Split_3 + do_overlap

Circular_kernel_3/include/CGAL/Circular_kernel_3/internal_function_has_on_spherical_kernel.h

@@ -185,7 +185,71 @@ namespace CGAL {
       return non_oriented_equal<SK>(l, la.supporting_line());
     }
 
-    // TO DO
+
+    template< class SK>
+    inline
+    Sign
+    compute_sign_of_cross_product(const typename SK::Root_of_2 &x1, 
+                                  const typename SK::Root_of_2 &y1,
+                                  const typename SK::Root_of_2 &z1,
+                                  const typename SK::Root_of_2 &x2, 
+                                  const typename SK::Root_of_2 &y2,
+                                  const typename SK::Root_of_2 &z2) {
+      typedef typename SK::Root_of_2 Root_of_2;
+      const Root_of_2 cx = y1 * z2 - z1 * y2;
+      const Root_of_2 cy = z1 * x2 - x1 * z2;
+      const Root_of_2 cz = x1 * y2 - y1 * x2;
+      if(!is_zero(cx)) return sign(cx);
+      if(!is_zero(cy)) return sign(cy);
+      return sign(cz);
+    }
+
+    template< class SK>
+    inline
+    Sign
+    compute_sign_of_cross_product(const typename SK::FT &x1, 
+                                  const typename SK::FT &y1,
+                                  const typename SK::FT &z1,
+                                  const typename SK::FT &x2, 
+                                  const typename SK::FT &y2,
+                                  const typename SK::FT &z2) {
+      typedef typename SK::FT FT;
+      const FT cx = y1 * z2 - z1 * y2;
+      const FT cy = z1 * x2 - x1 * z2;
+      const FT cz = x1 * y2 - y1 * x2;
+      if(!is_zero(cx)) return sign(cx);
+      if(!is_zero(cy)) return sign(cy);
+      return sign(cz);
+    }
+
+    template< class SK>
+    inline
+    Sign
+    compute_sign_of_cross_product(const typename SK::Circular_arc_point_3 &p1, 
+                                  const typename SK::Circular_arc_point_3 &p2,
+                                  const typename SK::Point_3 &c) {
+      return compute_sign_of_cross_product<SK>(p1.x()-c.x(),
+                                               p1.y()-c.y(),
+                                               p1.z()-c.z(),
+                                               p2.x()-c.x(),
+                                               p2.y()-c.y(),
+                                               p2.z()-c.z());
+    }
+
+    template< class SK>
+    inline
+    Sign
+    compute_sign_of_cross_product(const typename SK::Point_3 &p1, 
+                                  const typename SK::Point_3 &p2,
+                                  const typename SK::Point_3 &c) {
+      return compute_sign_of_cross_product<SK>(p1.x()-c.x(),
+                                               p1.y()-c.y(),
+                                               p1.z()-c.z(),
+                                               p2.x()-c.x(),
+                                               p2.y()-c.y(),
+                                               p2.z()-c.z());
+    }
+
     template <class SK>
     inline
     bool