+    Comparison_result cmpy = CGAL_NTS compare(py, qy);
+    return cmpy * sign_of_determinant(dpy, dpz, dqy, dqz);
+}
+
+
 } //namespace CGAL
 
 #endif  // CGAL_PREDICATES_KERNEL_FTC2_H

Homogeneous_kernel/include/CGAL/Homogeneous/Homogeneous_base.h

@@ -69,6 +69,7 @@
 #include <CGAL/Homogeneous/distance_predicatesH3.h>
 #include <CGAL/Homogeneous/predicates_on_pointsH3.h>
 #include <CGAL/Homogeneous/predicates_on_pointsH2.h>
+#include <CGAL/Homogeneous/constructions_on_weighted_points_homogeneous_2.h>
 
 #include <CGAL/representation_tags.h>
 #include <CGAL/Homogeneous/function_objects.h>

Homogeneous_kernel/include/CGAL/Homogeneous/Regular_triangulation_rtH2.h

@@ -1,10 +1,10 @@
 // Copyright (c) 1999  INRIA Sophia-Antipolis (France).
 // All rights reserved.
 //
-// This file is part of CGAL (www.cgal.org).
+// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
-// You can redistribute it and/or modify it under the terms of the GNU
+// modify it under the terms of the GNU Lesser General Public License as
-// General Public License as published by the Free Software Foundation,
+// published by the Free Software Foundation; either version 3 of the License,
-// either version 3 of the License, or (at your option) any later version.
+// or (at your option) any later version.
 //
 // Licensees holding a valid commercial license may use this file in
 // accordance with the commercial license agreement provided with the software.

Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h

@@ -30,6 +30,7 @@
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/predicates/sign_of_determinant.h>
 #include <CGAL/Homogeneous/Regular_triangulation_rtH3.h>
+#include <CGAL/Homogeneous/Regular_triangulation_rtH2.h>
 
 namespace CGAL {
 
@@ -4285,6 +4286,9 @@ namespace HomogeneousKernelFunctors {
       return s.rep().orientation();
     }
   };
+
+
+
 template < typename K >
 class Power_side_of_power_sphere_3
 {

Triangulation_2/include/CGAL/Regular_triangulation_euclidean_traits_2.h

@@ -29,11 +29,6 @@
 #include <CGAL/Kernel_traits.h>
 #include <CGAL/representation_tags.h>
 
-#include <CGAL/predicates/Regular_triangulation_ftC2.h>
-#include <CGAL/constructions_on_weighted_points_cartesian_2.h>
-
-#include <CGAL/predicates/Regular_triangulation_rtH2.h>
-#include <CGAL/constructions_on_weighted_points_homogeneous_2.h>
 
 namespace CGAL { 
 

Triangulation_2/include/CGAL/predicates/Regular_triangulation_ftC2.h

@@ -1,97 +0,0 @@
-// Copyright (c) 1999  INRIA Sophia-Antipolis (France).
-// All rights reserved.
-//
-// This file is part of CGAL (www.cgal.org).
-// You can redistribute it and/or modify it under the terms of the GNU
-// General Public License as published by the Free Software Foundation,
-// either version 3 of the License, or (at your option) any later version.
-//
-// Licensees holding a valid commercial license may use this file in
-// accordance with the commercial license agreement provided with the software.
-//
-// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
-// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
-//
-// $URL$
-// $Id$
-// 
-//
-// Author(s)     : Sylvain Pion
-//                 Mariette Yvinec <Mariette.Yvinec@sophia.inria.fr>
-
-#ifndef CGAL_REGULAR_TRIANGULATION_FTC2_H
-#define CGAL_REGULAR_TRIANGULATION_FTC2_H
-
-#include <CGAL/number_utils.h>
-
-// This file contains the low level cartesian predicates
-// used by the 2D regular triangulation.
-
-namespace CGAL {
-
-template <class FT>
-Comparison_result
-compare_power_distanceC2(const FT& px, const FT& py, const FT& pwt,
-			 const FT& qx, const FT& qy, const FT& qwt,
-			 const FT& rx, const FT& ry)
-{
-  // returns SMALLER if r is closer to p w.r.t. the power metric
-  FT d1 = CGAL_NTS square(rx - px) + CGAL_NTS square(ry - py) - pwt;
-  FT d2 = CGAL_NTS square(rx - qx) + CGAL_NTS square(ry - qy) - qwt;
-  return CGAL_NTS compare(d1, d2);
-}
-
-
-template <class FT>
-Oriented_side
-power_testC2( const FT &px, const FT &py, const FT &pwt,
-              const FT &qx, const FT &qy, const FT &qwt,
-              const FT &rx, const FT &ry, const FT &rwt,
-              const FT &tx, const FT &ty, const FT &twt)
-{
-    // Note: maybe this can be further optimized like the usual in_circle() ?
-
-    // We translate the 4 points so that T becomes the origin.
-    FT dpx = px - tx;
-    FT dpy = py - ty;
-    FT dpz = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) - pwt + twt;
-    FT dqx = qx - tx;
-    FT dqy = qy - ty;
-    FT dqz = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - qwt + twt;
-    FT drx = rx - tx;
-    FT dry = ry - ty;
-    FT drz = CGAL_NTS square(drx) + CGAL_NTS square(dry) - rwt + twt;
-
-    return sign_of_determinant(dpx, dpy, dpz,
-                                  dqx, dqy, dqz,
-                                  drx, dry, drz);
-}
-
-
-template <class FT>
-Oriented_side
-power_testC2( const FT &px, const FT &py, const FT &pwt,
-	      const FT &qx, const FT &qy, const FT &qwt,
-	      const FT &tx, const FT &ty, const FT &twt)
-{
-    // Same translation as above.
-    FT dpx = px - tx;
-    FT dpy = py - ty;
-    FT dpz = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) - pwt + twt;
-    FT dqx = qx - tx;
-    FT dqy = qy - ty;
-    FT dqz = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - qwt + twt;
-
-    // We do an orthogonal projection on the (x) axis, if possible.
-    Comparison_result cmpx = CGAL_NTS compare(px, qx);
-    if (cmpx != EQUAL)
-	return cmpx * sign_of_determinant(dpx, dpz, dqx, dqz);
-
-    // If not possible, then on the (y) axis.
-    Comparison_result cmpy = CGAL_NTS compare(py, qy);
-    return cmpy * sign_of_determinant(dpy, dpz, dqy, dqz);
-}
-
-} //namespace CGAL
-
-#endif // CGAL_REGULAR_TRIANGULATION_FTC2_H