diff DEPENDENCIES/generic/include/boost/polygon/interval_concept.hpp @ 16:2665513ce2d3

Add boost headers

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/DEPENDENCIES/generic/include/boost/polygon/interval_concept.hpp	Tue Aug 05 11:11:38 2014 +0100
@@ -0,0 +1,935 @@
+// Boost.Polygon library interval_concept.hpp header file
+
+// Copyright (c) Intel Corporation 2008.
+// Copyright (c) 2008-2012 Simonson Lucanus.
+// Copyright (c) 2012-2012 Andrii Sydorchuk.
+
+// See http://www.boost.org for updates, documentation, and revision history.
+// Use, modification and distribution is subject to the Boost Software License,
+// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_POLYGON_INTERVAL_CONCEPT_HPP
+#define BOOST_POLYGON_INTERVAL_CONCEPT_HPP
+
+#include "isotropy.hpp"
+#include "interval_traits.hpp"
+
+namespace boost {
+namespace polygon {
+
+struct interval_concept {};
+
+template <typename ConceptType>
+struct is_interval_concept {
+  typedef gtl_no type;
+};
+
+template <>
+struct is_interval_concept<interval_concept> {
+  typedef gtl_yes type;
+};
+
+template <typename ConceptType>
+struct is_mutable_interval_concept {
+  typedef gtl_no type;
+};
+
+template <>
+struct is_mutable_interval_concept<interval_concept> {
+  typedef gtl_yes type;
+};
+
+template <typename GeometryType, typename BoolType>
+struct interval_coordinate_type_by_concept {
+  typedef void type;
+};
+
+template <typename GeometryType>
+struct interval_coordinate_type_by_concept<GeometryType, gtl_yes> {
+  typedef typename interval_traits<GeometryType>::coordinate_type type;
+};
+
+template <typename GeometryType>
+struct interval_coordinate_type {
+  typedef typename interval_coordinate_type_by_concept<
+    GeometryType,
+    typename is_interval_concept<
+      typename geometry_concept<GeometryType>::type
+    >::type
+  >::type type;
+};
+
+template <typename GeometryType, typename BoolType>
+struct interval_difference_type_by_concept {
+  typedef void type;
+};
+
+template <typename GeometryType>
+struct interval_difference_type_by_concept<GeometryType, gtl_yes> {
+  typedef typename coordinate_traits<
+    typename interval_traits<GeometryType>::coordinate_type
+  >::coordinate_difference type;
+};
+
+template <typename GeometryType>
+struct interval_difference_type {
+  typedef typename interval_difference_type_by_concept<
+    GeometryType,
+    typename is_interval_concept<
+      typename geometry_concept<GeometryType>::type
+    >::type
+  >::type type;
+};
+
+struct y_i_get : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_get,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  typename interval_coordinate_type<IntervalType>::type
+>::type get(const IntervalType& interval, direction_1d dir) {
+  return interval_traits<IntervalType>::get(interval, dir);
+}
+
+struct y_i_set : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_set,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  void
+>::type set(IntervalType& interval, direction_1d dir,
+    typename interval_mutable_traits<IntervalType>::coordinate_type value) {
+  interval_mutable_traits<IntervalType>::set(interval, dir, value);
+}
+
+struct y_i_construct : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_construct,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  IntervalType
+>::type construct(
+    typename interval_mutable_traits<IntervalType>::coordinate_type low,
+    typename interval_mutable_traits<IntervalType>::coordinate_type high) {
+  if (low > high) {
+    (std::swap)(low, high);
+  }
+  return interval_mutable_traits<IntervalType>::construct(low, high);
+}
+
+struct y_i_copy_construct : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_copy_construct,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  IntervalType1
+>::type copy_construct(const IntervalType2& interval) {
+  return construct<IntervalType1>(get(interval, LOW), get(interval, HIGH));
+}
+
+struct y_i_assign : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_assign,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  IntervalType1
+>::type& assign(IntervalType1& lvalue, const IntervalType2& rvalue) {
+  set(lvalue, LOW, get(rvalue, LOW));
+  set(lvalue, HIGH, get(rvalue, HIGH));
+  return lvalue;
+}
+
+struct y_i_low : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_low,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  typename interval_coordinate_type<IntervalType>::type
+>::type low(const IntervalType& interval) {
+  return get(interval, LOW);
+}
+
+struct y_i_high : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_high,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  typename interval_coordinate_type<IntervalType>::type
+>::type high(const IntervalType& interval) {
+  return get(interval, HIGH);
+}
+
+struct y_i_low2 : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_low2,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  void
+>::type low(IntervalType& interval,
+    typename interval_mutable_traits<IntervalType>::coordinate_type value) {
+  set(interval, LOW, value);
+}
+
+struct y_i_high2 : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_high2,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  void
+>::type high(IntervalType& interval,
+    typename interval_mutable_traits<IntervalType>::coordinate_type value) {
+  set(interval, HIGH, value);
+}
+
+struct y_i_equivalence : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_equivalence,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  bool
+>::type equivalence(
+    const IntervalType1& interval1,
+    const IntervalType2& interval2) {
+  return (get(interval1, LOW) == get(interval2, LOW)) &&
+         (get(interval1, HIGH) == get(interval2, HIGH));
+}
+
+struct y_i_contains : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_contains,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  bool
+>::type contains(
+    const IntervalType& interval,
+    typename interval_coordinate_type<IntervalType>::type value,
+    bool consider_touch = true ) {
+  if (consider_touch) {
+    return value <= high(interval) && value >= low(interval);
+  } else {
+    return value < high(interval) && value > low(interval);
+  }
+}
+
+struct y_i_contains2 : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_contains2,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  bool
+>::type contains(
+    const IntervalType1& interval1,
+    const IntervalType2& interval2,
+    bool consider_touch = true) {
+  return contains(interval1, get(interval2, LOW), consider_touch) &&
+         contains(interval1, get(interval2, HIGH), consider_touch);
+}
+
+struct y_i_center : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_center,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  typename interval_coordinate_type<IntervalType>::type
+>::type center(const IntervalType& interval) {
+  return (high(interval) + low(interval)) / 2;
+}
+
+struct y_i_delta : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_delta,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  typename interval_difference_type<IntervalType>::type
+>::type delta(const IntervalType& interval) {
+  typedef typename interval_difference_type<IntervalType>::type diff_type;
+  return static_cast<diff_type>(high(interval)) -
+         static_cast<diff_type>(low(interval));
+}
+
+struct y_i_flip : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_flip,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+IntervalType>::type& flip(
+    IntervalType& interval,
+    typename interval_coordinate_type<IntervalType>::type axis = 0) {
+  typename interval_coordinate_type<IntervalType>::type newLow, newHigh;
+  newLow  = 2 * axis - high(interval);
+  newHigh = 2 * axis - low(interval);
+  low(interval, newLow);
+  high(interval, newHigh);
+  return interval;
+}
+
+struct y_i_scale_up : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_scale_up,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  IntervalType
+>::type& scale_up(
+    IntervalType& interval,
+    typename interval_coordinate_type<IntervalType>::type factor) {
+  typename interval_coordinate_type<IntervalType>::type newHigh =
+      high(interval) * factor;
+  low(interval, low(interval) * factor);
+  high(interval, (newHigh));
+  return interval;
+}
+
+struct y_i_scale_down : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_scale_down,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  IntervalType
+>::type& scale_down(
+    IntervalType& interval,
+    typename interval_coordinate_type<IntervalType>::type factor) {
+  typedef typename interval_coordinate_type<IntervalType>::type Unit;
+  typename interval_coordinate_type<IntervalType>::type newHigh =
+      high(interval) / factor;
+  low(interval, low(interval) / factor);
+  high(interval, (newHigh));
+  return interval;
+}
+
+// TODO(asydorchuk): Deprecated.
+struct y_i_scale : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_scale,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  IntervalType
+>::type& scale(IntervalType& interval, double factor) {
+  typedef typename interval_coordinate_type<IntervalType>::type Unit;
+  Unit newHigh = scaling_policy<Unit>::round(
+      static_cast<double>(high(interval)) * factor);
+  low(interval, scaling_policy<Unit>::round(
+      static_cast<double>(low(interval)) * factor));
+  high(interval, (newHigh));
+  return interval;
+}
+
+struct y_i_move : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_move,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  IntervalType
+>::type& move(
+    IntervalType& interval,
+    typename interval_difference_type<IntervalType>::type displacement) {
+  typedef typename interval_coordinate_type<IntervalType>::type ctype;
+  typedef typename coordinate_traits<ctype>::coordinate_difference Unit;
+  low(interval, static_cast<ctype>(
+      static_cast<Unit>(low(interval)) + displacement));
+  high(interval, static_cast<ctype>(
+      static_cast<Unit>(high(interval)) + displacement));
+  return interval;
+}
+
+struct y_i_convolve : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_convolve,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  IntervalType
+>::type& convolve(
+    IntervalType& interval,
+    typename interval_coordinate_type<IntervalType>::type value) {
+    typedef typename interval_coordinate_type<IntervalType>::type Unit;
+  Unit newLow  = low(interval) + value;
+  Unit newHigh = high(interval) + value;
+  low(interval, newLow);
+  high(interval, newHigh);
+  return interval;
+}
+
+struct y_i_deconvolve : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_deconvolve,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  IntervalType
+>::type& deconvolve(
+    IntervalType& interval,
+    typename interval_coordinate_type<IntervalType>::type value) {
+    typedef typename interval_coordinate_type<IntervalType>::type Unit;
+  Unit newLow  = low(interval) - value;
+  Unit newHigh = high(interval) - value;
+  low(interval, newLow);
+  high(interval, newHigh);
+  return interval;
+}
+
+struct y_i_convolve2 : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_convolve2,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  IntervalType1
+>::type& convolve(IntervalType1& lvalue, const IntervalType2& rvalue) {
+  typedef typename interval_coordinate_type<IntervalType1>::type Unit;
+  Unit newLow  = low(lvalue) + low(rvalue);
+  Unit newHigh = high(lvalue) + high(rvalue);
+  low(lvalue, newLow);
+  high(lvalue, newHigh);
+  return lvalue;
+}
+
+struct y_i_deconvolve2 : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_deconvolve2,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  IntervalType1
+>::type& deconvolve(IntervalType1& lvalue, const IntervalType2& rvalue) {
+  typedef typename interval_coordinate_type<IntervalType1>::type Unit;
+  Unit newLow  = low(lvalue) - low(rvalue);
+  Unit newHigh = high(lvalue) - high(rvalue);
+  low(lvalue, newLow);
+  high(lvalue, newHigh);
+  return lvalue;
+}
+
+struct y_i_reconvolve : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_reconvolve,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  IntervalType1
+>::type& reflected_convolve(
+    IntervalType1& lvalue,
+    const IntervalType2& rvalue) {
+  typedef typename interval_coordinate_type<IntervalType1>::type Unit;
+  Unit newLow  = low(lvalue) - high(rvalue);
+  Unit newHigh = high(lvalue) - low(rvalue);
+  low(lvalue, newLow);
+  high(lvalue, newHigh);
+  return lvalue;
+}
+
+struct y_i_redeconvolve : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_redeconvolve,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  IntervalType1
+>::type& reflected_deconvolve(
+    IntervalType1& lvalue,
+    const IntervalType2& rvalue) {
+  typedef typename interval_coordinate_type<IntervalType1>::type Unit;
+  Unit newLow  = low(lvalue)  + high(rvalue);
+  Unit newHigh = high(lvalue) + low(rvalue);
+  low(lvalue, newLow);
+  high(lvalue, newHigh);
+  return lvalue;
+}
+
+struct y_i_e_dist1 : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<y_i_e_dist1,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  typename interval_difference_type<IntervalType>::type
+>::type euclidean_distance(
+    const IntervalType& interval,
+    typename interval_coordinate_type<IntervalType>::type position) {
+  typedef typename interval_difference_type<IntervalType>::type Unit;
+  Unit dist[3] = {
+      0,
+      (Unit)low(interval) - (Unit)position,
+      (Unit)position - (Unit)high(interval)
+  };
+  return dist[(dist[1] > 0) + ((dist[2] > 0) << 1)];
+}
+
+struct y_i_e_dist2 : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_e_dist2,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  typename interval_difference_type<IntervalType1>::type
+>::type euclidean_distance(
+    const IntervalType1& interval1,
+    const IntervalType2& interval2) {
+  typedef typename interval_difference_type<IntervalType1>::type Unit;
+  Unit dist[3] = {
+      0,
+      (Unit)low(interval1) - (Unit)high(interval2),
+      (Unit)low(interval2) - (Unit)high(interval1)
+  };
+  return dist[(dist[1] > 0) + ((dist[2] > 0) << 1)];
+}
+
+struct y_i_e_intersects : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_e_intersects,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  bool
+>::type intersects(
+    const IntervalType1& interval1,
+    const IntervalType2& interval2,
+    bool consider_touch = true) {
+  return consider_touch ?
+      (low(interval1) <= high(interval2)) &&
+      (high(interval1) >= low(interval2)) :
+      (low(interval1) < high(interval2)) &&
+      (high(interval1) > low(interval2));
+}
+
+struct y_i_e_bintersect : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_e_bintersect,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  bool
+>::type boundaries_intersect(
+    const IntervalType1& interval1,
+    const IntervalType2& interval2,
+    bool consider_touch = true) {
+  return (contains(interval1, low(interval2), consider_touch) ||
+          contains(interval1, high(interval2), consider_touch)) &&
+         (contains(interval2, low(interval1), consider_touch) ||
+          contains(interval2, high(interval1), consider_touch));
+}
+
+struct y_i_intersect : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_intersect,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  bool
+>::type intersect(
+    IntervalType1& lvalue,
+    const IntervalType2& rvalue,
+    bool consider_touch = true) {
+  typedef typename interval_coordinate_type<IntervalType1>::type Unit;
+  Unit lowVal = (std::max)(low(lvalue), low(rvalue));
+  Unit highVal = (std::min)(high(lvalue), high(rvalue));
+  bool valid = consider_touch ? lowVal <= highVal : lowVal < highVal;
+  if (valid) {
+    low(lvalue, lowVal);
+    high(lvalue, highVal);
+  }
+  return valid;
+}
+
+struct y_i_g_intersect : gtl_yes {};
+
+// TODO(asydorchuk): Deprecated.
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_g_intersect,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  IntervalType1
+>::type& generalized_intersect(
+    IntervalType1& lvalue,
+    const IntervalType2& rvalue) {
+  typedef typename interval_coordinate_type<IntervalType1>::type Unit;
+  Unit coords[4] = {low(lvalue), high(lvalue), low(rvalue), high(rvalue)};
+  // TODO(asydorchuk): consider implementing faster sorting of small
+  // fixed length range.
+  polygon_sort(coords, coords+4);
+  low(lvalue, coords[1]);
+  high(lvalue, coords[2]);
+  return lvalue;
+}
+
+struct y_i_abuts1 : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_abuts1,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  bool
+>::type abuts(
+    const IntervalType1& interval1,
+    const IntervalType2& interval2,
+    direction_1d dir) {
+  return dir.to_int() ? low(interval2) == high(interval1) :
+                        low(interval1) == high(interval2);
+}
+
+struct y_i_abuts2 : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_abuts2,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  bool
+>::type abuts(
+    const IntervalType1& interval1,
+    const IntervalType2& interval2) {
+  return abuts(interval1, interval2, HIGH) ||
+         abuts(interval1, interval2, LOW);
+}
+
+struct y_i_bloat : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_bloat,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  IntervalType
+>::type& bloat(
+    IntervalType& interval,
+    typename interval_coordinate_type<IntervalType>::type bloating) {
+  low(interval, low(interval) - bloating);
+  high(interval, high(interval) + bloating);
+  return interval;
+}
+
+struct y_i_bloat2 : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_bloat2,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  IntervalType
+>::type& bloat(
+    IntervalType& interval,
+    direction_1d dir,
+    typename interval_coordinate_type<IntervalType>::type bloating) {
+  set(interval, dir, get(interval, dir) + dir.get_sign() * bloating);
+  return interval;
+}
+
+struct y_i_shrink : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_shrink,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  IntervalType
+>::type& shrink(
+    IntervalType& interval,
+    typename interval_coordinate_type<IntervalType>::type shrinking) {
+  return bloat(interval, -shrinking);
+}
+
+struct y_i_shrink2 : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_shrink2,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  IntervalType
+>::type& shrink(
+    IntervalType& interval,
+    direction_1d dir,
+    typename interval_coordinate_type<IntervalType>::type shrinking) {
+  return bloat(interval, dir, -shrinking);
+}
+
+struct y_i_encompass : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_encompass,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type
+  >::type,
+  bool
+>::type encompass(IntervalType1& interval1, const IntervalType2& interval2) {
+  bool retval = !contains(interval1, interval2, true);
+  low(interval1, (std::min)(low(interval1), low(interval2)));
+  high(interval1, (std::max)(high(interval1), high(interval2)));
+  return retval;
+}
+
+struct y_i_encompass2 : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_encompass2,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  bool
+>::type encompass(
+    IntervalType& interval,
+    typename interval_coordinate_type<IntervalType>::type value) {
+  bool retval = !contains(interval, value, true);
+  low(interval, (std::min)(low(interval), value));
+  high(interval, (std::max)(high(interval), value));
+  return retval;
+}
+
+struct y_i_get_half : gtl_yes {};
+
+template <typename IntervalType>
+typename enable_if<
+  typename gtl_and<
+    y_i_get_half,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType>::type
+    >::type
+  >::type,
+  IntervalType
+>::type get_half(const IntervalType& interval, direction_1d dir) {
+  typedef typename interval_coordinate_type<IntervalType>::type Unit;
+  Unit c = (get(interval, LOW) + get(interval, HIGH)) / 2;
+  return construct<IntervalType>(
+      (dir == LOW) ? get(interval, LOW) : c,
+      (dir == LOW) ? c : get(interval, HIGH));
+}
+
+struct y_i_join_with : gtl_yes {};
+
+template <typename IntervalType1, typename IntervalType2>
+typename enable_if<
+  typename gtl_and_3<
+    y_i_join_with,
+    typename is_mutable_interval_concept<
+      typename geometry_concept<IntervalType1>::type
+    >::type,
+    typename is_interval_concept<
+      typename geometry_concept<IntervalType2>::type
+    >::type>::type,
+  bool
+>::type join_with(IntervalType1& interval1, const IntervalType2& interval2) {
+  if (abuts(interval1, interval2)) {
+    encompass(interval1, interval2);
+    return true;
+  }
+  return false;
+}
+}  // polygon
+}  // boost
+
+#endif  // BOOST_POLYGON_INTERVAL_CONCEPT_HPP