diff --git a/include/boost/geometry/algorithms/detail/buffer/buffer_inserter.hpp b/include/boost/geometry/algorithms/detail/buffer/buffer_inserter.hpp
index 3e691f4d7..eb76b94f2 100644
--- a/include/boost/geometry/algorithms/detail/buffer/buffer_inserter.hpp
+++ b/include/boost/geometry/algorithms/detail/buffer/buffer_inserter.hpp
@@ -43,7 +43,6 @@ struct buffer_range
 {
     typedef typename point_type<RingOutput>::type output_point_type;
     typedef typename coordinate_type<RingOutput>::type coordinate_type;
-    typedef model::referring_segment<output_point_type const> segment_type;
 
 
     template
@@ -103,11 +102,9 @@ struct buffer_range
             RobustPolicy const& )
     {
 
-        segment_type previous_segment(prev_perp1, prev_perp2);
-        segment_type segment(perp1, perp2);
         output_point_type intersection_point;
-        if (line_line_intersection<output_point_type, segment_type>::apply(
-                    segment, previous_segment, intersection_point))
+        if (line_line_intersection::apply(
+                    perp1, perp2, prev_perp1, prev_perp2, intersection_point))
         {
             std::vector<output_point_type> range_out;
             if (join_strategy.apply(intersection_point,
@@ -247,7 +244,6 @@ struct buffer_point
 {
     typedef typename point_type<RingOutput>::type output_point_type;
     typedef typename coordinate_type<RingOutput>::type coordinate_type;
-    typedef model::referring_segment<output_point_type const> segment_type;
 
     typedef typename geometry::select_most_precise
         <
diff --git a/include/boost/geometry/algorithms/detail/buffer/line_line_intersection.hpp b/include/boost/geometry/algorithms/detail/buffer/line_line_intersection.hpp
index bdcb2b585..68608b33b 100644
--- a/include/boost/geometry/algorithms/detail/buffer/line_line_intersection.hpp
+++ b/include/boost/geometry/algorithms/detail/buffer/line_line_intersection.hpp
@@ -24,7 +24,6 @@ namespace detail { namespace buffer
 // TODO: once change this to proper strategy
 // It is different from current segment intersection because these are not segments but lines
 // If we have the Line concept, we can create a strategy
-template <typename Point, typename Line1, typename Line2 = Line1>
 struct line_line_intersection
 {
     template <typename A, typename B, typename C, typename D>
@@ -42,16 +41,14 @@ struct line_line_intersection
             && math::sign(dy1) == math::sign(dy2);
     }
 
-    static inline bool apply(Line1 const& line1, Line2 const& line2, Point& ip)
+    template <typename Point>
+    static inline bool apply(Point const& pi, Point const& pj,
+        Point const& qi, Point const& qj, Point& ip)
     {
         // See http://mathworld.wolfram.com/Line-LineIntersection.html
         typedef typename coordinate_type<Point>::type coordinate_type;
-        coordinate_type x1 = get<0,0>(line1), y1 = get<0,1>(line1);
-        coordinate_type x2 = get<1,0>(line1), y2 = get<1,1>(line1);
-        coordinate_type x3 = get<0,0>(line2), y3 = get<0,1>(line2);
-        coordinate_type x4 = get<1,0>(line2), y4 = get<1,1>(line2);
 
-        coordinate_type denominator = det(x1 - x2, y1 - y2, x3 - x4, y3 - y4);
+        coordinate_type denominator = det(get<0>(pi) - get<0>(pj), get<1>(pi) - get<1>(pj), get<0>(qi) - get<0>(qj), get<1>(qi) - get<1>(qj));
 
         // TODO: maybe use something else then denominator (sides?) to determine this.
 
@@ -74,7 +71,10 @@ struct line_line_intersection
             // +---------------/ x3,y4
             // x4,y4
             // We then calculate the IP from one of the segments up to a certain distance
-            if (parallel_continue(x4 - x3, y4 - y3, x2 - x1, y2 - y1))
+            if (parallel_continue(get<0>(qj) - get<0>(qi),
+                    get<1>(qj) - get<1>(qi),
+                    get<0>(pj) - get<0>(pi),
+                    get<1>(pj) - get<1>(pi)))
             {
                 return false;
             }
@@ -82,13 +82,11 @@ struct line_line_intersection
             denominator = limit;
         }
 
-        coordinate_type d1 = det(x1, y1, x2, y2);
-        coordinate_type d2 = det(x3, y3, x4, y4);
-        coordinate_type px = det(d1, x1 - x2, d2, x3 - x4) / denominator;
-        coordinate_type py = det(d1, y1 - y2, d2, y3 - y4) / denominator;
+        coordinate_type d1 = det(get<0>(pi), get<1>(pi), get<0>(pj), get<1>(pj));
+        coordinate_type d2 = det(get<0>(qi), get<1>(qi), get<0>(qj), get<1>(qj));
 
-        set<0>(ip, px);
-        set<1>(ip, py);
+        set<0>(ip, det(d1, get<0>(pi) - get<0>(pj), d2, get<0>(qi) - get<0>(qj)) / denominator);
+        set<1>(ip, det(d1, get<1>(pi) - get<1>(pj), d2, get<1>(qi) - get<1>(qj)) / denominator);
 
         return true;
     }