Add 2D navigation mesh baking

Adds 2D navigation mesh baking.

thirdparty/clipper2/LICENSE

@@ -0,0 +1,23 @@
+Boost Software License - Version 1.0 - August 17th, 2003
+
+Permission is hereby granted, free of charge, to any person or organization
+obtaining a copy of the software and accompanying documentation covered by
+this license (the "Software") to use, reproduce, display, distribute,
+execute, and transmit the Software, and to prepare derivative works of the
+Software, and to permit third-parties to whom the Software is furnished to
+do so, all subject to the following:
+
+The copyright notices in the Software and this entire statement, including
+the above license grant, this restriction and the following disclaimer,
+must be included in all copies of the Software, in whole or in part, and
+all derivative works of the Software, unless such copies or derivative
+works are solely in the form of machine-executable object code generated by
+a source language processor.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
+SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
+FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+DEALINGS IN THE SOFTWARE.

thirdparty/clipper2/clipper2-exceptions.patch

@@ -0,0 +1,35 @@
+diff --git a/thirdparty/clipper2/include/clipper2/clipper.core.h b/thirdparty/clipper2/include/clipper2/clipper.core.h
+index c7522cb900..086d1b659c 100644
+--- a/thirdparty/clipper2/include/clipper2/clipper.core.h
++++ b/thirdparty/clipper2/include/clipper2/clipper.core.h
+@@ -20,6 +20,8 @@
+ #include <climits>
+ #include <numeric>
+ 
++#define CLIPPER2_THROW(exception) std::abort()
++
+ namespace Clipper2Lib
+ {
+ 
+@@ -65,16 +67,16 @@ namespace Clipper2Lib
+     switch (error_code)
+     {
+     case precision_error_i:
+-      throw Clipper2Exception(precision_error);
++      CLIPPER2_THROW(Clipper2Exception(precision_error));
+     case scale_error_i:
+-      throw Clipper2Exception(scale_error);
++      CLIPPER2_THROW(Clipper2Exception(scale_error));
+     case non_pair_error_i:
+-      throw Clipper2Exception(non_pair_error);
++      CLIPPER2_THROW(Clipper2Exception(non_pair_error));
+     case range_error_i:
+-      throw Clipper2Exception(range_error);
++      CLIPPER2_THROW(Clipper2Exception(range_error));
+     }
+ #else
+-    ++error_code; // only to stop compiler warning
++    if(error_code) {}; // only to stop compiler 'parameter not used' warning
+ #endif
+   }
+ 

thirdparty/clipper2/include/clipper2/clipper.core.h

@@ -0,0 +1,846 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  22 March 2023                                                   *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2023                                         *
+* Purpose   :  Core Clipper Library structures and functions                   *
+* License   :  http://www.boost.org/LICENSE_1_0.txt                            *
+*******************************************************************************/
+
+#ifndef CLIPPER_CORE_H
+#define CLIPPER_CORE_H
+
+#include <cstdint>
+#include <cstdlib>
+#include <cmath>
+#include <vector>
+#include <string>
+#include <iostream>
+#include <algorithm>
+#include <climits>
+#include <numeric>
+
+#define CLIPPER2_THROW(exception) std::abort()
+
+namespace Clipper2Lib
+{
+
+#if (defined(__cpp_exceptions) && __cpp_exceptions) || (defined(__EXCEPTIONS) && __EXCEPTIONS)
+
+  class Clipper2Exception : public std::exception {
+  public:
+    explicit Clipper2Exception(const char* description) :
+      m_descr(description) {}
+    virtual const char* what() const throw() override { return m_descr.c_str(); }
+  private:
+    std::string m_descr;
+  };
+
+  static const char* precision_error =
+    "Precision exceeds the permitted range";
+  static const char* range_error =
+    "Values exceed permitted range";
+  static const char* scale_error =
+    "Invalid scale (either 0 or too large)";
+  static const char* non_pair_error =
+    "There must be 2 values for each coordinate";
+#endif
+
+  // error codes (2^n)
+  const int precision_error_i   = 1; // non-fatal
+  const int scale_error_i       = 2; // non-fatal 
+  const int non_pair_error_i    = 4; // non-fatal 
+  const int range_error_i = 64;
+
+  static const double PI = 3.141592653589793238;
+  static const int64_t MAX_COORD = INT64_MAX >> 2;
+  static const int64_t MIN_COORD = -MAX_COORD;
+  static const int64_t INVALID = INT64_MAX;
+  const double max_coord = static_cast<double>(MAX_COORD);
+  const double min_coord = static_cast<double>(MIN_COORD);
+
+  static const double MAX_DBL = (std::numeric_limits<double>::max)();
+
+  static void DoError(int error_code)
+  {
+#if (defined(__cpp_exceptions) && __cpp_exceptions) || (defined(__EXCEPTIONS) && __EXCEPTIONS)
+    switch (error_code)
+    {
+    case precision_error_i:
+      CLIPPER2_THROW(Clipper2Exception(precision_error));
+    case scale_error_i:
+      CLIPPER2_THROW(Clipper2Exception(scale_error));
+    case non_pair_error_i:
+      CLIPPER2_THROW(Clipper2Exception(non_pair_error));
+    case range_error_i:
+      CLIPPER2_THROW(Clipper2Exception(range_error));
+    }
+#else
+    if(error_code) {}; // only to stop compiler 'parameter not used' warning
+#endif
+  }
+
+  //By far the most widely used filling rules for polygons are EvenOdd
+  //and NonZero, sometimes called Alternate and Winding respectively.
+  //https://en.wikipedia.org/wiki/Nonzero-rule
+  enum class FillRule { EvenOdd, NonZero, Positive, Negative };
+
+  // Point ------------------------------------------------------------------------
+
+  template <typename T>
+  struct Point {
+    T x;
+    T y;
+#ifdef USINGZ
+    int64_t z;
+
+    template <typename T2>
+    inline void Init(const T2 x_ = 0, const T2 y_ = 0, const int64_t z_ = 0)
+    {
+      if constexpr (std::numeric_limits<T>::is_integer &&
+        !std::numeric_limits<T2>::is_integer)
+      {
+        x = static_cast<T>(std::round(x_));
+        y = static_cast<T>(std::round(y_));
+        z = z_;
+      }
+      else
+      {
+        x = static_cast<T>(x_);
+        y = static_cast<T>(y_);
+        z = z_;
+      }
+    }
+
+    explicit Point() : x(0), y(0), z(0) {};
+
+    template <typename T2>
+    Point(const T2 x_, const T2 y_, const int64_t z_ = 0)
+    {
+      Init(x_, y_);
+      z = z_;
+    }
+
+    template <typename T2>
+    explicit Point<T>(const Point<T2>& p)
+    {
+      Init(p.x, p.y, p.z);
+    }
+
+    Point operator * (const double scale) const
+    {
+      return Point(x * scale, y * scale, z);
+    }
+
+
+    friend std::ostream& operator<<(std::ostream& os, const Point& point)
+    {
+      os << point.x << "," << point.y << "," << point.z << " ";
+      return os;
+    }
+
+#else
+
+    template <typename T2>
+    inline void Init(const T2 x_ = 0, const T2 y_ = 0)
+    {
+      if constexpr (std::numeric_limits<T>::is_integer &&
+        !std::numeric_limits<T2>::is_integer)
+      {
+        x = static_cast<T>(std::round(x_));
+        y = static_cast<T>(std::round(y_));
+      }
+      else
+      {
+        x = static_cast<T>(x_);
+        y = static_cast<T>(y_);
+      }
+    }
+
+    explicit Point() : x(0), y(0) {};
+
+    template <typename T2>
+    Point(const T2 x_, const T2 y_) { Init(x_, y_); }
+
+    template <typename T2>
+    explicit Point<T>(const Point<T2>& p) { Init(p.x, p.y); }
+
+    Point operator * (const double scale) const
+    {
+      return Point(x * scale, y * scale);
+    }
+
+    friend std::ostream& operator<<(std::ostream& os, const Point& point)
+    {
+      os << point.x << "," << point.y << " ";
+      return os;
+    }
+#endif
+
+    friend bool operator==(const Point& a, const Point& b)
+    {
+      return a.x == b.x && a.y == b.y;
+    }
+
+    friend bool operator!=(const Point& a, const Point& b)
+    {
+      return !(a == b);
+    }
+
+    inline Point<T> operator-() const
+    {
+      return Point<T>(-x, -y);
+    }
+
+    inline Point operator+(const Point& b) const
+    {
+      return Point(x + b.x, y + b.y);
+    }
+
+    inline Point operator-(const Point& b) const
+    {
+      return Point(x - b.x, y - b.y);
+    }
+
+    inline void Negate() { x = -x; y = -y; }
+
+  };
+
+  //nb: using 'using' here (instead of typedef) as they can be used in templates
+  using Point64 = Point<int64_t>;
+  using PointD = Point<double>;
+
+  template <typename T>
+  using Path = std::vector<Point<T>>;
+  template <typename T>
+  using Paths = std::vector<Path<T>>;
+
+  using Path64 = Path<int64_t>;
+  using PathD = Path<double>;
+  using Paths64 = std::vector< Path64>;
+  using PathsD = std::vector< PathD>;
+
+  // Rect ------------------------------------------------------------------------
+
+  template <typename T>
+  struct Rect;
+
+  using Rect64 = Rect<int64_t>;
+  using RectD = Rect<double>;
+
+  template <typename T>
+  struct Rect {
+    T left;
+    T top;
+    T right;
+    T bottom;
+
+    Rect() :
+      left(0),
+      top(0),
+      right(0),
+      bottom(0) {}
+
+    Rect(T l, T t, T r, T b) :
+      left(l),
+      top(t),
+      right(r),
+      bottom(b) {}
+
+    Rect(bool is_valid)
+    {
+      if (is_valid)
+      {
+        left = right = top = bottom = 0;
+      }
+      else
+      {
+        left = top = std::numeric_limits<T>::max();
+        right = bottom = -std::numeric_limits<int64_t>::max();
+      }
+    }
+
+    T Width() const { return right - left; }
+    T Height() const { return bottom - top; }
+    void Width(T width) { right = left + width; }
+    void Height(T height) { bottom = top + height; }
+
+    Point<T> MidPoint() const
+    {
+      return Point<T>((left + right) / 2, (top + bottom) / 2);
+    }
+
+    Path<T> AsPath() const
+    {
+      Path<T> result;
+      result.reserve(4);
+      result.push_back(Point<T>(left, top));
+      result.push_back(Point<T>(right, top));
+      result.push_back(Point<T>(right, bottom));
+      result.push_back(Point<T>(left, bottom));
+      return result;
+    }
+
+    bool Contains(const Point<T>& pt) const
+    {
+      return pt.x > left && pt.x < right&& pt.y > top && pt.y < bottom;
+    }
+
+    bool Contains(const Rect<T>& rec) const
+    {
+      return rec.left >= left && rec.right <= right &&
+        rec.top >= top && rec.bottom <= bottom;
+    }
+
+    void Scale(double scale) {
+      left *= scale;
+      top *= scale;
+      right *= scale;
+      bottom *= scale;
+    }
+
+    bool IsEmpty() const { return bottom <= top || right <= left; };
+
+    bool Intersects(const Rect<T>& rec) const
+    {
+      return ((std::max)(left, rec.left) <= (std::min)(right, rec.right)) &&
+        ((std::max)(top, rec.top) <= (std::min)(bottom, rec.bottom));
+    };
+
+    friend std::ostream& operator<<(std::ostream& os, const Rect<T>& rect) {
+      os << "("
+        << rect.left << "," << rect.top << "," << rect.right << "," << rect.bottom
+        << ")";
+      return os;
+    }
+  };
+
+  template <typename T1, typename T2>
+  inline Rect<T1> ScaleRect(const Rect<T2>& rect, double scale)
+  {
+    Rect<T1> result;
+
+    if constexpr (std::numeric_limits<T1>::is_integer &&
+      !std::numeric_limits<T2>::is_integer)
+    {
+      result.left = static_cast<T1>(std::round(rect.left * scale));
+      result.top = static_cast<T1>(std::round(rect.top * scale));
+      result.right = static_cast<T1>(std::round(rect.right * scale));
+      result.bottom = static_cast<T1>(std::round(rect.bottom * scale));
+    }
+    else
+    {
+      result.left = rect.left * scale;
+      result.top = rect.top * scale;
+      result.right = rect.right * scale;
+      result.bottom = rect.bottom * scale;
+    }
+    return result;
+  }
+
+  static const Rect64 MaxInvalidRect64 = Rect64(
+    INT64_MAX, INT64_MAX, INT64_MIN, INT64_MIN);
+  static const RectD MaxInvalidRectD = RectD(
+    MAX_DBL, MAX_DBL, -MAX_DBL, -MAX_DBL);
+
+  template <typename T>
+  Rect<T> GetBounds(const Path<T>& path)
+  {
+    auto xmin = std::numeric_limits<T>::max();
+    auto ymin = std::numeric_limits<T>::max();
+    auto xmax = std::numeric_limits<T>::lowest();
+    auto ymax = std::numeric_limits<T>::lowest();
+    for (const auto& p : path)
+    {
+      if (p.x < xmin) xmin = p.x;
+      if (p.x > xmax) xmax = p.x;
+      if (p.y < ymin) ymin = p.y;
+      if (p.y > ymax) ymax = p.y;
+    }
+    return Rect<T>(xmin, ymin, xmax, ymax);
+  }
+
+  template <typename T>
+  Rect<T> GetBounds(const Paths<T>& paths)
+  {
+    auto xmin = std::numeric_limits<T>::max();
+    auto ymin = std::numeric_limits<T>::max();
+    auto xmax = std::numeric_limits<T>::lowest();
+    auto ymax = std::numeric_limits<T>::lowest();
+    for (const Path<T>& path : paths)
+      for (const Point<T>& p : path)
+      {
+      if (p.x < xmin) xmin = p.x;
+      if (p.x > xmax) xmax = p.x;
+      if (p.y < ymin) ymin = p.y;
+      if (p.y > ymax) ymax = p.y;
+      }
+    return Rect<T>(xmin, ymin, xmax, ymax);
+  }
+
+  template <typename T>
+  std::ostream& operator << (std::ostream& outstream, const Path<T>& path)
+  {
+    if (!path.empty())
+    {
+      auto pt = path.cbegin(), last = path.cend() - 1;
+      while (pt != last)
+        outstream << *pt++ << ", ";
+      outstream << *last << std::endl;
+    }
+    return outstream;
+  }
+
+  template <typename T>
+  std::ostream& operator << (std::ostream& outstream, const Paths<T>& paths)
+  {
+    for (auto p : paths)
+      outstream << p;
+    return outstream;
+  }
+
+
+  template <typename T1, typename T2>
+  inline Path<T1> ScalePath(const Path<T2>& path, 
+    double scale_x, double scale_y, int& error_code)
+  {
+    Path<T1> result;
+    if (scale_x == 0 || scale_y == 0)
+    {
+      error_code |= scale_error_i;
+      DoError(scale_error_i);
+      // if no exception, treat as non-fatal error
+      if (scale_x == 0) scale_x = 1.0;
+      if (scale_y == 0) scale_y = 1.0;
+    }
+
+    result.reserve(path.size());
+#ifdef USINGZ
+    std::transform(path.begin(), path.end(), back_inserter(result),
+      [scale_x, scale_y](const auto& pt) 
+      { return Point<T1>(pt.x * scale_x, pt.y * scale_y, pt.z); });
+#else
+    std::transform(path.begin(), path.end(), back_inserter(result),
+      [scale_x, scale_y](const auto& pt) 
+      { return Point<T1>(pt.x * scale_x, pt.y * scale_y); });
+#endif
+    return result;
+  }
+
+  template <typename T1, typename T2>
+  inline Path<T1> ScalePath(const Path<T2>& path, 
+    double scale, int& error_code)
+  {
+    return ScalePath<T1, T2>(path, scale, scale, error_code);
+  }
+
+  template <typename T1, typename T2>
+  inline Paths<T1> ScalePaths(const Paths<T2>& paths, 
+    double scale_x, double scale_y, int& error_code)
+  {
+    Paths<T1> result;
+
+    if constexpr (std::numeric_limits<T1>::is_integer &&
+      !std::numeric_limits<T2>::is_integer)
+    {
+      RectD r = GetBounds(paths);
+      if ((r.left * scale_x) < min_coord ||
+        (r.right * scale_x) > max_coord ||
+        (r.top * scale_y) < min_coord ||
+        (r.bottom * scale_y) > max_coord)
+      { 
+        error_code |= range_error_i;
+        DoError(range_error_i);
+        return result; // empty path
+      }
+    }
+
+    result.reserve(paths.size());
+    std::transform(paths.begin(), paths.end(), back_inserter(result),
+      [=, &error_code](const auto& path)
+      { return ScalePath<T1, T2>(path, scale_x, scale_y, error_code); });
+    return result;
+  }
+
+  template <typename T1, typename T2>
+  inline Paths<T1> ScalePaths(const Paths<T2>& paths, 
+    double scale, int& error_code)
+  {
+    return ScalePaths<T1, T2>(paths, scale, scale, error_code);
+  }
+
+  template <typename T1, typename T2>
+  inline Path<T1> TransformPath(const Path<T2>& path)
+  {
+    Path<T1> result;
+    result.reserve(path.size());
+    std::transform(path.cbegin(), path.cend(), std::back_inserter(result),
+      [](const Point<T2>& pt) {return Point<T1>(pt); });
+    return result;
+  }
+
+  template <typename T1, typename T2>
+  inline Paths<T1> TransformPaths(const Paths<T2>& paths)
+  {
+    Paths<T1> result;
+    std::transform(paths.cbegin(), paths.cend(), std::back_inserter(result),
+      [](const Path<T2>& path) {return TransformPath<T1, T2>(path); });
+    return result;
+  }
+
+  inline PathD Path64ToPathD(const Path64& path)
+  {
+    return TransformPath<double, int64_t>(path);
+  }
+
+  inline PathsD Paths64ToPathsD(const Paths64& paths)
+  {
+    return TransformPaths<double, int64_t>(paths);
+  }
+
+  inline Path64 PathDToPath64(const PathD& path)
+  {
+    return TransformPath<int64_t, double>(path);
+  }
+
+  inline Paths64 PathsDToPaths64(const PathsD& paths)
+  {
+    return TransformPaths<int64_t, double>(paths);
+  }
+
+  template<typename T>
+  inline double Sqr(T val)
+  {
+    return static_cast<double>(val) * static_cast<double>(val);
+  }
+
+  template<typename T>
+  inline bool NearEqual(const Point<T>& p1,
+    const Point<T>& p2, double max_dist_sqrd)
+  {
+    return Sqr(p1.x - p2.x) + Sqr(p1.y - p2.y) < max_dist_sqrd;
+  }
+
+  template<typename T>
+  inline Path<T> StripNearEqual(const Path<T>& path,
+    double max_dist_sqrd, bool is_closed_path)
+  {
+    if (path.size() == 0) return Path<T>();
+    Path<T> result;
+    result.reserve(path.size());
+    typename Path<T>::const_iterator path_iter = path.cbegin();
+    Point<T> first_pt = *path_iter++, last_pt = first_pt;
+    result.push_back(first_pt);
+    for (; path_iter != path.cend(); ++path_iter)
+    {
+      if (!NearEqual(*path_iter, last_pt, max_dist_sqrd))
+      {
+        last_pt = *path_iter;
+        result.push_back(last_pt);
+      }
+    }
+    if (!is_closed_path) return result;
+    while (result.size() > 1 &&
+      NearEqual(result.back(), first_pt, max_dist_sqrd)) result.pop_back();
+    return result;
+  }
+
+  template<typename T>
+  inline Paths<T> StripNearEqual(const Paths<T>& paths,
+    double max_dist_sqrd, bool is_closed_path)
+  {
+    Paths<T> result;
+    result.reserve(paths.size());
+    for (typename Paths<T>::const_iterator paths_citer = paths.cbegin();
+      paths_citer != paths.cend(); ++paths_citer)
+    {
+      result.push_back(StripNearEqual(*paths_citer, max_dist_sqrd, is_closed_path));
+    }
+    return result;
+  }
+
+  template<typename T>
+  inline Path<T> StripDuplicates(const Path<T>& path, bool is_closed_path)
+  {
+    if (path.size() == 0) return Path<T>();
+    Path<T> result;
+    result.reserve(path.size());
+    typename Path<T>::const_iterator path_iter = path.cbegin();
+    Point<T> first_pt = *path_iter++, last_pt = first_pt;
+    result.push_back(first_pt);
+    for (; path_iter != path.cend(); ++path_iter)
+    {
+      if (*path_iter != last_pt)
+      {
+        last_pt = *path_iter;
+        result.push_back(last_pt);
+      }
+    }
+    if (!is_closed_path) return result;
+    while (result.size() > 1 && result.back() == first_pt) result.pop_back();
+    return result;
+  }
+
+  template<typename T>
+  inline Paths<T> StripDuplicates(const Paths<T>& paths, bool is_closed_path)
+  {
+    Paths<T> result;
+    result.reserve(paths.size());
+    for (typename Paths<T>::const_iterator paths_citer = paths.cbegin();
+      paths_citer != paths.cend(); ++paths_citer)
+    {
+      result.push_back(StripDuplicates(*paths_citer, is_closed_path));
+    }
+    return result;
+  }
+
+  // Miscellaneous ------------------------------------------------------------
+
+  inline void CheckPrecision(int& precision, int& error_code)
+  {
+    if (precision >= -8 && precision <= 8) return;
+    error_code |= precision_error_i; // non-fatal error
+    DoError(precision_error_i);      // unless exceptions enabled
+    precision = precision > 8 ? 8 : -8;
+  }
+
+  inline void CheckPrecision(int& precision)
+  {
+    int error_code = 0;
+    CheckPrecision(precision, error_code);
+  }
+
+  template <typename T>
+  inline double CrossProduct(const Point<T>& pt1, const Point<T>& pt2, const Point<T>& pt3) {
+    return (static_cast<double>(pt2.x - pt1.x) * static_cast<double>(pt3.y -
+      pt2.y) - static_cast<double>(pt2.y - pt1.y) * static_cast<double>(pt3.x - pt2.x));
+  }
+
+  template <typename T>
+  inline double CrossProduct(const Point<T>& vec1, const Point<T>& vec2)
+  {
+    return static_cast<double>(vec1.y * vec2.x) - static_cast<double>(vec2.y * vec1.x);
+  }
+
+  template <typename T>
+  inline double DotProduct(const Point<T>& pt1, const Point<T>& pt2, const Point<T>& pt3) {
+    return (static_cast<double>(pt2.x - pt1.x) * static_cast<double>(pt3.x - pt2.x) +
+      static_cast<double>(pt2.y - pt1.y) * static_cast<double>(pt3.y - pt2.y));
+  }
+
+  template <typename T>
+  inline double DotProduct(const Point<T>& vec1, const Point<T>& vec2)
+  {
+    return static_cast<double>(vec1.x * vec2.x) + static_cast<double>(vec1.y * vec2.y);
+  }
+
+  template <typename T>
+  inline double DistanceSqr(const Point<T> pt1, const Point<T> pt2)
+  {
+    return Sqr(pt1.x - pt2.x) + Sqr(pt1.y - pt2.y);
+  }
+
+  template <typename T>
+  inline double DistanceFromLineSqrd(const Point<T>& pt, const Point<T>& ln1, const Point<T>& ln2)
+  {
+    //perpendicular distance of point (x³,y³) = (Ax³ + By³ + C)/Sqrt(A² + B²)
+    //see http://en.wikipedia.org/wiki/Perpendicular_distance
+    double A = static_cast<double>(ln1.y - ln2.y);
+    double B = static_cast<double>(ln2.x - ln1.x);
+    double C = A * ln1.x + B * ln1.y;
+    C = A * pt.x + B * pt.y - C;
+    return (C * C) / (A * A + B * B);
+  }
+
+  template <typename T>
+  inline double Area(const Path<T>& path)
+  {
+    size_t cnt = path.size();
+    if (cnt < 3) return 0.0;
+    double a = 0.0;
+    typename Path<T>::const_iterator it1, it2 = path.cend() - 1, stop = it2;
+    if (!(cnt & 1)) ++stop;
+    for (it1 = path.cbegin(); it1 != stop;)
+    {
+      a += static_cast<double>(it2->y + it1->y) * (it2->x - it1->x);
+      it2 = it1 + 1;
+      a += static_cast<double>(it1->y + it2->y) * (it1->x - it2->x);
+      it1 += 2;
+    }
+    if (cnt & 1)
+      a += static_cast<double>(it2->y + it1->y) * (it2->x - it1->x);
+    return a * 0.5;
+  }
+
+  template <typename T>
+  inline double Area(const Paths<T>& paths)
+  {
+    double a = 0.0;
+    for (typename Paths<T>::const_iterator paths_iter = paths.cbegin();
+      paths_iter != paths.cend(); ++paths_iter)
+    {
+      a += Area<T>(*paths_iter);
+    }
+    return a;
+  }
+
+  template <typename T>
+  inline bool IsPositive(const Path<T>& poly)
+  {
+    // A curve has positive orientation [and area] if a region 'R' 
+    // is on the left when traveling around the outside of 'R'.
+    //https://mathworld.wolfram.com/CurveOrientation.html
+    //nb: This statement is premised on using Cartesian coordinates
+    return Area<T>(poly) >= 0;
+  }
+
+  inline int64_t CheckCastInt64(double val)
+  {
+    if ((val >= max_coord) || (val <= min_coord)) return INVALID;
+    else return static_cast<int64_t>(val);
+  }
+
+  inline bool GetIntersectPoint(const Point64& ln1a, const Point64& ln1b,
+    const Point64& ln2a, const Point64& ln2b, Point64& ip)
+  {  
+    // https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
+
+    double dx1 = static_cast<double>(ln1b.x - ln1a.x);
+    double dy1 = static_cast<double>(ln1b.y - ln1a.y);
+    double dx2 = static_cast<double>(ln2b.x - ln2a.x);
+    double dy2 = static_cast<double>(ln2b.y - ln2a.y);
+    double det = dy1 * dx2 - dy2 * dx1;
+    if (det == 0.0) return 0;
+    double qx = dx1 * ln1a.y - dy1 * ln1a.x;
+    double qy = dx2 * ln2a.y - dy2 * ln2a.x;
+    ip.x = CheckCastInt64((dx1 * qy - dx2 * qx) / det);
+    ip.y = CheckCastInt64((dy1 * qy - dy2 * qx) / det);
+    return (ip.x != INVALID && ip.y != INVALID);
+  }
+
+  inline bool SegmentsIntersect(const Point64& seg1a, const Point64& seg1b,
+    const Point64& seg2a, const Point64& seg2b, bool inclusive = false)
+  {
+    if (inclusive)
+    {
+      double res1 = CrossProduct(seg1a, seg2a, seg2b);
+      double res2 = CrossProduct(seg1b, seg2a, seg2b);
+      if (res1 * res2 > 0) return false;
+      double res3 = CrossProduct(seg2a, seg1a, seg1b);
+      double res4 = CrossProduct(seg2b, seg1a, seg1b);
+      if (res3 * res4 > 0) return false;
+      return (res1 || res2 || res3 || res4); // ensures not collinear
+    }
+    else {
+      return (CrossProduct(seg1a, seg2a, seg2b) *
+        CrossProduct(seg1b, seg2a, seg2b) < 0) &&
+        (CrossProduct(seg2a, seg1a, seg1b) *
+          CrossProduct(seg2b, seg1a, seg1b) < 0);
+    }
+  }
+
+  inline Point64 GetClosestPointOnSegment(const Point64& offPt,
+    const Point64& seg1, const Point64& seg2)
+  {
+    if (seg1.x == seg2.x && seg1.y == seg2.y) return seg1;
+    double dx = static_cast<double>(seg2.x - seg1.x);
+    double dy = static_cast<double>(seg2.y - seg1.y);
+    double q =
+      (static_cast<double>(offPt.x - seg1.x) * dx +
+        static_cast<double>(offPt.y - seg1.y) * dy) /
+      (Sqr(dx) + Sqr(dy));
+    if (q < 0) q = 0; else if (q > 1) q = 1;
+    return Point64(
+      seg1.x + static_cast<int64_t>(nearbyint(q * dx)),
+      seg1.y + static_cast<int64_t>(nearbyint(q * dy)));
+  }
+
+  enum class PointInPolygonResult { IsOn, IsInside, IsOutside };
+
+  template <typename T>
+  inline PointInPolygonResult PointInPolygon(const Point<T>& pt, const Path<T>& polygon)
+  {
+    if (polygon.size() < 3)
+      return PointInPolygonResult::IsOutside;
+
+    int val = 0;
+    typename Path<T>::const_iterator cbegin = polygon.cbegin(), first = cbegin, curr, prev;
+    typename Path<T>::const_iterator cend = polygon.cend();
+
+    while (first != cend && first->y == pt.y) ++first;
+    if (first == cend) // not a proper polygon
+      return PointInPolygonResult::IsOutside;
+
+    bool is_above = first->y < pt.y, starting_above = is_above;
+    curr = first +1; 
+    while (true)
+    {
+      if (curr == cend)
+      {
+        if (cend == first || first == cbegin) break;
+        cend = first;
+        curr = cbegin;
+      }
+      
+      if (is_above)
+      {
+        while (curr != cend && curr->y < pt.y) ++curr;
+        if (curr == cend) continue;
+      }
+      else
+      {
+        while (curr != cend && curr->y > pt.y) ++curr;
+        if (curr == cend) continue;
+      }
+
+      if (curr == cbegin) 
+        prev = polygon.cend() - 1; //nb: NOT cend (since might equal first)
+      else  
+        prev = curr - 1;
+
+      if (curr->y == pt.y)
+      {
+        if (curr->x == pt.x || 
+          (curr->y == prev->y &&
+            ((pt.x < prev->x) != (pt.x < curr->x))))
+              return PointInPolygonResult::IsOn;
+        ++curr;
+        if (curr == first) break;
+        continue;
+      }
+
+      if (pt.x < curr->x && pt.x < prev->x)
+      {
+        // we're only interested in edges crossing on the left
+      }
+      else if (pt.x > prev->x && pt.x > curr->x)
+        val = 1 - val; // toggle val
+      else
+      {
+        double d = CrossProduct(*prev, *curr, pt);
+        if (d == 0) return PointInPolygonResult::IsOn;
+        if ((d < 0) == is_above) val = 1 - val;
+      }
+      is_above = !is_above;
+      ++curr;
+    }
+    
+    if (is_above != starting_above)
+    {
+      cend = polygon.cend();
+      if (curr == cend) curr = cbegin;
+      if (curr == cbegin) prev = cend - 1;
+      else prev = curr - 1;
+      double d = CrossProduct(*prev, *curr, pt);
+      if (d == 0) return PointInPolygonResult::IsOn;
+      if ((d < 0) == is_above) val = 1 - val;
+    }
+
+    return (val == 0) ?
+      PointInPolygonResult::IsOutside :
+      PointInPolygonResult::IsInside;
+  }
+
+}  // namespace
+
+#endif  // CLIPPER_CORE_H

thirdparty/clipper2/include/clipper2/clipper.engine.h

@@ -0,0 +1,610 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  26 March 2023                                                   *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2023                                         *
+* Purpose   :  This is the main polygon clipping module                        *
+* License   :  http://www.boost.org/LICENSE_1_0.txt                            *
+*******************************************************************************/
+
+#ifndef CLIPPER_ENGINE_H
+#define CLIPPER_ENGINE_H
+
+constexpr auto CLIPPER2_VERSION = "1.2.2";
+
+#include <cstdlib>
+#include <iostream>
+#include <queue>
+#include <vector>
+#include <functional>
+#include <numeric>
+#include <memory>
+
+#include "clipper.core.h"
+
+namespace Clipper2Lib {
+
+	struct Scanline;
+	struct IntersectNode;
+	struct Active;
+	struct Vertex;
+	struct LocalMinima;
+	struct OutRec;
+	struct HorzSegment;
+
+	//Note: all clipping operations except for Difference are commutative.
+	enum class ClipType { None, Intersection, Union, Difference, Xor };
+	
+	enum class PathType { Subject, Clip };
+	enum class JoinWith { None, Left, Right };
+
+	enum class VertexFlags : uint32_t {
+		None = 0, OpenStart = 1, OpenEnd = 2, LocalMax = 4, LocalMin = 8
+	};
+
+	constexpr enum VertexFlags operator &(enum VertexFlags a, enum VertexFlags b) 
+	{
+		return (enum VertexFlags)(uint32_t(a) & uint32_t(b));
+	}
+
+	constexpr enum VertexFlags operator |(enum VertexFlags a, enum VertexFlags b)
+	{
+		return (enum VertexFlags)(uint32_t(a) | uint32_t(b));
+	}
+
+	struct Vertex {
+		Point64 pt;
+		Vertex* next = nullptr;
+		Vertex* prev = nullptr;
+		VertexFlags flags = VertexFlags::None;
+	};
+
+	struct OutPt {
+		Point64 pt;
+		OutPt*	next = nullptr;
+		OutPt*	prev = nullptr;
+		OutRec* outrec;
+		HorzSegment* horz = nullptr;
+
+		OutPt(const Point64& pt_, OutRec* outrec_): pt(pt_), outrec(outrec_) {
+			next = this;
+			prev = this;
+		}
+	};
+
+	class PolyPath;
+	class PolyPath64;
+	class PolyPathD;
+	using PolyTree64 = PolyPath64;
+	using PolyTreeD = PolyPathD;
+
+	struct OutRec;
+	typedef std::vector<OutRec*> OutRecList;
+
+	//OutRec: contains a path in the clipping solution. Edges in the AEL will
+	//have OutRec pointers assigned when they form part of the clipping solution.
+	struct OutRec {
+		size_t idx = 0;
+		OutRec* owner = nullptr;
+		Active* front_edge = nullptr;
+		Active* back_edge = nullptr;
+		OutPt* pts = nullptr;
+		PolyPath* polypath = nullptr;
+		OutRecList* splits = nullptr;
+		Rect64 bounds = {};
+		Path64 path;
+		bool is_open = false;
+		bool horz_done = false;
+		~OutRec() { 
+			if (splits) delete splits;
+			// nb: don't delete the split pointers
+			// as these are owned by ClipperBase's outrec_list_
+		};
+	};
+
+	///////////////////////////////////////////////////////////////////
+	//Important: UP and DOWN here are premised on Y-axis positive down
+	//displays, which is the orientation used in Clipper's development.
+	///////////////////////////////////////////////////////////////////
+	
+	struct Active {
+		Point64 bot;
+		Point64 top;
+		int64_t curr_x = 0;		//current (updated at every new scanline)
+		double dx = 0.0;
+		int wind_dx = 1;			//1 or -1 depending on winding direction
+		int wind_cnt = 0;
+		int wind_cnt2 = 0;		//winding count of the opposite polytype
+		OutRec* outrec = nullptr;
+		//AEL: 'active edge list' (Vatti's AET - active edge table)
+		//     a linked list of all edges (from left to right) that are present
+		//     (or 'active') within the current scanbeam (a horizontal 'beam' that
+		//     sweeps from bottom to top over the paths in the clipping operation).
+		Active* prev_in_ael = nullptr;
+		Active* next_in_ael = nullptr;
+		//SEL: 'sorted edge list' (Vatti's ST - sorted table)
+		//     linked list used when sorting edges into their new positions at the
+		//     top of scanbeams, but also (re)used to process horizontals.
+		Active* prev_in_sel = nullptr;
+		Active* next_in_sel = nullptr;
+		Active* jump = nullptr;
+		Vertex* vertex_top = nullptr;
+		LocalMinima* local_min = nullptr;  // the bottom of an edge 'bound' (also Vatti)
+		bool is_left_bound = false;
+		JoinWith join_with = JoinWith::None;
+	};
+
+	struct LocalMinima {
+		Vertex* vertex;
+		PathType polytype;
+		bool is_open;
+		LocalMinima(Vertex* v, PathType pt, bool open) :
+			vertex(v), polytype(pt), is_open(open){}
+	};
+
+	struct IntersectNode {
+		Point64 pt;
+		Active* edge1;
+		Active* edge2;
+		IntersectNode() : pt(Point64(0,0)), edge1(NULL), edge2(NULL) {}
+			IntersectNode(Active* e1, Active* e2, Point64& pt_) :
+			pt(pt_), edge1(e1), edge2(e2) {}
+	};
+
+	struct HorzSegment {
+		OutPt* left_op;
+		OutPt* right_op = nullptr;
+		bool left_to_right = true;
+		HorzSegment() : left_op(nullptr) { }
+		explicit HorzSegment(OutPt* op) : left_op(op) { }
+	};
+
+	struct HorzJoin {
+		OutPt* op1 = nullptr;
+		OutPt* op2 = nullptr;
+		HorzJoin() {};
+		explicit HorzJoin(OutPt* ltr, OutPt* rtl) : op1(ltr), op2(rtl) { }
+	};
+
+#ifdef USINGZ
+		typedef std::function<void(const Point64& e1bot, const Point64& e1top,
+		const Point64& e2bot, const Point64& e2top, Point64& pt)> ZCallback64;
+
+	typedef std::function<void(const PointD& e1bot, const PointD& e1top,
+		const PointD& e2bot, const PointD& e2top, PointD& pt)> ZCallbackD;
+#endif
+
+	typedef std::vector<HorzSegment> HorzSegmentList;
+	typedef std::unique_ptr<LocalMinima> LocalMinima_ptr;
+	typedef std::vector<LocalMinima_ptr> LocalMinimaList;
+	typedef std::vector<IntersectNode> IntersectNodeList;
+
+	// ClipperBase -------------------------------------------------------------
+
+	class ClipperBase {
+	private:
+		ClipType cliptype_ = ClipType::None;
+		FillRule fillrule_ = FillRule::EvenOdd;
+		FillRule fillpos = FillRule::Positive;
+		int64_t bot_y_ = 0;
+		bool minima_list_sorted_ = false;
+		bool using_polytree_ = false;
+		Active* actives_ = nullptr;
+		Active *sel_ = nullptr;
+		LocalMinimaList minima_list_;		//pointers in case of memory reallocs
+		LocalMinimaList::iterator current_locmin_iter_;
+		std::vector<Vertex*> vertex_lists_;
+		std::priority_queue<int64_t> scanline_list_;
+		IntersectNodeList intersect_nodes_;
+    HorzSegmentList horz_seg_list_;
+		std::vector<HorzJoin> horz_join_list_;
+		void Reset();
+		inline void InsertScanline(int64_t y);
+		inline bool PopScanline(int64_t &y);
+		inline bool PopLocalMinima(int64_t y, LocalMinima*& local_minima);
+		void DisposeAllOutRecs();
+		void DisposeVerticesAndLocalMinima();
+		void DeleteEdges(Active*& e);
+		inline void AddLocMin(Vertex &vert, PathType polytype, bool is_open);
+		bool IsContributingClosed(const Active &e) const;
+		inline bool IsContributingOpen(const Active &e) const;
+		void SetWindCountForClosedPathEdge(Active &edge);
+		void SetWindCountForOpenPathEdge(Active &e);
+		void InsertLocalMinimaIntoAEL(int64_t bot_y);
+		void InsertLeftEdge(Active &e);
+		inline void PushHorz(Active &e);
+		inline bool PopHorz(Active *&e);
+		inline OutPt* StartOpenPath(Active &e, const Point64& pt);
+		inline void UpdateEdgeIntoAEL(Active *e);
+		OutPt* IntersectEdges(Active &e1, Active &e2, const Point64& pt);
+		inline void DeleteFromAEL(Active &e);
+		inline void AdjustCurrXAndCopyToSEL(const int64_t top_y);
+		void DoIntersections(const int64_t top_y);
+		void AddNewIntersectNode(Active &e1, Active &e2, const int64_t top_y);
+		bool BuildIntersectList(const int64_t top_y);
+		void ProcessIntersectList();
+		void SwapPositionsInAEL(Active& edge1, Active& edge2);
+		OutRec* NewOutRec();
+		OutPt* AddOutPt(const Active &e, const Point64& pt);
+		OutPt* AddLocalMinPoly(Active &e1, Active &e2, 
+			const Point64& pt, bool is_new = false);
+		OutPt* AddLocalMaxPoly(Active &e1, Active &e2, const Point64& pt);
+		void DoHorizontal(Active &horz);
+		bool ResetHorzDirection(const Active &horz, const Vertex* max_vertex,
+			int64_t &horz_left, int64_t &horz_right);
+		void DoTopOfScanbeam(const int64_t top_y);
+		Active *DoMaxima(Active &e);
+		void JoinOutrecPaths(Active &e1, Active &e2);
+		void CompleteSplit(OutPt* op1, OutPt* op2, OutRec& outrec);
+		void FixSelfIntersects(OutRec* outrec);
+		void DoSplitOp(OutRec* outRec, OutPt* splitOp);
+		
+		inline void AddTrialHorzJoin(OutPt* op);
+		void ConvertHorzSegsToJoins();
+		void ProcessHorzJoins();
+
+		void Split(Active& e, const Point64& pt);
+		inline void CheckJoinLeft(Active& e, 
+			const Point64& pt, bool check_curr_x = false);
+		inline void CheckJoinRight(Active& e,
+			const Point64& pt, bool check_curr_x = false);
+	protected:
+		int error_code_ = 0;
+		bool has_open_paths_ = false;
+		bool succeeded_ = true;
+		OutRecList outrec_list_; //pointers in case list memory reallocated
+		bool ExecuteInternal(ClipType ct, FillRule ft, bool use_polytrees);
+		void CleanCollinear(OutRec* outrec);
+		bool CheckBounds(OutRec* outrec);
+		void RecursiveCheckOwners(OutRec* outrec, PolyPath* polypath);
+		void DeepCheckOwners(OutRec* outrec, PolyPath* polypath);
+#ifdef USINGZ
+		ZCallback64 zCallback_ = nullptr;
+		void SetZ(const Active& e1, const Active& e2, Point64& pt);
+#endif
+		void CleanUp();  // unlike Clear, CleanUp preserves added paths
+		void AddPath(const Path64& path, PathType polytype, bool is_open);
+		void AddPaths(const Paths64& paths, PathType polytype, bool is_open);
+	public:
+		virtual ~ClipperBase();
+		int ErrorCode() { return error_code_; };
+		bool PreserveCollinear = true;
+		bool ReverseSolution = false;
+		void Clear();
+#ifdef USINGZ
+		int64_t DefaultZ = 0;
+#endif
+	};
+
+	// PolyPath / PolyTree --------------------------------------------------------
+
+	//PolyTree: is intended as a READ-ONLY data structure for CLOSED paths returned
+	//by clipping operations. While this structure is more complex than the
+	//alternative Paths structure, it does preserve path 'ownership' - ie those
+	//paths that contain (or own) other paths. This will be useful to some users.
+
+	class PolyPath {
+	protected:
+		PolyPath* parent_;
+	public:
+		PolyPath(PolyPath* parent = nullptr): parent_(parent){}
+		virtual ~PolyPath() {};
+		//https://en.cppreference.com/w/cpp/language/rule_of_three
+		PolyPath(const PolyPath&) = delete;
+		PolyPath& operator=(const PolyPath&) = delete;
+
+		unsigned Level() const
+		{
+			unsigned result = 0;
+			const PolyPath* p = parent_;
+			while (p) { ++result; p = p->parent_; }
+			return result;
+		}
+
+		virtual PolyPath* AddChild(const Path64& path) = 0;
+
+		virtual void Clear() = 0;
+		virtual size_t Count() const { return 0; }
+
+		const PolyPath* Parent() const { return parent_; }
+
+		bool IsHole() const 
+		{
+			unsigned lvl = Level();
+			//Even levels except level 0
+			return lvl && !(lvl & 1);
+		}		
+	};
+
+	typedef typename std::vector<std::unique_ptr<PolyPath64>> PolyPath64List;
+	typedef typename std::vector<std::unique_ptr<PolyPathD>>  PolyPathDList;
+
+	class PolyPath64 : public PolyPath {
+	private:
+		PolyPath64List childs_;
+		Path64 polygon_;
+	public:
+		explicit PolyPath64(PolyPath64* parent = nullptr) : PolyPath(parent) {}
+
+		~PolyPath64() {
+			childs_.resize(0);
+		}
+
+		const PolyPath64* operator [] (size_t index) const
+		{ 
+			return childs_[index].get(); 
+		} 
+
+		const PolyPath64* Child(size_t index) const
+		{
+			return childs_[index].get();
+		}
+
+		PolyPath64List::const_iterator begin() const { return childs_.cbegin(); }
+		PolyPath64List::const_iterator end() const { return childs_.cend(); }
+
+		PolyPath64* AddChild(const Path64& path) override
+		{
+			auto p = std::make_unique<PolyPath64>(this);
+			auto* result = childs_.emplace_back(std::move(p)).get();
+			result->polygon_ = path;
+			return result;
+		}
+
+		void Clear() override
+		{
+			childs_.resize(0);
+		}
+
+		size_t Count() const override
+		{
+			return childs_.size();
+		}
+
+		const Path64& Polygon() const { return polygon_; };
+
+		double Area() const
+		{
+			return std::accumulate(childs_.cbegin(), childs_.cend(),
+				Clipper2Lib::Area<int64_t>(polygon_),
+				[](double a, const auto& child) {return a + child->Area(); });
+		}
+
+	};
+
+	class PolyPathD : public PolyPath {
+	private:
+		PolyPathDList childs_;
+		double inv_scale_;
+		PathD polygon_;
+	public:
+		explicit PolyPathD(PolyPathD* parent = nullptr) : PolyPath(parent)
+		{
+			inv_scale_ = parent ? parent->inv_scale_ : 1.0;
+		}
+
+		~PolyPathD() {
+			childs_.resize(0);
+		}
+
+		const PolyPathD* operator [] (size_t index) const
+		{ 
+			return childs_[index].get();
+		}
+
+		const PolyPathD* Child(size_t index) const
+		{
+			return childs_[index].get();
+		}
+
+		PolyPathDList::const_iterator begin() const { return childs_.cbegin(); }
+		PolyPathDList::const_iterator end() const { return childs_.cend(); }
+
+		void SetInvScale(double value) { inv_scale_ = value; }
+		double InvScale() { return inv_scale_; }
+		PolyPathD* AddChild(const Path64& path) override
+		{
+			int error_code = 0;
+			auto p = std::make_unique<PolyPathD>(this);
+			PolyPathD* result = childs_.emplace_back(std::move(p)).get();
+			result->polygon_ = ScalePath<double, int64_t>(path, inv_scale_, error_code);
+			return result;
+		}
+
+		void Clear() override
+		{
+			childs_.resize(0);
+		}
+
+		size_t Count() const override
+		{
+			return childs_.size();
+		}
+
+		const PathD& Polygon() const { return polygon_; };
+
+		double Area() const
+		{
+			return std::accumulate(childs_.begin(), childs_.end(),
+				Clipper2Lib::Area<double>(polygon_),
+				[](double a, const auto& child) {return a + child->Area(); });
+		}
+	};
+
+	class Clipper64 : public ClipperBase
+	{
+	private:
+		void BuildPaths64(Paths64& solutionClosed, Paths64* solutionOpen);
+		void BuildTree64(PolyPath64& polytree, Paths64& open_paths);
+	public:
+#ifdef USINGZ
+		void SetZCallback(ZCallback64 cb) { zCallback_ = cb; }
+#endif
+
+		void AddSubject(const Paths64& subjects)
+		{
+			AddPaths(subjects, PathType::Subject, false);
+		}
+		void AddOpenSubject(const Paths64& open_subjects)
+		{
+			AddPaths(open_subjects, PathType::Subject, true);
+		}
+		void AddClip(const Paths64& clips)
+		{
+			AddPaths(clips, PathType::Clip, false);
+		}
+
+		bool Execute(ClipType clip_type,
+			FillRule fill_rule, Paths64& closed_paths)
+		{
+			Paths64 dummy;
+			return Execute(clip_type, fill_rule, closed_paths, dummy);
+		}
+
+		bool Execute(ClipType clip_type, FillRule fill_rule, 
+			Paths64& closed_paths, Paths64& open_paths)
+		{
+			closed_paths.clear();
+			open_paths.clear();
+			if (ExecuteInternal(clip_type, fill_rule, false))
+					BuildPaths64(closed_paths, &open_paths);
+			CleanUp();
+			return succeeded_;
+		}
+
+		bool Execute(ClipType clip_type, FillRule fill_rule, PolyTree64& polytree)
+		{
+			Paths64 dummy;
+			return Execute(clip_type, fill_rule, polytree, dummy);
+		}
+
+		bool Execute(ClipType clip_type,
+			FillRule fill_rule, PolyTree64& polytree, Paths64& open_paths)
+		{
+			if (ExecuteInternal(clip_type, fill_rule, true))
+			{
+				open_paths.clear();
+				polytree.Clear();
+				BuildTree64(polytree, open_paths);
+			}
+			CleanUp();
+			return succeeded_;
+		}
+	};
+
+	class ClipperD : public ClipperBase {
+	private:
+		double scale_ = 1.0, invScale_ = 1.0;
+#ifdef USINGZ
+		ZCallbackD zCallbackD_ = nullptr;
+#endif
+		void BuildPathsD(PathsD& solutionClosed, PathsD* solutionOpen);
+		void BuildTreeD(PolyPathD& polytree, PathsD& open_paths);
+	public:
+		explicit ClipperD(int precision = 2) : ClipperBase()
+		{
+			CheckPrecision(precision, error_code_);
+			// to optimize scaling / descaling precision
+			// set the scale to a power of double's radix (2) (#25)
+			scale_ = std::pow(std::numeric_limits<double>::radix,
+				std::ilogb(std::pow(10, precision)) + 1);
+			invScale_ = 1 / scale_;
+		}
+
+#ifdef USINGZ
+		void SetZCallback(ZCallbackD cb) { zCallbackD_ = cb; };
+
+		void ZCB(const Point64& e1bot, const Point64& e1top,
+			const Point64& e2bot, const Point64& e2top, Point64& pt)
+		{
+			// de-scale (x & y)
+			// temporarily convert integers to their initial float values
+			// this will slow clipping marginally but will make it much easier
+			// to understand the coordinates passed to the callback function
+			PointD tmp = PointD(pt) * invScale_;
+			PointD e1b = PointD(e1bot) * invScale_;
+			PointD e1t = PointD(e1top) * invScale_;
+			PointD e2b = PointD(e2bot) * invScale_;
+			PointD e2t = PointD(e2top) * invScale_;
+			zCallbackD_(e1b,e1t, e2b, e2t, tmp);
+			pt.z = tmp.z; // only update 'z'
+		};
+
+		void CheckCallback()
+		{
+			if(zCallbackD_)
+				// if the user defined float point callback has been assigned 
+				// then assign the proxy callback function
+				ClipperBase::zCallback_ = 
+					std::bind(&ClipperD::ZCB, this, std::placeholders::_1,
+					std::placeholders::_2, std::placeholders::_3,
+					std::placeholders::_4, std::placeholders::_5); 
+			else
+				ClipperBase::zCallback_ = nullptr;
+		}
+
+#endif
+
+		void AddSubject(const PathsD& subjects)
+		{
+			AddPaths(ScalePaths<int64_t, double>(subjects, scale_, error_code_), PathType::Subject, false);
+		}
+
+		void AddOpenSubject(const PathsD& open_subjects)
+		{
+			AddPaths(ScalePaths<int64_t, double>(open_subjects, scale_, error_code_), PathType::Subject, true);
+		}
+
+		void AddClip(const PathsD& clips)
+		{
+			AddPaths(ScalePaths<int64_t, double>(clips, scale_, error_code_), PathType::Clip, false);
+		}
+
+		bool Execute(ClipType clip_type, FillRule fill_rule, PathsD& closed_paths)
+		{
+			PathsD dummy;
+			return Execute(clip_type, fill_rule, closed_paths, dummy);
+		}
+
+		bool Execute(ClipType clip_type,
+			FillRule fill_rule, PathsD& closed_paths, PathsD& open_paths)
+		{
+#ifdef USINGZ
+			CheckCallback();
+#endif
+			if (ExecuteInternal(clip_type, fill_rule, false))
+			{
+				BuildPathsD(closed_paths, &open_paths);
+			}
+			CleanUp();
+			return succeeded_;
+		}
+
+		bool Execute(ClipType clip_type, FillRule fill_rule, PolyTreeD& polytree)
+		{
+			PathsD dummy;
+			return Execute(clip_type, fill_rule, polytree, dummy);
+		}
+
+		bool Execute(ClipType clip_type,
+			FillRule fill_rule, PolyTreeD& polytree, PathsD& open_paths)
+		{
+#ifdef USINGZ
+			CheckCallback();
+#endif
+			if (ExecuteInternal(clip_type, fill_rule, true))
+			{
+				polytree.Clear();
+				polytree.SetInvScale(invScale_);
+				open_paths.clear();
+				BuildTreeD(polytree, open_paths);
+			}
+			CleanUp();
+			return succeeded_;
+		}
+
+	};
+
+}  // namespace 
+
+#endif  // CLIPPER_ENGINE_H

thirdparty/clipper2/include/clipper2/clipper.export.h

@@ -0,0 +1,774 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  23 March 2023                                                   *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2023                                         *
+* Purpose   :  This module exports the Clipper2 Library (ie DLL/so)            *
+* License   :  http://www.boost.org/LICENSE_1_0.txt                            *
+*******************************************************************************/
+
+// The exported functions below refer to simple structures that
+// can be understood across multiple languages. Consequently
+// Path64, PathD, Polytree64 etc are converted from C++ classes
+// (std::vector<> etc) into the following data structures:
+//
+// CPath64 (int64_t*) & CPathD (double_t*):
+// Path64 and PathD are converted into arrays of x,y coordinates.
+// However in these arrays the first x,y coordinate pair is a
+// counter with 'x' containing the number of following coordinate
+// pairs. ('y' should be 0, with one exception explained below.)
+// __________________________________
+// |counter|coord1|coord2|...|coordN|
+// |N ,0   |x1, y1|x2, y2|...|xN, yN|
+// __________________________________
+//
+// CPaths64 (int64_t**) & CPathsD (double_t**):
+// These are arrays of pointers to CPath64 and CPathD where
+// the first pointer is to a 'counter path'. This 'counter
+// path' has a single x,y coord pair with 'y' (not 'x')
+// containing the number of paths that follow. ('x' = 0).
+// _______________________________
+// |counter|path1|path2|...|pathN|
+// |addr0  |addr1|addr2|...|addrN| (*addr0[0]=0; *addr0[1]=N)
+// _______________________________
+//
+// The structures of CPolytree64 and CPolytreeD are defined
+// below and these structures don't need to be explained here.
+
+#ifndef CLIPPER2_EXPORT_H
+#define CLIPPER2_EXPORT_H
+
+#include <cstdlib>
+#include <vector>
+
+#include "clipper2/clipper.core.h"
+#include "clipper2/clipper.engine.h"
+#include "clipper2/clipper.offset.h"
+#include "clipper2/clipper.rectclip.h"
+
+namespace Clipper2Lib {
+
+typedef int64_t* CPath64;
+typedef int64_t** CPaths64;
+typedef double* CPathD;
+typedef double** CPathsD;
+
+typedef struct CPolyPath64 {
+  CPath64       polygon;
+  uint32_t      is_hole;
+  uint32_t      child_count;
+  CPolyPath64*  childs;
+}
+CPolyTree64;
+
+typedef struct CPolyPathD {
+  CPathD        polygon;
+  uint32_t      is_hole;
+  uint32_t      child_count;
+  CPolyPathD*   childs;
+}
+CPolyTreeD;
+
+template <typename T>
+struct CRect {
+  T left;
+  T top;
+  T right;
+  T bottom;
+};
+
+typedef CRect<int64_t> CRect64;
+typedef CRect<double> CRectD;
+
+template <typename T>
+inline bool CRectIsEmpty(const CRect<T>& rect)
+{
+  return (rect.right <= rect.left) || (rect.bottom <= rect.top);
+}
+
+template <typename T>
+inline Rect<T> CRectToRect(const CRect<T>& rect)
+{
+  Rect<T> result;
+  result.left = rect.left;
+  result.top = rect.top;
+  result.right = rect.right;
+  result.bottom = rect.bottom;
+  return result;
+}
+
+#define EXTERN_DLL_EXPORT extern "C" __declspec(dllexport)
+
+//////////////////////////////////////////////////////
+// EXPORTED FUNCTION DEFINITIONS
+//////////////////////////////////////////////////////
+
+EXTERN_DLL_EXPORT const char* Version();
+
+// Some of the functions below will return data in the various CPath
+// and CPolyTree structures which are pointers to heap allocated
+// memory. Eventually this memory will need to be released with one
+// of the following 'DisposeExported' functions.  (This may be the
+// only safe way to release this memory since the executable
+// accessing these exported functions may use a memory manager that
+// allocates and releases heap memory in a different way. Also,
+// CPath structures that have been constructed by the executable
+// should not be destroyed using these 'DisposeExported' functions.)
+EXTERN_DLL_EXPORT void DisposeExportedCPath64(CPath64 p);
+EXTERN_DLL_EXPORT void DisposeExportedCPaths64(CPaths64& pp);
+EXTERN_DLL_EXPORT void DisposeExportedCPathD(CPathD p);
+EXTERN_DLL_EXPORT void DisposeExportedCPathsD(CPathsD& pp);
+EXTERN_DLL_EXPORT void DisposeExportedCPolyTree64(CPolyTree64*& cpt);
+EXTERN_DLL_EXPORT void DisposeExportedCPolyTreeD(CPolyTreeD*& cpt);
+
+// Boolean clipping:
+// cliptype: None=0, Intersection=1, Union=2, Difference=3, Xor=4
+// fillrule: EvenOdd=0, NonZero=1, Positive=2, Negative=3
+EXTERN_DLL_EXPORT int BooleanOp64(uint8_t cliptype,
+  uint8_t fillrule, const CPaths64 subjects,
+  const CPaths64 subjects_open, const CPaths64 clips,
+  CPaths64& solution, CPaths64& solution_open,
+  bool preserve_collinear = true, bool reverse_solution = false);
+EXTERN_DLL_EXPORT int BooleanOpPt64(uint8_t cliptype,
+  uint8_t fillrule, const CPaths64 subjects,
+  const CPaths64 subjects_open, const CPaths64 clips,
+  CPolyTree64*& solution, CPaths64& solution_open,
+  bool preserve_collinear = true, bool reverse_solution = false);
+EXTERN_DLL_EXPORT int BooleanOpD(uint8_t cliptype,
+  uint8_t fillrule, const CPathsD subjects,
+  const CPathsD subjects_open, const CPathsD clips,
+  CPathsD& solution, CPathsD& solution_open, int precision = 2,
+  bool preserve_collinear = true, bool reverse_solution = false);
+EXTERN_DLL_EXPORT int BooleanOpPtD(uint8_t cliptype,
+  uint8_t fillrule, const CPathsD subjects,
+  const CPathsD subjects_open, const CPathsD clips,
+  CPolyTreeD*& solution, CPathsD& solution_open, int precision = 2,
+  bool preserve_collinear = true, bool reverse_solution = false);
+
+// Polygon offsetting (inflate/deflate):
+// jointype: Square=0, Round=1, Miter=2
+// endtype: Polygon=0, Joined=1, Butt=2, Square=3, Round=4
+EXTERN_DLL_EXPORT CPaths64 InflatePaths64(const CPaths64 paths,
+  double delta, uint8_t jointype, uint8_t endtype, 
+  double miter_limit = 2.0, double arc_tolerance = 0.0, 
+  bool reverse_solution = false);
+EXTERN_DLL_EXPORT CPathsD InflatePathsD(const CPathsD paths,
+  double delta, uint8_t jointype, uint8_t endtype,
+  int precision = 2, double miter_limit = 2.0,
+  double arc_tolerance = 0.0, bool reverse_solution = false);
+
+// ExecuteRectClip & ExecuteRectClipLines:
+EXTERN_DLL_EXPORT CPaths64 ExecuteRectClip64(const CRect64& rect,
+  const CPaths64 paths, bool convex_only = false);
+EXTERN_DLL_EXPORT CPathsD ExecuteRectClipD(const CRectD& rect,
+  const CPathsD paths, int precision = 2, bool convex_only = false);
+EXTERN_DLL_EXPORT CPaths64 ExecuteRectClipLines64(const CRect64& rect,
+  const CPaths64 paths);
+EXTERN_DLL_EXPORT CPathsD ExecuteRectClipLinesD(const CRectD& rect,
+  const CPathsD paths, int precision = 2);
+
+//////////////////////////////////////////////////////
+// INTERNAL FUNCTIONS
+//////////////////////////////////////////////////////
+
+inline CPath64 CreateCPath64(size_t cnt1, size_t cnt2);
+inline CPath64 CreateCPath64(const Path64& p);
+inline CPaths64 CreateCPaths64(const Paths64& pp);
+inline Path64 ConvertCPath64(const CPath64& p);
+inline Paths64 ConvertCPaths64(const CPaths64& pp);
+
+inline CPathD CreateCPathD(size_t cnt1, size_t cnt2);
+inline CPathD CreateCPathD(const PathD& p);
+inline CPathsD CreateCPathsD(const PathsD& pp);
+inline PathD ConvertCPathD(const CPathD& p);
+inline PathsD ConvertCPathsD(const CPathsD& pp);
+
+// the following function avoid multiple conversions
+inline CPathD CreateCPathD(const Path64& p, double scale);
+inline CPathsD CreateCPathsD(const Paths64& pp, double scale);
+inline Path64 ConvertCPathD(const CPathD& p, double scale);
+inline Paths64 ConvertCPathsD(const CPathsD& pp, double scale);
+
+inline CPolyTree64* CreateCPolyTree64(const PolyTree64& pt);
+inline CPolyTreeD* CreateCPolyTreeD(const PolyTree64& pt, double scale);
+
+EXTERN_DLL_EXPORT const char* Version()
+{
+  return CLIPPER2_VERSION;
+}
+
+EXTERN_DLL_EXPORT void DisposeExportedCPath64(CPath64 p)
+{
+  if (p) delete[] p;
+}
+
+EXTERN_DLL_EXPORT void DisposeExportedCPaths64(CPaths64& pp)
+{
+  if (!pp) return;
+  CPaths64 v = pp;
+  CPath64 cnts = *v;
+  const size_t cnt = static_cast<size_t>(cnts[1]);
+  for (size_t i = 0; i <= cnt; ++i) //nb: cnt +1
+    DisposeExportedCPath64(*v++);
+  delete[] pp;
+  pp = nullptr;
+}
+
+EXTERN_DLL_EXPORT void DisposeExportedCPathD(CPathD p)
+{
+  if (p) delete[] p;
+}
+
+EXTERN_DLL_EXPORT void DisposeExportedCPathsD(CPathsD& pp)
+{
+  if (!pp) return;
+  CPathsD v = pp;
+  CPathD cnts = *v;
+  size_t cnt = static_cast<size_t>(cnts[1]);
+  for (size_t i = 0; i <= cnt; ++i) //nb: cnt +1
+    DisposeExportedCPathD(*v++);
+  delete[] pp;
+  pp = nullptr;
+}
+
+EXTERN_DLL_EXPORT int BooleanOp64(uint8_t cliptype, 
+  uint8_t fillrule, const CPaths64 subjects,
+  const CPaths64 subjects_open, const CPaths64 clips,
+  CPaths64& solution, CPaths64& solution_open,
+  bool preserve_collinear, bool reverse_solution)
+{
+  if (cliptype > static_cast<uint8_t>(ClipType::Xor)) return -4;
+  if (fillrule > static_cast<uint8_t>(FillRule::Negative)) return -3;
+  
+  Paths64 sub, sub_open, clp, sol, sol_open;
+  sub       = ConvertCPaths64(subjects);
+  sub_open  = ConvertCPaths64(subjects_open);
+  clp       = ConvertCPaths64(clips);
+
+  Clipper64 clipper;
+  clipper.PreserveCollinear = preserve_collinear;
+  clipper.ReverseSolution = reverse_solution;
+  if (sub.size() > 0) clipper.AddSubject(sub);
+  if (sub_open.size() > 0) clipper.AddOpenSubject(sub_open);
+  if (clp.size() > 0) clipper.AddClip(clp);
+  if (!clipper.Execute(ClipType(cliptype), FillRule(fillrule), sol, sol_open)) 
+    return -1; // clipping bug - should never happen :)
+  solution = CreateCPaths64(sol);
+  solution_open = CreateCPaths64(sol_open);
+  return 0; //success !!
+}
+
+EXTERN_DLL_EXPORT int BooleanOpPt64(uint8_t cliptype,
+  uint8_t fillrule, const CPaths64 subjects,
+  const CPaths64 subjects_open, const CPaths64 clips,
+  CPolyTree64*& solution, CPaths64& solution_open,
+  bool preserve_collinear, bool reverse_solution)
+{
+  if (cliptype > static_cast<uint8_t>(ClipType::Xor)) return -4;
+  if (fillrule > static_cast<uint8_t>(FillRule::Negative)) return -3;
+  Paths64 sub, sub_open, clp, sol_open;
+  sub = ConvertCPaths64(subjects);
+  sub_open = ConvertCPaths64(subjects_open);
+  clp = ConvertCPaths64(clips);
+
+  PolyTree64 pt;
+  Clipper64 clipper;
+  clipper.PreserveCollinear = preserve_collinear;
+  clipper.ReverseSolution = reverse_solution;
+  if (sub.size() > 0) clipper.AddSubject(sub);
+  if (sub_open.size() > 0) clipper.AddOpenSubject(sub_open);
+  if (clp.size() > 0) clipper.AddClip(clp);
+  if (!clipper.Execute(ClipType(cliptype), FillRule(fillrule), pt, sol_open))
+    return -1; // clipping bug - should never happen :)
+
+  solution = CreateCPolyTree64(pt);
+  solution_open = CreateCPaths64(sol_open);
+  return 0; //success !!
+}
+
+EXTERN_DLL_EXPORT int BooleanOpD(uint8_t cliptype,
+  uint8_t fillrule, const CPathsD subjects,
+  const CPathsD subjects_open, const CPathsD clips,
+  CPathsD& solution, CPathsD& solution_open, int precision,
+  bool preserve_collinear, bool reverse_solution)
+{
+  if (precision < -8 || precision > 8) return -5;
+  if (cliptype > static_cast<uint8_t>(ClipType::Xor)) return -4;
+  if (fillrule > static_cast<uint8_t>(FillRule::Negative)) return -3;
+  const double scale = std::pow(10, precision);
+
+  Paths64 sub, sub_open, clp, sol, sol_open;
+  sub       = ConvertCPathsD(subjects, scale);
+  sub_open  = ConvertCPathsD(subjects_open, scale);
+  clp       = ConvertCPathsD(clips, scale);
+
+  Clipper64 clipper;
+  clipper.PreserveCollinear = preserve_collinear;
+  clipper.ReverseSolution = reverse_solution;
+  if (sub.size() > 0) clipper.AddSubject(sub);
+  if (sub_open.size() > 0)
+    clipper.AddOpenSubject(sub_open);
+  if (clp.size() > 0) clipper.AddClip(clp);
+  if (!clipper.Execute(ClipType(cliptype),
+    FillRule(fillrule), sol, sol_open)) return -1;
+
+  if (sol.size() > 0) solution = CreateCPathsD(sol, 1 / scale);
+  if (sol_open.size() > 0)
+    solution_open = CreateCPathsD(sol_open, 1 / scale);
+  return 0;
+}
+
+EXTERN_DLL_EXPORT int BooleanOpPtD(uint8_t cliptype,
+  uint8_t fillrule, const CPathsD subjects,
+  const CPathsD subjects_open, const CPathsD clips,
+  CPolyTreeD*& solution, CPathsD& solution_open, int precision,
+  bool preserve_collinear, bool reverse_solution)
+{
+  if (precision < -8 || precision > 8) return -5;
+  if (cliptype > static_cast<uint8_t>(ClipType::Xor)) return -4;
+  if (fillrule > static_cast<uint8_t>(FillRule::Negative)) return -3;
+  
+  const double scale = std::pow(10, precision);
+  Paths64 sub, sub_open, clp, sol_open;
+  sub       = ConvertCPathsD(subjects, scale);
+  sub_open  = ConvertCPathsD(subjects_open, scale);
+  clp       = ConvertCPathsD(clips, scale);
+
+  PolyTree64 sol;
+  Clipper64 clipper;
+  clipper.PreserveCollinear = preserve_collinear;
+  clipper.ReverseSolution = reverse_solution;
+  if (sub.size() > 0) clipper.AddSubject(sub);
+  if (sub_open.size() > 0)
+    clipper.AddOpenSubject(sub_open);
+  if (clp.size() > 0) clipper.AddClip(clp);
+  if (!clipper.Execute(ClipType(cliptype),
+    FillRule(fillrule), sol, sol_open)) return -1;
+
+  solution = CreateCPolyTreeD(sol, 1 / scale);
+  if (sol_open.size() > 0)
+    solution_open = CreateCPathsD(sol_open, 1 / scale);
+  return 0;
+}
+
+EXTERN_DLL_EXPORT CPaths64 InflatePaths64(const CPaths64 paths,
+  double delta, uint8_t jointype, uint8_t endtype, double miter_limit,
+  double arc_tolerance, bool reverse_solution)
+{
+  Paths64 pp;
+  pp = ConvertCPaths64(paths);
+
+  ClipperOffset clip_offset( miter_limit, 
+    arc_tolerance, reverse_solution);
+  clip_offset.AddPaths(pp, JoinType(jointype), EndType(endtype));
+  Paths64 result; 
+  clip_offset.Execute(delta, result);
+  return CreateCPaths64(result);
+}
+
+EXTERN_DLL_EXPORT CPathsD InflatePathsD(const CPathsD paths,
+  double delta, uint8_t jointype, uint8_t endtype,
+  int precision, double miter_limit,
+  double arc_tolerance, bool reverse_solution)
+{
+  if (precision < -8 || precision > 8 || !paths) return nullptr;
+  const double scale = std::pow(10, precision);
+  ClipperOffset clip_offset(miter_limit, arc_tolerance, reverse_solution);
+  Paths64 pp = ConvertCPathsD(paths, scale);
+  clip_offset.AddPaths(pp, JoinType(jointype), EndType(endtype));
+  Paths64 result;
+  clip_offset.Execute(delta * scale, result);
+  return CreateCPathsD(result, 1/scale);
+}
+
+EXTERN_DLL_EXPORT CPaths64 ExecuteRectClip64(const CRect64& rect,
+  const CPaths64 paths, bool convex_only)
+{
+  if (CRectIsEmpty(rect) || !paths) return nullptr;
+  Rect64 r64 = CRectToRect(rect);
+  class RectClip rc(r64);
+  Paths64 pp = ConvertCPaths64(paths);
+  Paths64 result = rc.Execute(pp, convex_only);
+  return CreateCPaths64(result);
+}
+
+EXTERN_DLL_EXPORT CPathsD ExecuteRectClipD(const CRectD& rect,
+  const CPathsD paths, int precision, bool convex_only)
+{
+  if (CRectIsEmpty(rect) || !paths) return nullptr;
+  if (precision < -8 || precision > 8) return nullptr;
+  const double scale = std::pow(10, precision);
+
+  RectD r = CRectToRect(rect);
+  Rect64 rec = ScaleRect<int64_t, double>(r, scale);
+  Paths64 pp = ConvertCPathsD(paths, scale);
+  class RectClip rc(rec);
+  Paths64 result = rc.Execute(pp, convex_only);
+  return CreateCPathsD(result, 1/scale);
+}
+
+EXTERN_DLL_EXPORT CPaths64 ExecuteRectClipLines64(const CRect64& rect,
+  const CPaths64 paths)
+{
+  if (CRectIsEmpty(rect) || !paths) return nullptr;
+  Rect64 r = CRectToRect(rect);
+  class RectClipLines rcl (r);
+  Paths64 pp = ConvertCPaths64(paths);
+  Paths64 result = rcl.Execute(pp);
+  return CreateCPaths64(result);
+}
+
+EXTERN_DLL_EXPORT CPathsD ExecuteRectClipLinesD(const CRectD& rect,
+  const CPathsD paths, int precision)
+{
+  if (CRectIsEmpty(rect) || !paths) return nullptr;
+  if (precision < -8 || precision > 8) return nullptr;
+  const double scale = std::pow(10, precision);
+  Rect64 r = ScaleRect<int64_t, double>(CRectToRect(rect), scale);
+  class RectClipLines rcl(r);
+  Paths64 pp = ConvertCPathsD(paths, scale);
+  Paths64 result = rcl.Execute(pp);
+  return CreateCPathsD(result, 1/scale);
+}
+
+inline CPath64 CreateCPath64(size_t cnt1, size_t cnt2)
+{
+  // allocates memory for CPath64, fills in the counter, and
+  // returns the structure ready to be filled with path data
+  CPath64 result = new int64_t[2 + cnt1 *2];
+  result[0] = cnt1;
+  result[1] = cnt2;
+  return result;
+}
+
+inline CPath64 CreateCPath64(const Path64& p)
+{
+  // allocates memory for CPath64, fills the counter
+  // and returns the memory filled with path data
+  size_t cnt = p.size();
+  if (!cnt) return nullptr;
+  CPath64 result = CreateCPath64(cnt, 0);
+  CPath64 v = result;
+  v += 2; // skip counters
+  for (const Point64& pt : p)
+  {
+    *v++ = pt.x;
+    *v++ = pt.y;
+  }
+  return result;
+}
+
+inline Path64 ConvertCPath64(const CPath64& p)
+{
+  Path64 result;
+  if (p && *p)
+  {
+    CPath64 v = p;
+    const size_t cnt = static_cast<size_t>(p[0]);
+    v += 2; // skip counters
+    result.reserve(cnt);
+    for (size_t i = 0; i < cnt; ++i)
+    {
+      // x,y here avoids right to left function evaluation
+      // result.push_back(Point64(*v++, *v++));
+      int64_t x = *v++;
+      int64_t y = *v++;
+      result.push_back(Point64(x, y));
+    }
+  }
+  return result;
+}
+
+inline CPaths64 CreateCPaths64(const Paths64& pp)
+{
+  // allocates memory for multiple CPath64 and
+  // and returns this memory filled with path data
+  size_t cnt = pp.size(), cnt2 = cnt;
+
+  // don't allocate space for empty paths
+  for (size_t i = 0; i < cnt; ++i)
+    if (!pp[i].size()) --cnt2;
+  if (!cnt2) return nullptr;
+
+  CPaths64 result = new int64_t* [cnt2 + 1];
+  CPaths64 v = result;
+  *v++ = CreateCPath64(0, cnt2); // assign a counter path
+  for (const Path64& p : pp)
+  {
+    *v = CreateCPath64(p);
+    if (*v) ++v;
+  }
+  return result;
+}
+
+inline Paths64 ConvertCPaths64(const CPaths64& pp)
+{
+  Paths64 result;
+  if (pp) 
+  {
+    CPaths64 v = pp;
+    CPath64 cnts = pp[0];
+    const size_t cnt = static_cast<size_t>(cnts[1]); // nb 2nd cnt
+    ++v; // skip cnts
+    result.reserve(cnt);
+    for (size_t i = 0; i < cnt; ++i)
+      result.push_back(ConvertCPath64(*v++));
+  }
+  return result;
+}
+
+inline CPathD CreateCPathD(size_t cnt1, size_t cnt2)
+{
+  // allocates memory for CPathD, fills in the counter, and
+  // returns the structure ready to be filled with path data
+  CPathD result = new double[2 + cnt1 * 2];
+  result[0] = static_cast<double>(cnt1);
+  result[1] = static_cast<double>(cnt2);
+  return result;
+}
+
+inline CPathD CreateCPathD(const PathD& p)
+{
+  // allocates memory for CPath, fills the counter
+  // and returns the memory fills with path data
+  size_t cnt = p.size();
+  if (!cnt) return nullptr; 
+  CPathD result = CreateCPathD(cnt, 0);
+  CPathD v = result;
+  v += 2; // skip counters
+  for (const PointD& pt : p)
+  {
+    *v++ = pt.x;
+    *v++ = pt.y;
+  }
+  return result;
+}
+
+inline PathD ConvertCPathD(const CPathD& p)
+{
+  PathD result;
+  if (p)
+  {
+    CPathD v = p;
+    size_t cnt = static_cast<size_t>(v[0]);
+    v += 2; // skip counters
+    result.reserve(cnt);
+    for (size_t i = 0; i < cnt; ++i)
+    {
+      // x,y here avoids right to left function evaluation
+      // result.push_back(PointD(*v++, *v++));
+      double x = *v++;
+      double y = *v++;
+      result.push_back(PointD(x, y));
+    }
+  }
+  return result;
+}
+
+inline CPathsD CreateCPathsD(const PathsD& pp)
+{
+  size_t cnt = pp.size(), cnt2 = cnt;
+  // don't allocate space for empty paths
+  for (size_t i = 0; i < cnt; ++i)
+    if (!pp[i].size()) --cnt2;
+  if (!cnt2) return nullptr;
+  CPathsD result = new double * [cnt2 + 1];
+  CPathsD v = result;
+  *v++ = CreateCPathD(0, cnt2); // assign counter path
+  for (const PathD& p : pp)
+  {
+    *v = CreateCPathD(p);
+    if (*v) { ++v; }
+  }
+  return result;
+}
+
+inline PathsD ConvertCPathsD(const CPathsD& pp)
+{
+  PathsD result;
+  if (pp)
+  {
+    CPathsD v = pp;
+    CPathD cnts = v[0];
+    size_t cnt = static_cast<size_t>(cnts[1]);
+    ++v; // skip cnts path
+    result.reserve(cnt);
+    for (size_t i = 0; i < cnt; ++i)
+      result.push_back(ConvertCPathD(*v++));
+  }
+  return result;
+}
+
+inline Path64 ConvertCPathD(const CPathD& p, double scale)
+{
+  Path64 result;
+  if (p)
+  {
+    CPathD v = p;
+    size_t cnt = static_cast<size_t>(*v);
+    v += 2; // skip counters
+    result.reserve(cnt);
+    for (size_t i = 0; i < cnt; ++i)
+    {
+      // x,y here avoids right to left function evaluation
+      // result.push_back(PointD(*v++, *v++));
+      double x = *v++ * scale;
+      double y = *v++ * scale;
+      result.push_back(Point64(x, y));
+    }
+  }
+  return result;
+}
+
+inline Paths64 ConvertCPathsD(const CPathsD& pp, double scale)
+{
+  Paths64 result;
+  if (pp)
+  {
+    CPathsD v = pp;
+    CPathD cnts = v[0];
+    size_t cnt = static_cast<size_t>(cnts[1]);
+    result.reserve(cnt);
+    ++v; // skip cnts path
+    for (size_t i = 0; i < cnt; ++i)
+      result.push_back(ConvertCPathD(*v++, scale));
+  }
+  return result;
+}
+
+inline CPathD CreateCPathD(const Path64& p, double scale)
+{
+  // allocates memory for CPathD, fills in the counter, and
+  // returns the structure filled with *scaled* path data
+  size_t cnt = p.size();
+  if (!cnt) return nullptr;
+  CPathD result = CreateCPathD(cnt, 0);
+  CPathD v = result;
+  v += 2; // skip cnts 
+  for (const Point64& pt : p)
+  {
+    *v++ = pt.x * scale;
+    *v++ = pt.y * scale;
+  }
+  return result;
+}
+
+inline CPathsD CreateCPathsD(const Paths64& pp, double scale)
+{
+  // allocates memory for *multiple* CPathD, and
+  // returns the structure filled with scaled path data
+  size_t cnt = pp.size(), cnt2 = cnt;
+  // don't allocate space for empty paths
+  for (size_t i = 0; i < cnt; ++i)
+    if (!pp[i].size()) --cnt2;
+  if (!cnt2) return nullptr;
+  CPathsD result = new double* [cnt2 + 1];
+  CPathsD v = result;
+  *v++ = CreateCPathD(0, cnt2);
+  for (const Path64& p : pp)
+  {
+    *v = CreateCPathD(p, scale);
+    if (*v) ++v;
+  }
+  return result;
+}
+
+inline void InitCPolyPath64(CPolyTree64* cpt, 
+  bool is_hole, const std::unique_ptr <PolyPath64>& pp)
+{
+  cpt->polygon = CreateCPath64(pp->Polygon());
+  cpt->is_hole = is_hole;
+  size_t child_cnt = pp->Count();
+  cpt->child_count = static_cast<uint32_t>(child_cnt);
+  cpt->childs = nullptr;
+  if (!child_cnt) return;
+  cpt->childs = new CPolyPath64[child_cnt];
+  CPolyPath64* child = cpt->childs;
+  for (const std::unique_ptr <PolyPath64>& pp_child : *pp)
+    InitCPolyPath64(child++, !is_hole, pp_child);  
+}
+
+inline CPolyTree64* CreateCPolyTree64(const PolyTree64& pt)
+{
+  CPolyTree64* result = new CPolyTree64();
+  result->polygon = nullptr;
+  result->is_hole = false;
+  size_t child_cnt = pt.Count();
+  result->childs = nullptr;
+  result->child_count = static_cast<uint32_t>(child_cnt);
+  if (!child_cnt) return result;
+  result->childs = new CPolyPath64[child_cnt];
+  CPolyPath64* child = result->childs;
+  for (const std::unique_ptr <PolyPath64>& pp : pt)
+    InitCPolyPath64(child++, true, pp);
+  return result;
+}
+
+inline void DisposeCPolyPath64(CPolyPath64* cpp) 
+{
+  if (!cpp->child_count) return;
+  CPolyPath64* child = cpp->childs;
+  for (size_t i = 0; i < cpp->child_count; ++i)
+    DisposeCPolyPath64(child);
+  delete[] cpp->childs;
+}
+
+EXTERN_DLL_EXPORT void DisposeExportedCPolyTree64(CPolyTree64*& cpt)
+{
+  if (!cpt) return;
+  DisposeCPolyPath64(cpt);
+  delete cpt;
+  cpt = nullptr;
+}
+
+inline void InitCPolyPathD(CPolyTreeD* cpt,
+  bool is_hole, const std::unique_ptr <PolyPath64>& pp, double scale)
+{
+  cpt->polygon = CreateCPathD(pp->Polygon(), scale);
+  cpt->is_hole = is_hole;
+  size_t child_cnt = pp->Count();
+  cpt->child_count = static_cast<uint32_t>(child_cnt);
+  cpt->childs = nullptr;
+  if (!child_cnt) return;
+  cpt->childs = new CPolyPathD[child_cnt];
+  CPolyPathD* child = cpt->childs;
+  for (const std::unique_ptr <PolyPath64>& pp_child : *pp)
+    InitCPolyPathD(child++, !is_hole, pp_child, scale);
+}
+
+inline CPolyTreeD* CreateCPolyTreeD(const PolyTree64& pt, double scale)
+{
+  CPolyTreeD* result = new CPolyTreeD();
+  result->polygon = nullptr;
+  result->is_hole = false;
+  size_t child_cnt = pt.Count();
+  result->child_count = static_cast<uint32_t>(child_cnt);
+  result->childs = nullptr;
+  if (!child_cnt) return result;
+  result->childs = new CPolyPathD[child_cnt];
+  CPolyPathD* child = result->childs;
+  for (const std::unique_ptr <PolyPath64>& pp : pt)
+    InitCPolyPathD(child++, true, pp, scale);
+  return result;
+}
+
+inline void DisposeCPolyPathD(CPolyPathD* cpp)
+{
+  if (!cpp->child_count) return;
+  CPolyPathD* child = cpp->childs;
+  for (size_t i = 0; i < cpp->child_count; ++i)
+    DisposeCPolyPathD(child++);
+  delete[] cpp->childs;
+}
+
+EXTERN_DLL_EXPORT void DisposeExportedCPolyTreeD(CPolyTreeD*& cpt)
+{
+  if (!cpt) return;
+  DisposeCPolyPathD(cpt);
+  delete cpt;
+  cpt = nullptr;
+}
+
+}  // end Clipper2Lib namespace
+  
+#endif  // CLIPPER2_EXPORT_H

thirdparty/clipper2/include/clipper2/clipper.h

@@ -0,0 +1,776 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  23 March 2023                                                   *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2023                                         *
+* Purpose   :  This module provides a simple interface to the Clipper Library  *
+* License   :  http://www.boost.org/LICENSE_1_0.txt                            *
+*******************************************************************************/
+
+#ifndef CLIPPER_H
+#define CLIPPER_H
+
+#include <cstdlib>
+#include <type_traits>
+#include <vector>
+
+#include "clipper.core.h"
+#include "clipper.engine.h"
+#include "clipper.offset.h"
+#include "clipper.minkowski.h"
+#include "clipper.rectclip.h"
+
+namespace Clipper2Lib {
+
+  inline Paths64 BooleanOp(ClipType cliptype, FillRule fillrule,
+    const Paths64& subjects, const Paths64& clips)
+  {    
+    Paths64 result;
+    Clipper64 clipper;
+    clipper.AddSubject(subjects);
+    clipper.AddClip(clips);
+    clipper.Execute(cliptype, fillrule, result);
+    return result;
+  }
+
+  inline void BooleanOp(ClipType cliptype, FillRule fillrule,
+    const Paths64& subjects, const Paths64& clips, PolyTree64& solution)
+  {
+    Paths64 sol_open;
+    Clipper64 clipper;
+    clipper.AddSubject(subjects);
+    clipper.AddClip(clips);
+    clipper.Execute(cliptype, fillrule, solution, sol_open);
+  }
+
+  inline PathsD BooleanOp(ClipType cliptype, FillRule fillrule,
+    const PathsD& subjects, const PathsD& clips, int precision = 2)
+  {
+    int error_code = 0;
+    CheckPrecision(precision, error_code);
+    PathsD result;
+    if (error_code) return result;
+    ClipperD clipper(precision);
+    clipper.AddSubject(subjects);
+    clipper.AddClip(clips);
+    clipper.Execute(cliptype, fillrule, result);
+    return result;
+  }
+
+  inline void BooleanOp(ClipType cliptype, FillRule fillrule,
+    const PathsD& subjects, const PathsD& clips, 
+    PolyTreeD& polytree, int precision = 2)
+  {
+    polytree.Clear();
+    int error_code = 0;
+    CheckPrecision(precision, error_code);
+    if (error_code) return;
+    ClipperD clipper(precision);
+    clipper.AddSubject(subjects);
+    clipper.AddClip(clips);
+    clipper.Execute(cliptype, fillrule, polytree);
+  }
+
+  inline Paths64 Intersect(const Paths64& subjects, const Paths64& clips, FillRule fillrule)
+  {
+    return BooleanOp(ClipType::Intersection, fillrule, subjects, clips);
+  }
+  
+  inline PathsD Intersect(const PathsD& subjects, const PathsD& clips, FillRule fillrule, int decimal_prec = 2)
+  {
+    return BooleanOp(ClipType::Intersection, fillrule, subjects, clips, decimal_prec);
+  }
+
+  inline Paths64 Union(const Paths64& subjects, const Paths64& clips, FillRule fillrule)
+  {
+    return BooleanOp(ClipType::Union, fillrule, subjects, clips);
+  }
+
+  inline PathsD Union(const PathsD& subjects, const PathsD& clips, FillRule fillrule, int decimal_prec = 2)
+  {
+    return BooleanOp(ClipType::Union, fillrule, subjects, clips, decimal_prec);
+  }
+
+  inline Paths64 Union(const Paths64& subjects, FillRule fillrule)
+  {
+    Paths64 result;
+    Clipper64 clipper;
+    clipper.AddSubject(subjects);
+    clipper.Execute(ClipType::Union, fillrule, result);
+    return result;
+  }
+
+  inline PathsD Union(const PathsD& subjects, FillRule fillrule, int precision = 2)
+  {
+    PathsD result;
+    int error_code = 0;
+    CheckPrecision(precision, error_code);
+    if (error_code) return result;
+    ClipperD clipper(precision);
+    clipper.AddSubject(subjects);
+    clipper.Execute(ClipType::Union, fillrule, result);
+    return result;
+  }
+
+  inline Paths64 Difference(const Paths64& subjects, const Paths64& clips, FillRule fillrule)
+  {
+    return BooleanOp(ClipType::Difference, fillrule, subjects, clips);
+  }
+
+  inline PathsD Difference(const PathsD& subjects, const PathsD& clips, FillRule fillrule, int decimal_prec = 2)
+  {
+    return BooleanOp(ClipType::Difference, fillrule, subjects, clips, decimal_prec);
+  }
+
+  inline Paths64 Xor(const Paths64& subjects, const Paths64& clips, FillRule fillrule)
+  {
+    return BooleanOp(ClipType::Xor, fillrule, subjects, clips);
+  }
+
+  inline PathsD Xor(const PathsD& subjects, const PathsD& clips, FillRule fillrule, int decimal_prec = 2)
+  {
+    return BooleanOp(ClipType::Xor, fillrule, subjects, clips, decimal_prec);
+  }
+
+  inline Paths64 InflatePaths(const Paths64& paths, double delta,
+    JoinType jt, EndType et, double miter_limit = 2.0,
+    double arc_tolerance = 0.0)
+  {
+    if (!delta) return paths;
+    ClipperOffset clip_offset(miter_limit, arc_tolerance);
+    clip_offset.AddPaths(paths, jt, et);
+    Paths64 solution;
+    clip_offset.Execute(delta, solution);
+    return solution;
+  }
+
+  inline PathsD InflatePaths(const PathsD& paths, double delta,
+    JoinType jt, EndType et, double miter_limit = 2.0, 
+    int precision = 2, double arc_tolerance = 0.0)
+  {
+    int error_code = 0;
+    CheckPrecision(precision, error_code);
+    if (!delta) return paths;
+    if (error_code) return PathsD();
+    const double scale = std::pow(10, precision);
+    ClipperOffset clip_offset(miter_limit, arc_tolerance);
+    clip_offset.AddPaths(ScalePaths<int64_t,double>(paths, scale, error_code), jt, et);
+    if (error_code) return PathsD();
+    Paths64 solution;
+    clip_offset.Execute(delta * scale, solution);
+    return ScalePaths<double, int64_t>(solution, 1 / scale, error_code);
+  }
+
+  inline Path64 TranslatePath(const Path64& path, int64_t dx, int64_t dy)
+  {
+    Path64 result;
+    result.reserve(path.size());
+    std::transform(path.begin(), path.end(), back_inserter(result),
+      [dx, dy](const auto& pt) { return Point64(pt.x + dx, pt.y +dy); });
+    return result;
+  }
+
+  inline PathD TranslatePath(const PathD& path, double dx, double dy)
+  {
+    PathD result;
+    result.reserve(path.size());
+    std::transform(path.begin(), path.end(), back_inserter(result),
+      [dx, dy](const auto& pt) { return PointD(pt.x + dx, pt.y + dy); });
+    return result;
+  }
+
+  inline Paths64 TranslatePaths(const Paths64& paths, int64_t dx, int64_t dy)
+  {
+    Paths64 result;
+    result.reserve(paths.size());
+    std::transform(paths.begin(), paths.end(), back_inserter(result),
+      [dx, dy](const auto& path) { return TranslatePath(path, dx, dy); });
+    return result;
+  }
+
+  inline PathsD TranslatePaths(const PathsD& paths, double dx, double dy)
+  {
+    PathsD result;
+    result.reserve(paths.size());
+    std::transform(paths.begin(), paths.end(), back_inserter(result),
+      [dx, dy](const auto& path) { return TranslatePath(path, dx, dy); });
+    return result;
+  }
+
+  inline Paths64 ExecuteRectClip(const Rect64& rect, 
+    const Paths64& paths, bool convex_only = false)
+  {
+    if (rect.IsEmpty() || paths.empty()) return Paths64();
+    RectClip rc(rect);
+    return rc.Execute(paths, convex_only);
+  }
+
+  inline Paths64 ExecuteRectClip(const Rect64& rect,
+    const Path64& path, bool convex_only = false)
+  {
+    if (rect.IsEmpty() || path.empty()) return Paths64();
+    RectClip rc(rect);
+    return rc.Execute(Paths64{ path }, convex_only);
+  }
+
+  inline PathsD ExecuteRectClip(const RectD& rect,
+    const PathsD& paths, bool convex_only = false, int precision = 2)
+  {
+    if (rect.IsEmpty() || paths.empty()) return PathsD();
+    int error_code = 0;
+    CheckPrecision(precision, error_code);
+    if (error_code) return PathsD();
+    const double scale = std::pow(10, precision);
+    Rect64 r = ScaleRect<int64_t, double>(rect, scale);
+    RectClip rc(r);
+    Paths64 pp = ScalePaths<int64_t, double>(paths, scale, error_code);
+    if (error_code) return PathsD(); // ie: error_code result is lost 
+    return ScalePaths<double, int64_t>(
+      rc.Execute(pp, convex_only), 1 / scale, error_code);
+  }
+
+  inline PathsD ExecuteRectClip(const RectD& rect,
+    const PathD& path, bool convex_only = false, int precision = 2)
+  {
+    return ExecuteRectClip(rect, PathsD{ path }, convex_only, precision);
+  }
+
+  inline Paths64 ExecuteRectClipLines(const Rect64& rect, const Paths64& lines)
+  {
+    if (rect.IsEmpty() || lines.empty()) return Paths64();
+    RectClipLines rcl(rect);
+    return rcl.Execute(lines);
+  }
+
+  inline Paths64 ExecuteRectClipLines(const Rect64& rect, const Path64& line)
+  {
+    return ExecuteRectClipLines(rect, Paths64{ line });
+  }
+
+  inline PathsD ExecuteRectClipLines(const RectD& rect, const PathD& line, int precision = 2)
+  {
+    return ExecuteRectClip(rect, PathsD{ line }, precision);
+  }
+
+  inline PathsD ExecuteRectClipLines(const RectD& rect, const PathsD& lines, int precision = 2)
+  {
+    if (rect.IsEmpty() || lines.empty()) return PathsD();
+    int error_code = 0;
+    CheckPrecision(precision, error_code);
+    if (error_code) return PathsD();
+    const double scale = std::pow(10, precision);
+    Rect64 r = ScaleRect<int64_t, double>(rect, scale);
+    RectClipLines rcl(r);
+    Paths64 p = ScalePaths<int64_t, double>(lines, scale, error_code);
+    if (error_code) return PathsD();
+    p = rcl.Execute(p);
+    return ScalePaths<double, int64_t>(p, 1 / scale, error_code);
+  }
+
+  namespace details
+  {
+
+    inline void PolyPathToPaths64(const PolyPath64& polypath, Paths64& paths)
+    {
+      paths.push_back(polypath.Polygon());
+      for (const auto& child : polypath)
+        PolyPathToPaths64(*child, paths);
+    }
+
+    inline void PolyPathToPathsD(const PolyPathD& polypath, PathsD& paths)
+    {
+      paths.push_back(polypath.Polygon());
+      for (const auto& child : polypath)
+        PolyPathToPathsD(*child, paths);
+    }
+
+    inline bool PolyPath64ContainsChildren(const PolyPath64& pp)
+    {
+      for (const auto& child : pp)
+      {
+        // return false if this child isn't fully contained by its parent
+
+        // the following algorithm is a bit too crude, and doesn't account
+        // for rounding errors. A better algorithm is to return false when
+        // consecutive vertices are found outside the parent's polygon.
+
+        //const Path64& path = pp.Polygon();
+        //if (std::any_of(child->Polygon().cbegin(), child->Polygon().cend(),
+        //  [path](const auto& pt) {return (PointInPolygon(pt, path) ==
+        //    PointInPolygonResult::IsOutside); })) return false;
+
+        int outsideCnt = 0;
+        for (const Point64& pt : child->Polygon())
+        {
+          PointInPolygonResult result = PointInPolygon(pt, pp.Polygon());
+          if (result == PointInPolygonResult::IsInside) --outsideCnt;
+          else if (result == PointInPolygonResult::IsOutside) ++outsideCnt;
+          if (outsideCnt > 1) return false;
+          else if (outsideCnt < -1) break;
+        }
+
+        // now check any nested children too
+        if (child->Count() > 0 && !PolyPath64ContainsChildren(*child))
+          return false;
+      }
+      return true;
+    }
+
+    static void OutlinePolyPath(std::ostream& os, 
+      bool isHole, size_t count, const std::string& preamble)
+    {
+      std::string plural = (count == 1) ? "." : "s.";
+      if (isHole)
+      {
+        if (count)
+          os << preamble << "+- Hole with " << count <<
+          " nested polygon" << plural << std::endl;
+        else
+          os << preamble << "+- Hole" << std::endl;
+      }
+      else
+      {
+        if (count)
+          os << preamble << "+- Polygon with " << count <<
+          " hole" << plural << std::endl;
+        else
+          os << preamble << "+- Polygon" << std::endl;
+      }
+    }
+
+    static void OutlinePolyPath64(std::ostream& os, const PolyPath64& pp,
+      std::string preamble, bool last_child)
+    {
+      OutlinePolyPath(os, pp.IsHole(), pp.Count(), preamble);
+      preamble += (!last_child) ? "|  " : "   ";
+      if (pp.Count())
+      {
+        PolyPath64List::const_iterator it = pp.begin();
+        for (; it < pp.end() - 1; ++it)
+          OutlinePolyPath64(os, **it, preamble, false);
+        OutlinePolyPath64(os, **it, preamble, true);
+      }
+    }
+
+    static void OutlinePolyPathD(std::ostream& os, const PolyPathD& pp,
+      std::string preamble, bool last_child)
+    {
+      OutlinePolyPath(os, pp.IsHole(), pp.Count(), preamble);
+      preamble += (!last_child) ? "|  " : "   ";
+      if (pp.Count())
+      {
+        PolyPathDList::const_iterator it = pp.begin();
+        for (; it < pp.end() - 1; ++it)
+          OutlinePolyPathD(os, **it, preamble, false);
+        OutlinePolyPathD(os, **it, preamble, true);
+      }
+    }
+
+  } // end details namespace 
+
+  inline std::ostream& operator<< (std::ostream& os, const PolyTree64& pp)
+  {
+    PolyPath64List::const_iterator it = pp.begin();
+    for (; it < pp.end() - 1; ++it)
+      details::OutlinePolyPath64(os, **it, "   ", false);
+    details::OutlinePolyPath64(os, **it, "   ", true);
+    os << std::endl << std::endl;
+    if (!pp.Level()) os << std::endl;
+    return os;
+  }
+
+  inline std::ostream& operator<< (std::ostream& os, const PolyTreeD& pp)
+  {
+    PolyPathDList::const_iterator it = pp.begin();
+    for (; it < pp.end() - 1; ++it)
+      details::OutlinePolyPathD(os, **it, "   ", false);
+    details::OutlinePolyPathD(os, **it, "   ", true);
+    os << std::endl << std::endl;
+    if (!pp.Level()) os << std::endl;
+    return os;
+  }
+
+  inline Paths64 PolyTreeToPaths64(const PolyTree64& polytree)
+  {
+    Paths64 result;
+    for (const auto& child : polytree)
+      details::PolyPathToPaths64(*child, result);
+    return result;
+  }
+
+  inline PathsD PolyTreeToPathsD(const PolyTreeD& polytree)
+  {
+    PathsD result;
+    for (const auto& child : polytree)
+      details::PolyPathToPathsD(*child, result);
+    return result;
+  }
+
+  inline bool CheckPolytreeFullyContainsChildren(const PolyTree64& polytree)
+  {
+    for (const auto& child : polytree)
+      if (child->Count() > 0 && 
+        !details::PolyPath64ContainsChildren(*child))
+          return false;
+    return true;
+  }
+
+  namespace details {
+
+    template<typename T, typename U>
+    inline constexpr void MakePathGeneric(const T list, size_t size,
+      std::vector<U>& result)
+    {
+      for (size_t i = 0; i < size; ++i)
+#ifdef USINGZ
+        result[i / 2] = U{list[i], list[++i], 0};
+#else
+        result[i / 2] = U{list[i], list[++i]};
+#endif
+    }
+
+  } // end details namespace
+
+  template<typename T,
+    typename std::enable_if<
+      std::is_integral<T>::value &&
+      !std::is_same<char, T>::value, bool
+    >::type = true>
+  inline Path64 MakePath(const std::vector<T>& list)
+  {
+    const auto size = list.size() - list.size() % 2;
+    if (list.size() != size)
+      DoError(non_pair_error_i);  // non-fatal without exception handling
+    Path64 result(size / 2);      // else ignores unpaired value
+    details::MakePathGeneric(list, size, result);
+    return result;
+  }
+
+  template<typename T, std::size_t N,
+    typename std::enable_if<
+      std::is_integral<T>::value &&
+      !std::is_same<char, T>::value, bool
+    >::type = true>
+  inline Path64 MakePath(const T(&list)[N])
+  {
+    // Make the compiler error on unpaired value (i.e. no runtime effects).
+    static_assert(N % 2 == 0, "MakePath requires an even number of arguments");
+    Path64 result(N / 2);
+    details::MakePathGeneric(list, N, result);
+    return result;
+  }
+
+  template<typename T,
+    typename std::enable_if<
+      std::is_arithmetic<T>::value &&
+      !std::is_same<char, T>::value, bool
+    >::type = true>
+  inline PathD MakePathD(const std::vector<T>& list)
+  {
+    const auto size = list.size() - list.size() % 2;
+    if (list.size() != size)
+      DoError(non_pair_error_i);  // non-fatal without exception handling
+    PathD result(size / 2);       // else ignores unpaired value
+    details::MakePathGeneric(list, size, result);
+    return result;
+  }
+
+  template<typename T, std::size_t N,
+    typename std::enable_if<
+      std::is_arithmetic<T>::value &&
+      !std::is_same<char, T>::value, bool
+    >::type = true>
+  inline PathD MakePathD(const T(&list)[N])
+  {
+    // Make the compiler error on unpaired value (i.e. no runtime effects).
+    static_assert(N % 2 == 0, "MakePath requires an even number of arguments");
+    PathD result(N / 2);
+    details::MakePathGeneric(list, N, result);
+    return result;
+  }
+
+  inline Path64 TrimCollinear(const Path64& p, bool is_open_path = false)
+  {
+    size_t len = p.size();
+    if (len < 3)
+    {
+      if (!is_open_path || len < 2 || p[0] == p[1]) return Path64();
+      else return p;
+    }
+
+    Path64 dst;
+    dst.reserve(len);
+    Path64::const_iterator srcIt = p.cbegin(), prevIt, stop = p.cend() - 1;
+
+    if (!is_open_path)
+    {
+      while (srcIt != stop && !CrossProduct(*stop, *srcIt, *(srcIt + 1)))
+        ++srcIt;
+      while (srcIt != stop && !CrossProduct(*(stop - 1), *stop, *srcIt))
+        --stop;
+      if (srcIt == stop) return Path64();
+    }
+
+    prevIt = srcIt++;
+    dst.push_back(*prevIt);
+    for (; srcIt != stop; ++srcIt)
+    {
+      if (CrossProduct(*prevIt, *srcIt, *(srcIt + 1)))
+      {
+        prevIt = srcIt;
+        dst.push_back(*prevIt);
+      }
+    }
+
+    if (is_open_path)
+      dst.push_back(*srcIt);
+    else if (CrossProduct(*prevIt, *stop, dst[0]))
+      dst.push_back(*stop);
+    else
+    {
+      while (dst.size() > 2 &&
+        !CrossProduct(dst[dst.size() - 1], dst[dst.size() - 2], dst[0]))
+          dst.pop_back();
+      if (dst.size() < 3) return Path64();
+    }
+    return dst;
+  }
+
+  inline PathD TrimCollinear(const PathD& path, int precision, bool is_open_path = false)
+  {
+    int error_code = 0;
+    CheckPrecision(precision, error_code);
+    if (error_code) return PathD();
+    const double scale = std::pow(10, precision);
+    Path64 p = ScalePath<int64_t, double>(path, scale, error_code);
+    if (error_code) return PathD();
+    p = TrimCollinear(p, is_open_path);
+    return ScalePath<double, int64_t>(p, 1/scale, error_code);
+  }
+
+  template <typename T>
+  inline double Distance(const Point<T> pt1, const Point<T> pt2)
+  {
+    return std::sqrt(DistanceSqr(pt1, pt2));
+  }
+
+  template <typename T>
+  inline double Length(const Path<T>& path, bool is_closed_path = false)
+  {
+    double result = 0.0;
+    if (path.size() < 2) return result;
+    auto it = path.cbegin(), stop = path.end() - 1;
+    for (; it != stop; ++it)
+      result += Distance(*it, *(it + 1));
+    if (is_closed_path)
+      result += Distance(*stop, *path.cbegin());
+    return result;
+  }
+
+
+  template <typename T>
+  inline bool NearCollinear(const Point<T>& pt1, const Point<T>& pt2, const Point<T>& pt3, double sin_sqrd_min_angle_rads)
+  {
+    double cp = std::abs(CrossProduct(pt1, pt2, pt3));
+    return (cp * cp) / (DistanceSqr(pt1, pt2) * DistanceSqr(pt2, pt3)) < sin_sqrd_min_angle_rads;
+  }
+  
+  template <typename T>
+  inline Path<T> Ellipse(const Rect<T>& rect, int steps = 0)
+  {
+    return Ellipse(rect.MidPoint(), 
+      static_cast<double>(rect.Width()) *0.5, 
+      static_cast<double>(rect.Height()) * 0.5, steps);
+  }
+
+  template <typename T>
+  inline Path<T> Ellipse(const Point<T>& center,
+    double radiusX, double radiusY = 0, int steps = 0)
+  {
+    if (radiusX <= 0) return Path<T>();
+    if (radiusY <= 0) radiusY = radiusX;
+    if (steps <= 2)
+      steps = static_cast<int>(PI * sqrt((radiusX + radiusY) / 2));
+
+    double si = std::sin(2 * PI / steps);
+    double co = std::cos(2 * PI / steps);
+    double dx = co, dy = si;
+    Path<T> result;
+    result.reserve(steps);
+    result.push_back(Point<T>(center.x + radiusX, static_cast<double>(center.y)));
+    for (int i = 1; i < steps; ++i)
+    {
+      result.push_back(Point<T>(center.x + radiusX * dx, center.y + radiusY * dy));
+      double x = dx * co - dy * si;
+      dy = dy * co + dx * si;
+      dx = x;
+    }
+    return result;
+  }
+
+  template <typename T>
+  inline double PerpendicDistFromLineSqrd(const Point<T>& pt,
+    const Point<T>& line1, const Point<T>& line2)
+  {
+    double a = static_cast<double>(pt.x - line1.x);
+    double b = static_cast<double>(pt.y - line1.y);
+    double c = static_cast<double>(line2.x - line1.x);
+    double d = static_cast<double>(line2.y - line1.y);
+    if (c == 0 && d == 0) return 0;
+    return Sqr(a * d - c * b) / (c * c + d * d);
+  }
+
+  inline size_t GetNext(size_t current, size_t high, 
+    const std::vector<bool>& flags)
+  {
+    ++current;
+    while (current <= high && flags[current]) ++current;
+    if (current <= high) return current;
+    current = 0;
+    while (flags[current]) ++current;
+    return current;
+  }
+
+  inline size_t GetPrior(size_t current, size_t high, 
+    const std::vector<bool>& flags)
+  {
+    if (current == 0) current = high;
+    else --current;
+    while (current > 0 && flags[current]) --current;
+    if (!flags[current]) return current;
+    current = high;
+    while (flags[current]) --current;
+    return current;
+  }
+
+  template <typename T>
+  inline Path<T> SimplifyPath(const Path<T> path, 
+    double epsilon, bool isOpenPath = false)
+  {
+    const size_t len = path.size(), high = len -1;
+    const double epsSqr = Sqr(epsilon);
+    if (len < 4) return Path<T>(path);
+
+    std::vector<bool> flags(len);
+    std::vector<double> distSqr(len);
+    size_t prior = high, curr = 0, start, next, prior2, next2;
+    if (isOpenPath)
+    {
+      distSqr[0] = MAX_DBL;
+      distSqr[high] = MAX_DBL;
+    }
+    else 
+    {
+      distSqr[0] = PerpendicDistFromLineSqrd(path[0], path[high], path[1]);
+      distSqr[high] = PerpendicDistFromLineSqrd(path[high], path[0], path[high - 1]);
+    }
+    for (size_t i = 1; i < high; ++i)
+      distSqr[i] = PerpendicDistFromLineSqrd(path[i], path[i - 1], path[i + 1]);
+
+    for (;;)
+    {
+      if (distSqr[curr] > epsSqr)
+      {
+        start = curr;
+        do
+        {
+          curr = GetNext(curr, high, flags);
+        } while (curr != start && distSqr[curr] > epsSqr);
+        if (curr == start) break;
+      }
+      
+      prior = GetPrior(curr, high, flags);
+      next = GetNext(curr, high, flags);
+      if (next == prior) break;
+
+      if (distSqr[next] < distSqr[curr])
+      {
+        flags[next] = true;
+        next = GetNext(next, high, flags);
+        next2 = GetNext(next, high, flags);
+        distSqr[curr] = PerpendicDistFromLineSqrd(path[curr], path[prior], path[next]);
+        if (next != high || !isOpenPath)
+          distSqr[next] = PerpendicDistFromLineSqrd(path[next], path[curr], path[next2]);
+        curr = next;
+      }
+      else
+      {
+        flags[curr] = true;
+        curr = next;
+        next = GetNext(next, high, flags);
+        prior2 = GetPrior(prior, high, flags);
+        distSqr[curr] = PerpendicDistFromLineSqrd(path[curr], path[prior], path[next]);
+        if (prior != 0 || !isOpenPath)
+          distSqr[prior] = PerpendicDistFromLineSqrd(path[prior], path[prior2], path[curr]);
+      }
+    }
+    Path<T> result;
+    result.reserve(len);
+    for (typename Path<T>::size_type i = 0; i < len; ++i)
+      if (!flags[i]) result.push_back(path[i]);
+    return result;
+  }
+
+  template <typename T>
+  inline Paths<T> SimplifyPaths(const Paths<T> paths, 
+    double epsilon, bool isOpenPath = false)
+  {
+    Paths<T> result;
+    result.reserve(paths.size());
+    for (const auto& path : paths)
+      result.push_back(SimplifyPath(path, epsilon, isOpenPath));
+    return result;
+  }
+
+  template <typename T>
+  inline void RDP(const Path<T> path, std::size_t begin,
+    std::size_t end, double epsSqrd, std::vector<bool>& flags)
+  {
+    typename Path<T>::size_type idx = 0;
+    double max_d = 0;
+    while (end > begin && path[begin] == path[end]) flags[end--] = false;
+    for (typename Path<T>::size_type i = begin + 1; i < end; ++i)
+    {
+      // PerpendicDistFromLineSqrd - avoids expensive Sqrt()
+      double d = PerpendicDistFromLineSqrd(path[i], path[begin], path[end]);
+      if (d <= max_d) continue;
+      max_d = d;
+      idx = i;
+    }
+    if (max_d <= epsSqrd) return;
+    flags[idx] = true;
+    if (idx > begin + 1) RDP(path, begin, idx, epsSqrd, flags);
+    if (idx < end - 1) RDP(path, idx, end, epsSqrd, flags);
+  }
+
+  template <typename T>
+  inline Path<T> RamerDouglasPeucker(const Path<T>& path, double epsilon)
+  {
+    const typename Path<T>::size_type len = path.size();
+    if (len < 5) return Path<T>(path);
+    std::vector<bool> flags(len);
+    flags[0] = true;
+    flags[len - 1] = true;
+    RDP(path, 0, len - 1, Sqr(epsilon), flags);
+    Path<T> result;
+    result.reserve(len);
+    for (typename Path<T>::size_type i = 0; i < len; ++i)
+      if (flags[i])
+        result.push_back(path[i]);
+    return result;
+  }
+
+  template <typename T>
+  inline Paths<T> RamerDouglasPeucker(const Paths<T>& paths, double epsilon)
+  {
+    Paths<T> result;
+    result.reserve(paths.size());
+    std::transform(paths.begin(), paths.end(), back_inserter(result),
+      [epsilon](const auto& path)
+      { return RamerDouglasPeucker<T>(path, epsilon); });
+    return result;
+  }
+
+}  // end Clipper2Lib namespace
+
+#endif  // CLIPPER_H

thirdparty/clipper2/include/clipper2/clipper.minkowski.h

@@ -0,0 +1,120 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  28 January 2023                                                 *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2023                                         *
+* Purpose   :  Minkowski Sum and Difference                                    *
+* License   :  http://www.boost.org/LICENSE_1_0.txt                            *
+*******************************************************************************/
+
+#ifndef CLIPPER_MINKOWSKI_H
+#define CLIPPER_MINKOWSKI_H
+
+#include <cstdlib>
+#include <vector>
+#include <string>
+#include "clipper.core.h"
+
+namespace Clipper2Lib 
+{
+
+  namespace detail
+  {
+    inline Paths64 Minkowski(const Path64& pattern, const Path64& path, bool isSum, bool isClosed)
+    {
+      size_t delta = isClosed ? 0 : 1;
+      size_t patLen = pattern.size(), pathLen = path.size();
+      if (patLen == 0 || pathLen == 0) return Paths64();
+      Paths64 tmp;
+      tmp.reserve(pathLen);
+
+      if (isSum)
+      {
+        for (const Point64& p : path)
+        {
+          Path64 path2(pattern.size());
+          std::transform(pattern.cbegin(), pattern.cend(),
+            path2.begin(), [p](const Point64& pt2) {return p + pt2; });
+          tmp.push_back(path2);
+        }
+      }
+      else
+      {
+        for (const Point64& p : path)
+        {
+          Path64 path2(pattern.size());
+          std::transform(pattern.cbegin(), pattern.cend(),
+            path2.begin(), [p](const Point64& pt2) {return p - pt2; });
+          tmp.push_back(path2);
+        }
+      }
+
+      Paths64 result;
+      result.reserve((pathLen - delta) * patLen);
+      size_t g = isClosed ? pathLen - 1 : 0;
+      for (size_t h = patLen - 1, i = delta; i < pathLen; ++i)
+      {
+        for (size_t j = 0; j < patLen; j++)
+        {
+          Path64 quad;
+          quad.reserve(4);
+          {
+            quad.push_back(tmp[g][h]);
+            quad.push_back(tmp[i][h]);
+            quad.push_back(tmp[i][j]);
+            quad.push_back(tmp[g][j]);
+          };
+          if (!IsPositive(quad))
+            std::reverse(quad.begin(), quad.end());
+          result.push_back(quad);
+          h = j;
+        }
+        g = i;
+      }
+      return result;
+    }
+
+    inline Paths64 Union(const Paths64& subjects, FillRule fillrule)
+    {
+      Paths64 result;
+      Clipper64 clipper;
+      clipper.AddSubject(subjects);
+      clipper.Execute(ClipType::Union, fillrule, result);
+      return result;
+    }
+
+  } // namespace internal
+
+  inline Paths64 MinkowskiSum(const Path64& pattern, const Path64& path, bool isClosed)
+  {
+    return detail::Union(detail::Minkowski(pattern, path, true, isClosed), FillRule::NonZero);
+  }
+
+  inline PathsD MinkowskiSum(const PathD& pattern, const PathD& path, bool isClosed, int decimalPlaces = 2)
+  {
+    int error_code = 0;
+    double scale = pow(10, decimalPlaces);
+    Path64 pat64 = ScalePath<int64_t, double>(pattern, scale, error_code);
+    Path64 path64 = ScalePath<int64_t, double>(path, scale, error_code);
+    Paths64 tmp = detail::Union(detail::Minkowski(pat64, path64, true, isClosed), FillRule::NonZero);
+    return ScalePaths<double, int64_t>(tmp, 1 / scale, error_code);
+  }
+
+  inline Paths64 MinkowskiDiff(const Path64& pattern, const Path64& path, bool isClosed)
+  {
+    return detail::Union(detail::Minkowski(pattern, path, false, isClosed), FillRule::NonZero);
+  }
+
+  inline PathsD MinkowskiDiff(const PathD& pattern, const PathD& path, bool isClosed, int decimalPlaces = 2)
+  {
+    int error_code = 0;
+    double scale = pow(10, decimalPlaces);
+    Path64 pat64 = ScalePath<int64_t, double>(pattern, scale, error_code);
+    Path64 path64 = ScalePath<int64_t, double>(path, scale, error_code);
+    Paths64 tmp = detail::Union(detail::Minkowski(pat64, path64, false, isClosed), FillRule::NonZero);
+    return ScalePaths<double, int64_t>(tmp, 1 / scale, error_code);
+  }
+
+} // Clipper2Lib namespace
+
+#endif  // CLIPPER_MINKOWSKI_H

thirdparty/clipper2/include/clipper2/clipper.offset.h

@@ -0,0 +1,114 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  22 March 2023                                                   *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2023                                         *
+* Purpose   :  Path Offset (Inflate/Shrink)                                    *
+* License   :  http://www.boost.org/LICENSE_1_0.txt                            *
+*******************************************************************************/
+
+#ifndef CLIPPER_OFFSET_H_
+#define CLIPPER_OFFSET_H_
+
+#include "clipper.core.h"
+#include "clipper.engine.h"
+
+namespace Clipper2Lib {
+
+enum class JoinType { Square, Round, Miter };
+
+enum class EndType {Polygon, Joined, Butt, Square, Round};
+//Butt   : offsets both sides of a path, with square blunt ends
+//Square : offsets both sides of a path, with square extended ends
+//Round  : offsets both sides of a path, with round extended ends
+//Joined : offsets both sides of a path, with joined ends
+//Polygon: offsets only one side of a closed path
+
+
+class ClipperOffset {
+private:
+
+	class Group {
+	public:
+		Paths64 paths_in;
+		Paths64 paths_out;
+		Path64 path;
+		bool is_reversed = false;
+		JoinType join_type;
+		EndType end_type;
+		Group(const Paths64& _paths, JoinType _join_type, EndType _end_type) :
+			paths_in(_paths), join_type(_join_type), end_type(_end_type) {}
+	};
+
+	int   error_code_ = 0;
+	double delta_ = 0.0;
+	double group_delta_ = 0.0;
+	double abs_group_delta_ = 0.0;
+	double temp_lim_ = 0.0;
+	double steps_per_rad_ = 0.0;
+	double step_sin_ = 0.0;
+	double step_cos_ = 0.0;
+	PathD norms;
+	Paths64 solution;
+	std::vector<Group> groups_;
+	JoinType join_type_ = JoinType::Square;
+	EndType end_type_ = EndType::Polygon;
+
+	double miter_limit_ = 0.0;
+	double arc_tolerance_ = 0.0;
+	bool preserve_collinear_ = false;
+	bool reverse_solution_ = false;
+
+#ifdef USINGZ
+	ZCallback64 zCallback64_ = nullptr;
+#endif
+
+	void DoSquare(Group& group, const Path64& path, size_t j, size_t k);
+	void DoMiter(Group& group, const Path64& path, size_t j, size_t k, double cos_a);
+	void DoRound(Group& group, const Path64& path, size_t j, size_t k, double angle);
+	void BuildNormals(const Path64& path);
+	void OffsetPolygon(Group& group, Path64& path);
+	void OffsetOpenJoined(Group& group, Path64& path);
+	void OffsetOpenPath(Group& group, Path64& path);
+	void OffsetPoint(Group& group, Path64& path, size_t j, size_t& k);
+	void DoGroupOffset(Group &group);
+	void ExecuteInternal(double delta);
+public:
+	explicit ClipperOffset(double miter_limit = 2.0,
+		double arc_tolerance = 0.0,
+		bool preserve_collinear = false, 
+		bool reverse_solution = false) :
+		miter_limit_(miter_limit), arc_tolerance_(arc_tolerance),
+		preserve_collinear_(preserve_collinear),
+		reverse_solution_(reverse_solution) { };
+
+	~ClipperOffset() { Clear(); };
+
+	int ErrorCode() { return error_code_; };
+	void AddPath(const Path64& path, JoinType jt_, EndType et_);
+	void AddPaths(const Paths64& paths, JoinType jt_, EndType et_);
+	void Clear() { groups_.clear(); norms.clear(); };
+	
+	void Execute(double delta, Paths64& paths);
+	void Execute(double delta, PolyTree64& polytree);
+
+	double MiterLimit() const { return miter_limit_; }
+	void MiterLimit(double miter_limit) { miter_limit_ = miter_limit; }
+
+	//ArcTolerance: needed for rounded offsets (See offset_triginometry2.svg)
+	double ArcTolerance() const { return arc_tolerance_; }
+	void ArcTolerance(double arc_tolerance) { arc_tolerance_ = arc_tolerance; }
+
+	bool PreserveCollinear() const { return preserve_collinear_; }
+	void PreserveCollinear(bool preserve_collinear){preserve_collinear_ = preserve_collinear;}
+	
+	bool ReverseSolution() const { return reverse_solution_; }
+	void ReverseSolution(bool reverse_solution) {reverse_solution_ = reverse_solution;}
+
+#ifdef USINGZ
+	void SetZCallback(ZCallback64 cb) { zCallback64_ = cb; }
+#endif
+};
+
+}
+#endif /* CLIPPER_OFFSET_H_ */

thirdparty/clipper2/include/clipper2/clipper.rectclip.h

@@ -0,0 +1,82 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  9 February 2023                                                 *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2023                                         *
+* Purpose   :  FAST rectangular clipping                                       *
+* License   :  http://www.boost.org/LICENSE_1_0.txt                            *
+*******************************************************************************/
+
+#ifndef CLIPPER_RECTCLIP_H
+#define CLIPPER_RECTCLIP_H
+
+#include <cstdlib>
+#include <vector>
+#include <queue>
+#include "clipper.h"
+#include "clipper.core.h"
+
+namespace Clipper2Lib
+{
+
+  enum class Location { Left, Top, Right, Bottom, Inside };
+
+  class OutPt2;
+  typedef std::vector<OutPt2*> OutPt2List;
+
+  class OutPt2 {
+  public:
+    Point64 pt;
+    size_t owner_idx;
+    OutPt2List* edge;
+    OutPt2* next;
+    OutPt2* prev;
+  };
+
+  //------------------------------------------------------------------------------
+  // RectClip
+  //------------------------------------------------------------------------------
+
+  class RectClip {
+  private:
+    void ExecuteInternal(const Path64& path);
+    Path64 GetPath(OutPt2*& op);
+  protected:
+    const Rect64 rect_;
+    const Path64 rect_as_path_;
+    const Point64 rect_mp_;
+    Rect64 path_bounds_;
+    std::deque<OutPt2> op_container_;
+    OutPt2List results_;  // each path can be broken into multiples
+    OutPt2List edges_[8]; // clockwise and counter-clockwise
+    std::vector<Location> start_locs_;
+    void CheckEdges();
+    void TidyEdges(int idx, OutPt2List& cw, OutPt2List& ccw);
+    void GetNextLocation(const Path64& path,
+      Location& loc, int& i, int highI);
+    OutPt2* Add(Point64 pt, bool start_new = false);
+    void AddCorner(Location prev, Location curr);
+    void AddCorner(Location& loc, bool isClockwise);
+  public:
+    explicit RectClip(const Rect64& rect) :
+      rect_(rect),
+      rect_as_path_(rect.AsPath()),
+      rect_mp_(rect.MidPoint()) {}
+    Paths64 Execute(const Paths64& paths, bool convex_only = false);
+  };
+
+  //------------------------------------------------------------------------------
+  // RectClipLines
+  //------------------------------------------------------------------------------
+
+  class RectClipLines : public RectClip {
+  private:
+    void ExecuteInternal(const Path64& path);
+    Path64 GetPath(OutPt2*& op);
+  public:
+    explicit RectClipLines(const Rect64& rect) : RectClip(rect) {};
+    Paths64 Execute(const Paths64& paths);
+  };
+
+} // Clipper2Lib namespace
+#endif  // CLIPPER_RECTCLIP_H

thirdparty/clipper2/src/clipper.offset.cpp

@@ -0,0 +1,618 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  22 March 2023                                                   *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2023                                         *
+* Purpose   :  Path Offset (Inflate/Shrink)                                    *
+* License   :  http://www.boost.org/LICENSE_1_0.txt                            *
+*******************************************************************************/
+
+#include <cmath>
+#include "clipper2/clipper.h"
+#include "clipper2/clipper.offset.h"
+
+namespace Clipper2Lib {
+
+const double default_arc_tolerance = 0.25;
+const double floating_point_tolerance = 1e-12;
+
+//------------------------------------------------------------------------------
+// Miscellaneous methods
+//------------------------------------------------------------------------------
+
+void GetBoundsAndLowestPolyIdx(const Paths64& paths, Rect64& r, int & idx)
+{
+	idx = -1;
+	r = MaxInvalidRect64;
+	int64_t lpx = 0;
+	for (int i = 0; i < static_cast<int>(paths.size()); ++i)
+		for (const Point64& p : paths[i])
+		{
+			if (p.y >= r.bottom)
+			{
+				if (p.y > r.bottom || p.x < lpx)
+				{
+					idx = i;
+					lpx = p.x;
+					r.bottom = p.y;
+				}
+			}
+			else if (p.y < r.top) r.top = p.y;
+			if (p.x > r.right) r.right = p.x;
+			else if (p.x < r.left) r.left = p.x;
+		}
+	//if (idx < 0) r = Rect64(0, 0, 0, 0);
+	//if (r.top == INT64_MIN) r.bottom = r.top;
+	//if (r.left == INT64_MIN) r.left = r.right;
+}
+
+bool IsSafeOffset(const Rect64& r, double abs_delta)
+{
+	return r.left > min_coord + abs_delta &&
+		r.right < max_coord - abs_delta &&
+		r.top > min_coord + abs_delta &&
+		r.bottom < max_coord - abs_delta;
+}
+
+PointD GetUnitNormal(const Point64& pt1, const Point64& pt2)
+{
+	double dx, dy, inverse_hypot;
+	if (pt1 == pt2) return PointD(0.0, 0.0);
+	dx = static_cast<double>(pt2.x - pt1.x);
+	dy = static_cast<double>(pt2.y - pt1.y);
+	inverse_hypot = 1.0 / hypot(dx, dy);
+	dx *= inverse_hypot;
+	dy *= inverse_hypot;
+	return PointD(dy, -dx);
+}
+
+inline bool AlmostZero(double value, double epsilon = 0.001)
+{
+	return std::fabs(value) < epsilon;
+}
+
+inline double Hypot(double x, double y) 
+{
+	//see https://stackoverflow.com/a/32436148/359538
+	return std::sqrt(x * x + y * y);
+}
+
+inline PointD NormalizeVector(const PointD& vec)
+{
+	
+	double h = Hypot(vec.x, vec.y);
+	if (AlmostZero(h)) return PointD(0,0);
+	double inverseHypot = 1 / h;
+	return PointD(vec.x * inverseHypot, vec.y * inverseHypot);
+}
+
+inline PointD GetAvgUnitVector(const PointD& vec1, const PointD& vec2)
+{
+	return NormalizeVector(PointD(vec1.x + vec2.x, vec1.y + vec2.y));
+}
+
+inline bool IsClosedPath(EndType et)
+{
+	return et == EndType::Polygon || et == EndType::Joined;
+}
+
+inline Point64 GetPerpendic(const Point64& pt, const PointD& norm, double delta)
+{
+#ifdef USINGZ
+	return Point64(pt.x + norm.x * delta, pt.y + norm.y * delta, pt.z);
+#else
+	return Point64(pt.x + norm.x * delta, pt.y + norm.y * delta);
+#endif
+}
+
+inline PointD GetPerpendicD(const Point64& pt, const PointD& norm, double delta)
+{
+#ifdef USINGZ
+	return PointD(pt.x + norm.x * delta, pt.y + norm.y * delta, pt.z);
+#else
+	return PointD(pt.x + norm.x * delta, pt.y + norm.y * delta);
+#endif
+}
+
+inline void NegatePath(PathD& path)
+{
+	for (PointD& pt : path)
+	{
+		pt.x = -pt.x;
+		pt.y = -pt.y;
+#ifdef USINGZ
+		pt.z = pt.z;
+#endif
+	}
+}
+
+//------------------------------------------------------------------------------
+// ClipperOffset methods
+//------------------------------------------------------------------------------
+
+void ClipperOffset::AddPath(const Path64& path, JoinType jt_, EndType et_)
+{
+	Paths64 paths;
+	paths.push_back(path);
+	AddPaths(paths, jt_, et_);
+}
+
+void ClipperOffset::AddPaths(const Paths64 &paths, JoinType jt_, EndType et_)
+{
+	if (paths.size() == 0) return;
+	groups_.push_back(Group(paths, jt_, et_));
+}
+
+void ClipperOffset::BuildNormals(const Path64& path)
+{
+	norms.clear();
+	norms.reserve(path.size());
+	if (path.size() == 0) return;
+	Path64::const_iterator path_iter, path_last_iter = --path.cend();
+	for (path_iter = path.cbegin(); path_iter != path_last_iter; ++path_iter)
+		norms.push_back(GetUnitNormal(*path_iter,*(path_iter +1)));
+	norms.push_back(GetUnitNormal(*path_last_iter, *(path.cbegin())));
+}
+
+inline PointD TranslatePoint(const PointD& pt, double dx, double dy)
+{
+#ifdef USINGZ
+	return PointD(pt.x + dx, pt.y + dy, pt.z);
+#else
+	return PointD(pt.x + dx, pt.y + dy);
+#endif
+}
+
+inline PointD ReflectPoint(const PointD& pt, const PointD& pivot)
+{
+#ifdef USINGZ
+	return PointD(pivot.x + (pivot.x - pt.x), pivot.y + (pivot.y - pt.y), pt.z);
+#else
+	return PointD(pivot.x + (pivot.x - pt.x), pivot.y + (pivot.y - pt.y));
+#endif
+}
+
+PointD IntersectPoint(const PointD& pt1a, const PointD& pt1b,
+	const PointD& pt2a, const PointD& pt2b)
+{
+	if (pt1a.x == pt1b.x) //vertical
+	{
+		if (pt2a.x == pt2b.x) return PointD(0, 0);
+
+		double m2 = (pt2b.y - pt2a.y) / (pt2b.x - pt2a.x);
+		double b2 = pt2a.y - m2 * pt2a.x;
+		return PointD(pt1a.x, m2 * pt1a.x + b2);
+	}
+	else if (pt2a.x == pt2b.x) //vertical
+	{
+		double m1 = (pt1b.y - pt1a.y) / (pt1b.x - pt1a.x);
+		double b1 = pt1a.y - m1 * pt1a.x;
+		return PointD(pt2a.x, m1 * pt2a.x + b1);
+	}
+	else
+	{
+		double m1 = (pt1b.y - pt1a.y) / (pt1b.x - pt1a.x);
+		double b1 = pt1a.y - m1 * pt1a.x;
+		double m2 = (pt2b.y - pt2a.y) / (pt2b.x - pt2a.x);
+		double b2 = pt2a.y - m2 * pt2a.x;
+		if (m1 == m2) return PointD(0, 0);
+		double x = (b2 - b1) / (m1 - m2);
+		return PointD(x, m1 * x + b1);
+	}
+}
+
+void ClipperOffset::DoSquare(Group& group, const Path64& path, size_t j, size_t k)
+{
+	PointD vec;
+	if (j == k) 
+		vec = PointD(norms[0].y, -norms[0].x);
+	else
+		vec = GetAvgUnitVector(
+			PointD(-norms[k].y, norms[k].x),
+			PointD(norms[j].y, -norms[j].x));
+
+	// now offset the original vertex delta units along unit vector
+	PointD ptQ = PointD(path[j]);
+	ptQ = TranslatePoint(ptQ, abs_group_delta_ * vec.x, abs_group_delta_ * vec.y);
+	// get perpendicular vertices
+	PointD pt1 = TranslatePoint(ptQ, group_delta_ * vec.y, group_delta_ * -vec.x);
+	PointD pt2 = TranslatePoint(ptQ, group_delta_ * -vec.y, group_delta_ * vec.x);
+	// get 2 vertices along one edge offset
+	PointD pt3 = GetPerpendicD(path[k], norms[k], group_delta_);
+	if (j == k)
+	{
+		PointD pt4 = PointD(pt3.x + vec.x * group_delta_, pt3.y + vec.y * group_delta_);
+		PointD pt = IntersectPoint(pt1, pt2, pt3, pt4);
+#ifdef USINGZ
+		pt.z = ptQ.z;
+#endif
+		//get the second intersect point through reflecion
+		group.path.push_back(Point64(ReflectPoint(pt, ptQ)));
+		group.path.push_back(Point64(pt));
+	}
+	else
+	{
+		PointD pt4 = GetPerpendicD(path[j], norms[k], group_delta_);
+		PointD pt = IntersectPoint(pt1, pt2, pt3, pt4);
+#ifdef USINGZ
+		pt.z = ptQ.z;
+#endif
+		group.path.push_back(Point64(pt));
+		//get the second intersect point through reflecion
+		group.path.push_back(Point64(ReflectPoint(pt, ptQ)));
+	}
+}
+
+void ClipperOffset::DoMiter(Group& group, const Path64& path, size_t j, size_t k, double cos_a)
+{
+	double q = group_delta_ / (cos_a + 1);
+#ifdef USINGZ
+	group.path.push_back(Point64(
+		path[j].x + (norms[k].x + norms[j].x) * q,
+		path[j].y + (norms[k].y + norms[j].y) * q,
+		path[j].z));
+#else
+	group.path.push_back(Point64(
+		path[j].x + (norms[k].x + norms[j].x) * q,
+		path[j].y + (norms[k].y + norms[j].y) * q));
+#endif
+}
+
+void ClipperOffset::DoRound(Group& group, const Path64& path, size_t j, size_t k, double angle)
+{
+	Point64 pt = path[j];
+	PointD offsetVec = PointD(norms[k].x * group_delta_, norms[k].y * group_delta_);
+
+	if (j == k) offsetVec.Negate();
+#ifdef USINGZ
+	group.path.push_back(Point64(pt.x + offsetVec.x, pt.y + offsetVec.y, pt.z));
+#else
+	group.path.push_back(Point64(pt.x + offsetVec.x, pt.y + offsetVec.y));
+#endif
+	if (angle > -PI + 0.01)	// avoid 180deg concave
+	{
+		int steps = static_cast<int>(std::ceil(steps_per_rad_ * std::abs(angle))); // #448, #456
+		for (int i = 1; i < steps; ++i) // ie 1 less than steps
+		{
+			offsetVec = PointD(offsetVec.x * step_cos_ - step_sin_ * offsetVec.y,
+				offsetVec.x * step_sin_ + offsetVec.y * step_cos_);
+#ifdef USINGZ
+			group.path.push_back(Point64(pt.x + offsetVec.x, pt.y + offsetVec.y, pt.z));
+#else
+			group.path.push_back(Point64(pt.x + offsetVec.x, pt.y + offsetVec.y));
+#endif
+
+		}
+	}
+	group.path.push_back(GetPerpendic(path[j], norms[j], group_delta_));
+}
+
+void ClipperOffset::OffsetPoint(Group& group, Path64& path, size_t j, size_t& k)
+{
+	// Let A = change in angle where edges join
+	// A == 0: ie no change in angle (flat join)
+	// A == PI: edges 'spike'
+	// sin(A) < 0: right turning
+	// cos(A) < 0: change in angle is more than 90 degree
+
+	if (path[j] == path[k]) { k = j; return; }
+
+	double sin_a = CrossProduct(norms[j], norms[k]);
+	double cos_a = DotProduct(norms[j], norms[k]);
+	if (sin_a > 1.0) sin_a = 1.0;
+	else if (sin_a < -1.0) sin_a = -1.0;
+
+	if (cos_a > 0.99) // almost straight - less than 8 degrees
+	{
+		group.path.push_back(GetPerpendic(path[j], norms[k], group_delta_));
+		if (cos_a < 0.9998) // greater than 1 degree (#424)
+			group.path.push_back(GetPerpendic(path[j], norms[j], group_delta_)); // (#418)
+	}
+	else if (cos_a > -0.99 && (sin_a * group_delta_ < 0))
+	{
+		// is concave
+		group.path.push_back(GetPerpendic(path[j], norms[k], group_delta_));
+		// this extra point is the only (simple) way to ensure that
+		// path reversals are fully cleaned with the trailing clipper
+		group.path.push_back(path[j]); // (#405)
+		group.path.push_back(GetPerpendic(path[j], norms[j], group_delta_));
+	}	
+	else if (join_type_ == JoinType::Round)
+		DoRound(group, path, j, k, std::atan2(sin_a, cos_a));
+	else if (join_type_ == JoinType::Miter)
+	{
+		// miter unless the angle is so acute the miter would exceeds ML
+		if (cos_a > temp_lim_ - 1) DoMiter(group, path, j, k, cos_a);
+		else DoSquare(group, path, j, k);
+	}
+	// don't bother squaring angles that deviate < ~20 degrees because
+	// squaring will be indistinguishable from mitering and just be a lot slower
+	else if (cos_a > 0.9)
+		DoMiter(group, path, j, k, cos_a);
+	else
+		DoSquare(group, path, j, k);
+
+	k = j;
+}
+
+void ClipperOffset::OffsetPolygon(Group& group, Path64& path)
+{
+	for (Path64::size_type i = 0, j = path.size() -1; i < path.size(); j = i, ++i)
+		OffsetPoint(group, path, i, j);
+	group.paths_out.push_back(group.path);
+}
+
+void ClipperOffset::OffsetOpenJoined(Group& group, Path64& path)
+{
+	OffsetPolygon(group, path);
+	std::reverse(path.begin(), path.end());
+	
+	//rebuild normals // BuildNormals(path);
+	std::reverse(norms.begin(), norms.end());
+	norms.push_back(norms[0]);
+	norms.erase(norms.begin());
+	NegatePath(norms);
+
+	group.path.clear();
+	OffsetPolygon(group, path);
+}
+
+void ClipperOffset::OffsetOpenPath(Group& group, Path64& path)
+{
+	// do the line start cap
+	switch (end_type_)
+	{
+	case EndType::Butt:
+#ifdef USINGZ
+		group.path.push_back(Point64(
+			path[0].x - norms[0].x * group_delta_,
+			path[0].y - norms[0].y * group_delta_,
+			path[0].z));
+#else
+		group.path.push_back(Point64(
+			path[0].x - norms[0].x * group_delta_,
+			path[0].y - norms[0].y * group_delta_));
+#endif
+		group.path.push_back(GetPerpendic(path[0], norms[0], group_delta_));
+		break;
+	case EndType::Round:
+		DoRound(group, path, 0,0, PI);
+		break;
+	default:
+		DoSquare(group, path, 0, 0);
+		break;
+	}
+
+	size_t highI = path.size() - 1;
+
+	// offset the left side going forward
+	for (Path64::size_type i = 1, k = 0; i < highI; ++i)
+		OffsetPoint(group, path, i, k);
+
+	// reverse normals 
+	for (size_t i = highI; i > 0; --i)
+		norms[i] = PointD(-norms[i - 1].x, -norms[i - 1].y);
+	norms[0] = norms[highI];
+
+	// do the line end cap
+	switch (end_type_)
+	{
+	case EndType::Butt:
+#ifdef USINGZ
+		group.path.push_back(Point64(
+			path[highI].x - norms[highI].x * group_delta_,
+			path[highI].y - norms[highI].y * group_delta_,
+			path[highI].z));
+#else
+		group.path.push_back(Point64(
+			path[highI].x - norms[highI].x * group_delta_,
+			path[highI].y - norms[highI].y * group_delta_));
+#endif
+		group.path.push_back(GetPerpendic(path[highI], norms[highI], group_delta_));
+		break;
+	case EndType::Round:
+		DoRound(group, path, highI, highI, PI);
+		break;
+	default:
+		DoSquare(group, path, highI, highI);
+		break;
+	}
+
+	for (size_t i = highI, k = 0; i > 0; --i)
+		OffsetPoint(group, path, i, k);
+	group.paths_out.push_back(group.path);
+}
+
+void ClipperOffset::DoGroupOffset(Group& group)
+{
+	Rect64 r;
+	int idx = -1;
+	//the lowermost polygon must be an outer polygon. So we can use that as the
+	//designated orientation for outer polygons (needed for tidy-up clipping)
+	GetBoundsAndLowestPolyIdx(group.paths_in, r, idx);
+	if (idx < 0) return;
+
+	if (group.end_type == EndType::Polygon)
+	{
+		double area = Area(group.paths_in[idx]);
+		//if (area == 0) return; // probably unhelpful (#430)
+		group.is_reversed = (area < 0);
+		if (group.is_reversed) group_delta_ = -delta_;
+		else group_delta_ = delta_;
+	} 
+	else
+	{
+		group.is_reversed = false;
+		group_delta_ = std::abs(delta_) * 0.5;
+	}
+	abs_group_delta_ = std::fabs(group_delta_);
+
+	// do range checking
+	if (!IsSafeOffset(r, abs_group_delta_))
+	{
+		DoError(range_error_i);
+		error_code_ |= range_error_i;
+		return;
+	}
+
+	join_type_	= group.join_type;
+	end_type_ = group.end_type;
+
+	//calculate a sensible number of steps (for 360 deg for the given offset
+	if (group.join_type == JoinType::Round || group.end_type == EndType::Round)
+	{
+		// arcTol - when arc_tolerance_ is undefined (0), the amount of 
+		// curve imprecision that's allowed is based on the size of the 
+		// offset (delta). Obviously very large offsets will almost always 
+		// require much less precision. See also offset_triginometry2.svg
+		double arcTol = (arc_tolerance_ > floating_point_tolerance ?
+			std::min(abs_group_delta_, arc_tolerance_) :
+			std::log10(2 + abs_group_delta_) * default_arc_tolerance); 
+		double steps_per_360 = PI / std::acos(1 - arcTol / abs_group_delta_);
+		if (steps_per_360 > abs_group_delta_ * PI)
+			steps_per_360 = abs_group_delta_ * PI;  //ie avoids excessive precision
+
+		step_sin_ = std::sin(2 * PI / steps_per_360);
+		step_cos_ = std::cos(2 * PI / steps_per_360);
+		if (group_delta_ < 0.0) step_sin_ = -step_sin_;		
+		steps_per_rad_ = steps_per_360 / (2 *PI);
+	}
+
+	bool is_joined =
+		(end_type_ == EndType::Polygon) ||
+		(end_type_ == EndType::Joined);
+	Paths64::const_iterator path_iter;
+	for(path_iter = group.paths_in.cbegin(); path_iter != group.paths_in.cend(); ++path_iter)
+	{
+		Path64 path = StripDuplicates(*path_iter, is_joined);
+		Path64::size_type cnt = path.size();
+		if (cnt == 0 || ((cnt < 3) && group.end_type == EndType::Polygon)) 
+			continue;
+
+		group.path.clear();
+		if (cnt == 1) // single point - only valid with open paths
+		{
+			if (group_delta_ < 1) continue;
+			//single vertex so build a circle or square ...
+			if (group.join_type == JoinType::Round)
+			{
+				double radius = abs_group_delta_;
+				group.path = Ellipse(path[0], radius, radius);
+#ifdef USINGZ
+				for (auto& p : group.path) p.z = path[0].z;
+#endif
+			}
+			else
+			{
+				int d = (int)std::ceil(abs_group_delta_);
+				r = Rect64(path[0].x - d, path[0].y - d, path[0].x + d, path[0].y + d);
+				group.path = r.AsPath();
+#ifdef USINGZ
+				for (auto& p : group.path) p.z = path[0].z;
+#endif
+			}
+			group.paths_out.push_back(group.path);
+		}
+		else
+		{
+			if ((cnt == 2) && (group.end_type == EndType::Joined))
+			{
+				if (group.join_type == JoinType::Round)
+					end_type_ = EndType::Round;
+				else
+					end_type_ = EndType::Square;
+			}
+
+			BuildNormals(path);
+			if (end_type_ == EndType::Polygon) OffsetPolygon(group, path);
+			else if (end_type_ == EndType::Joined) OffsetOpenJoined(group, path);
+			else OffsetOpenPath(group, path);
+		}
+	}
+	solution.reserve(solution.size() + group.paths_out.size());
+	copy(group.paths_out.begin(), group.paths_out.end(), back_inserter(solution));
+	group.paths_out.clear();
+}
+
+void ClipperOffset::ExecuteInternal(double delta)
+{
+	error_code_ = 0;
+	solution.clear();
+	if (groups_.size() == 0) return;
+
+	if (std::abs(delta) < 0.5)
+	{
+		for (const Group& group : groups_)
+		{
+			solution.reserve(solution.size() + group.paths_in.size());
+			copy(group.paths_in.begin(), group.paths_in.end(), back_inserter(solution));
+		}
+	} 
+	else
+	{
+		temp_lim_ = (miter_limit_ <= 1) ?
+			2.0 :
+			2.0 / (miter_limit_ * miter_limit_);
+
+		delta_ = delta;
+		std::vector<Group>::iterator git;
+		for (git = groups_.begin(); git != groups_.end(); ++git)
+		{
+			DoGroupOffset(*git);
+			if (!error_code_) continue; // all OK
+			solution.clear();
+		}
+	}
+}
+
+void ClipperOffset::Execute(double delta, Paths64& paths)
+{
+	paths.clear();
+
+	ExecuteInternal(delta);
+	if (!solution.size()) return;
+
+	paths = solution;
+	//clean up self-intersections ...
+	Clipper64 c;
+	c.PreserveCollinear = false;
+	//the solution should retain the orientation of the input
+	c.ReverseSolution = reverse_solution_ != groups_[0].is_reversed;
+#ifdef USINGZ
+	if (zCallback64_) {
+		c.SetZCallback(zCallback64_);
+	}
+#endif
+	c.AddSubject(solution);
+	if (groups_[0].is_reversed)
+		c.Execute(ClipType::Union, FillRule::Negative, paths);
+	else
+		c.Execute(ClipType::Union, FillRule::Positive, paths);
+}
+
+
+void ClipperOffset::Execute(double delta, PolyTree64& polytree)
+{
+	polytree.Clear();
+
+	ExecuteInternal(delta);
+	if (!solution.size()) return;
+
+	//clean up self-intersections ...
+	Clipper64 c;
+	c.PreserveCollinear = false;
+	//the solution should retain the orientation of the input
+	c.ReverseSolution = reverse_solution_ != groups_[0].is_reversed;
+#ifdef USINGZ
+	if (zCallback64_) {
+		c.SetZCallback(zCallback64_);
+	}
+#endif
+	c.AddSubject(solution);
+	if (groups_[0].is_reversed)
+		c.Execute(ClipType::Union, FillRule::Negative, polytree);
+	else
+		c.Execute(ClipType::Union, FillRule::Positive, polytree);
+}
+
+} // namespace

thirdparty/clipper2/src/clipper.rectclip.cpp

@@ -0,0 +1,976 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  14 February 2023                                                *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2023                                         *
+* Purpose   :  FAST rectangular clipping                                       *
+* License   :  http://www.boost.org/LICENSE_1_0.txt                            *
+*******************************************************************************/
+
+#include <cmath>
+#include "clipper2/clipper.h"
+#include "clipper2/clipper.rectclip.h"
+
+namespace Clipper2Lib {
+
+  //------------------------------------------------------------------------------
+  // Miscellaneous methods
+  //------------------------------------------------------------------------------
+
+  inline bool Path1ContainsPath2(const Path64& path1, const Path64& path2)
+  {
+    int io_count = 0;
+    // precondition: no (significant) overlap
+    for (const Point64& pt : path2)
+    {
+      PointInPolygonResult pip = PointInPolygon(pt, path1);
+      switch (pip) 
+      {
+      case PointInPolygonResult::IsOutside: ++io_count; break;
+        case PointInPolygonResult::IsInside: --io_count; break;
+        default: continue;
+      }
+      if (std::abs(io_count) > 1) break;
+    }
+    return io_count <= 0;
+  }
+
+  inline bool GetLocation(const Rect64& rec,
+    const Point64& pt, Location& loc)
+  {
+    if (pt.x == rec.left && pt.y >= rec.top && pt.y <= rec.bottom)
+    {
+      loc = Location::Left;
+      return false;
+    }
+    else if (pt.x == rec.right && pt.y >= rec.top && pt.y <= rec.bottom)
+    {
+      loc = Location::Right;
+      return false;
+    }
+    else if (pt.y == rec.top && pt.x >= rec.left && pt.x <= rec.right)
+    {
+      loc = Location::Top;
+      return false;
+    }
+    else if (pt.y == rec.bottom && pt.x >= rec.left && pt.x <= rec.right)
+    {
+      loc = Location::Bottom;
+      return false;
+    }
+    else if (pt.x < rec.left) loc = Location::Left;
+    else if (pt.x > rec.right) loc = Location::Right;
+    else if (pt.y < rec.top) loc = Location::Top;
+    else if (pt.y > rec.bottom) loc = Location::Bottom;
+    else loc = Location::Inside;
+    return true;
+  }
+
+  inline bool GetIntersection(const Path64& rectPath,
+    const Point64& p, const Point64& p2, Location& loc, Point64& ip)
+  {
+    // gets the intersection closest to 'p'
+    // when Result = false, loc will remain unchanged
+    switch (loc)
+    {
+    case Location::Left:
+      if (SegmentsIntersect(p, p2, rectPath[0], rectPath[3], true))
+        GetIntersectPoint(p, p2, rectPath[0], rectPath[3], ip);
+      else if (p.y < rectPath[0].y &&
+        SegmentsIntersect(p, p2, rectPath[0], rectPath[1], true))
+      {
+        GetIntersectPoint(p, p2, rectPath[0], rectPath[1], ip);
+        loc = Location::Top;
+      }
+      else if (SegmentsIntersect(p, p2, rectPath[2], rectPath[3], true))
+      {
+        GetIntersectPoint(p, p2, rectPath[2], rectPath[3], ip);
+        loc = Location::Bottom;
+      }
+      else return false;
+      break;
+
+    case Location::Top:
+      if (SegmentsIntersect(p, p2, rectPath[0], rectPath[1], true))
+        GetIntersectPoint(p, p2, rectPath[0], rectPath[1], ip);
+      else if (p.x < rectPath[0].x &&
+        SegmentsIntersect(p, p2, rectPath[0], rectPath[3], true))
+      {
+        GetIntersectPoint(p, p2, rectPath[0], rectPath[3], ip);
+        loc = Location::Left;
+      }
+      else if (p.x > rectPath[1].x &&
+        SegmentsIntersect(p, p2, rectPath[1], rectPath[2], true))
+      {
+        GetIntersectPoint(p, p2, rectPath[1], rectPath[2], ip);
+        loc = Location::Right;
+      }
+      else return false;
+      break;
+
+    case Location::Right:
+      if (SegmentsIntersect(p, p2, rectPath[1], rectPath[2], true))
+        GetIntersectPoint(p, p2, rectPath[1], rectPath[2], ip);
+      else if (p.y < rectPath[0].y &&
+        SegmentsIntersect(p, p2, rectPath[0], rectPath[1], true))
+      {
+        GetIntersectPoint(p, p2, rectPath[0], rectPath[1], ip);
+        loc = Location::Top;
+      }
+      else if (SegmentsIntersect(p, p2, rectPath[2], rectPath[3], true))
+      {
+        GetIntersectPoint(p, p2, rectPath[2], rectPath[3], ip);
+        loc = Location::Bottom;
+      }
+      else return false;
+      break;
+
+    case Location::Bottom:
+      if (SegmentsIntersect(p, p2, rectPath[2], rectPath[3], true))
+        GetIntersectPoint(p, p2, rectPath[2], rectPath[3], ip);
+      else if (p.x < rectPath[3].x &&
+        SegmentsIntersect(p, p2, rectPath[0], rectPath[3], true))
+      {
+        GetIntersectPoint(p, p2, rectPath[0], rectPath[3], ip);
+        loc = Location::Left;
+      }
+      else if (p.x > rectPath[2].x &&
+        SegmentsIntersect(p, p2, rectPath[1], rectPath[2], true))
+      {
+        GetIntersectPoint(p, p2, rectPath[1], rectPath[2], ip);
+        loc = Location::Right;
+      }
+      else return false;
+      break;
+
+    default: // loc == rInside
+      if (SegmentsIntersect(p, p2, rectPath[0], rectPath[3], true))
+      {
+        GetIntersectPoint(p, p2, rectPath[0], rectPath[3], ip);
+        loc = Location::Left;
+      }
+      else if (SegmentsIntersect(p, p2, rectPath[0], rectPath[1], true))
+      {
+        GetIntersectPoint(p, p2, rectPath[0], rectPath[1], ip);
+        loc = Location::Top;
+      }
+      else if (SegmentsIntersect(p, p2, rectPath[1], rectPath[2], true))
+      {
+        GetIntersectPoint(p, p2, rectPath[1], rectPath[2], ip);
+        loc = Location::Right;
+      }
+      else if (SegmentsIntersect(p, p2, rectPath[2], rectPath[3], true))
+      {
+        GetIntersectPoint(p, p2, rectPath[2], rectPath[3], ip);
+        loc = Location::Bottom;
+      }
+      else return false;
+      break;
+    }
+    return true;
+  }
+
+  inline Location GetAdjacentLocation(Location loc, bool isClockwise)
+  {
+    int delta = (isClockwise) ? 1 : 3;
+    return static_cast<Location>((static_cast<int>(loc) + delta) % 4);
+  }
+
+  inline bool HeadingClockwise(Location prev, Location curr)
+  {
+    return (static_cast<int>(prev) + 1) % 4 == static_cast<int>(curr);
+  }
+
+  inline bool AreOpposites(Location prev, Location curr)
+  {
+    return abs(static_cast<int>(prev) - static_cast<int>(curr)) == 2;
+  }
+
+  inline bool IsClockwise(Location prev, Location curr,
+    const Point64& prev_pt, const Point64& curr_pt, const Point64& rect_mp)
+  {
+    if (AreOpposites(prev, curr))
+      return CrossProduct(prev_pt, rect_mp, curr_pt) < 0;
+    else
+      return HeadingClockwise(prev, curr);
+  }
+
+  inline OutPt2* UnlinkOp(OutPt2* op)
+  {
+    if (op->next == op) return nullptr;
+    op->prev->next = op->next;
+    op->next->prev = op->prev;
+    return op->next;
+  }
+
+  inline OutPt2* UnlinkOpBack(OutPt2* op)
+  {
+    if (op->next == op) return nullptr;
+    op->prev->next = op->next;
+    op->next->prev = op->prev;
+    return op->prev;
+  }
+
+  inline uint32_t GetEdgesForPt(const Point64& pt, const Rect64& rec)
+  {
+    uint32_t result = 0;
+    if (pt.x == rec.left) result = 1;
+    else if (pt.x == rec.right) result = 4;
+    if (pt.y == rec.top) result += 2;
+    else if (pt.y == rec.bottom) result += 8;
+    return result;
+  }
+
+  inline bool IsHeadingClockwise(const Point64& pt1, const Point64& pt2, int edgeIdx)
+  {
+    switch (edgeIdx)
+    {
+    case 0: return pt2.y < pt1.y;
+    case 1: return pt2.x > pt1.x;
+    case 2: return pt2.y > pt1.y;
+    default: return pt2.x < pt1.x;
+    }
+  }
+
+  inline bool HasHorzOverlap(const Point64& left1, const Point64& right1,
+    const Point64& left2, const Point64& right2)
+  {
+    return (left1.x < right2.x) && (right1.x > left2.x);
+  }
+
+  inline bool HasVertOverlap(const Point64& top1, const Point64& bottom1,
+    const Point64& top2, const Point64& bottom2)
+  {
+    return (top1.y < bottom2.y) && (bottom1.y > top2.y);
+  }
+
+  inline void AddToEdge(OutPt2List& edge, OutPt2* op)
+  {
+    if (op->edge) return;
+    op->edge = &edge;
+    edge.push_back(op);
+  }
+
+  inline void UncoupleEdge(OutPt2* op)
+  {
+    if (!op->edge) return;
+    for (size_t i = 0; i < op->edge->size(); ++i)
+    {
+      OutPt2* op2 = (*op->edge)[i];
+      if (op2 == op)
+      {
+        (*op->edge)[i] = nullptr;
+        break;
+      }
+    }
+    op->edge = nullptr;
+  }
+
+  inline void SetNewOwner(OutPt2* op, size_t new_idx)
+  {
+    op->owner_idx = new_idx;
+    OutPt2* op2 = op->next;
+    while (op2 != op)
+    {
+      op2->owner_idx = new_idx;
+      op2 = op2->next;
+    }
+  }
+
+  //----------------------------------------------------------------------------
+  // RectClip64
+  //----------------------------------------------------------------------------
+
+  OutPt2* RectClip::Add(Point64 pt, bool start_new)
+  {
+    // this method is only called by InternalExecute.
+    // Later splitting & rejoining won't create additional op's,
+    // though they will change the (non-storage) results_ count.
+    int curr_idx = static_cast<int>(results_.size()) - 1;
+    OutPt2* result;
+    if (curr_idx < 0 || start_new)
+    {
+      result = &op_container_.emplace_back(OutPt2());
+      result->pt = pt;
+      result->next = result;
+      result->prev = result;
+      results_.push_back(result);
+    }
+    else
+    {
+      OutPt2* prevOp = results_[curr_idx];
+      if (prevOp->pt == pt)  return prevOp;
+      result = &op_container_.emplace_back(OutPt2());
+      result->owner_idx = curr_idx;
+      result->pt = pt;
+      result->next = prevOp->next;
+      prevOp->next->prev = result;
+      prevOp->next = result;
+      result->prev = prevOp;
+      results_[curr_idx] = result;
+    }
+    return result;
+  }
+
+  void RectClip::AddCorner(Location prev, Location curr)
+  {
+    if (HeadingClockwise(prev, curr))
+      Add(rect_as_path_[static_cast<int>(prev)]);
+    else
+      Add(rect_as_path_[static_cast<int>(curr)]);
+  }
+
+  void RectClip::AddCorner(Location& loc, bool isClockwise)
+  {
+    if (isClockwise)
+    {
+      Add(rect_as_path_[static_cast<int>(loc)]);
+      loc = GetAdjacentLocation(loc, true);
+    }
+    else
+    {
+      loc = GetAdjacentLocation(loc, false);
+      Add(rect_as_path_[static_cast<int>(loc)]);
+    }
+  }
+
+  void RectClip::GetNextLocation(const Path64& path,
+    Location& loc, int& i, int highI)
+  {
+    switch (loc)
+    {
+    case Location::Left:
+      while (i <= highI && path[i].x <= rect_.left) ++i;
+      if (i > highI) break;
+      else if (path[i].x >= rect_.right) loc = Location::Right;
+      else if (path[i].y <= rect_.top) loc = Location::Top;
+      else if (path[i].y >= rect_.bottom) loc = Location::Bottom;
+      else loc = Location::Inside;
+      break;
+
+    case Location::Top:
+      while (i <= highI && path[i].y <= rect_.top) ++i;
+      if (i > highI) break;
+      else if (path[i].y >= rect_.bottom) loc = Location::Bottom;
+      else if (path[i].x <= rect_.left) loc = Location::Left;
+      else if (path[i].x >= rect_.right) loc = Location::Right;
+      else loc = Location::Inside;
+      break;
+
+    case Location::Right:
+      while (i <= highI && path[i].x >= rect_.right) ++i;
+      if (i > highI) break;
+      else if (path[i].x <= rect_.left) loc = Location::Left;
+      else if (path[i].y <= rect_.top) loc = Location::Top;
+      else if (path[i].y >= rect_.bottom) loc = Location::Bottom;
+      else loc = Location::Inside;
+      break;
+
+    case Location::Bottom:
+      while (i <= highI && path[i].y >= rect_.bottom) ++i;
+      if (i > highI) break;
+      else if (path[i].y <= rect_.top) loc = Location::Top;
+      else if (path[i].x <= rect_.left) loc = Location::Left;
+      else if (path[i].x >= rect_.right) loc = Location::Right;
+      else loc = Location::Inside;
+      break;
+
+    case Location::Inside:
+      while (i <= highI)
+      {
+        if (path[i].x < rect_.left) loc = Location::Left;
+        else if (path[i].x > rect_.right) loc = Location::Right;
+        else if (path[i].y > rect_.bottom) loc = Location::Bottom;
+        else if (path[i].y < rect_.top) loc = Location::Top;
+        else { Add(path[i]); ++i; continue; }
+        break; //inner loop
+      }
+      break;
+    } //switch          
+  }
+
+  void RectClip::ExecuteInternal(const Path64& path)
+  {
+    int i = 0, highI = static_cast<int>(path.size()) - 1;
+    Location prev = Location::Inside, loc;
+    Location crossing_loc = Location::Inside;
+    Location first_cross_ = Location::Inside;
+    if (!GetLocation(rect_, path[highI], loc))
+    {
+      i = highI - 1;
+      while (i >= 0 && !GetLocation(rect_, path[i], prev)) --i;
+      if (i < 0) 
+      {
+        // all of path must be inside fRect
+        for (const auto& pt : path) Add(pt);
+        return;
+      }
+      if (prev == Location::Inside) loc = Location::Inside;
+      i = 0;
+    }
+    Location startingLoc = loc;
+
+    ///////////////////////////////////////////////////
+    while (i <= highI)
+    {
+      prev = loc;
+      Location crossing_prev = crossing_loc;
+
+      GetNextLocation(path, loc, i, highI);
+
+      if (i > highI) break;
+      Point64 ip, ip2;
+      Point64 prev_pt = (i) ? 
+        path[static_cast<size_t>(i - 1)] : 
+        path[highI];
+
+      crossing_loc = loc;
+      if (!GetIntersection(rect_as_path_, 
+        path[i], prev_pt, crossing_loc, ip))
+      {
+        // ie remaining outside
+        if (crossing_prev == Location::Inside)
+        {
+          bool isClockw = IsClockwise(prev, loc, prev_pt, path[i], rect_mp_);
+          do {
+            start_locs_.push_back(prev);
+            prev = GetAdjacentLocation(prev, isClockw);
+          } while (prev != loc);
+          crossing_loc = crossing_prev; // still not crossed 
+        }
+        else if (prev != Location::Inside && prev != loc)
+        {
+          bool isClockw = IsClockwise(prev, loc, prev_pt, path[i], rect_mp_);
+          do {
+            AddCorner(prev, isClockw);
+          } while (prev != loc);
+        }
+        ++i;
+        continue;
+      }
+
+      ////////////////////////////////////////////////////
+      // we must be crossing the rect boundary to get here
+      ////////////////////////////////////////////////////
+
+      if (loc == Location::Inside) // path must be entering rect
+      {
+        if (first_cross_ == Location::Inside)
+        {
+          first_cross_ = crossing_loc;
+          start_locs_.push_back(prev);
+        }
+        else if (prev != crossing_loc)
+        {
+          bool isClockw = IsClockwise(prev, crossing_loc, prev_pt, path[i], rect_mp_);
+          do {
+            AddCorner(prev, isClockw);
+          } while (prev != crossing_loc);
+        }
+      }
+      else if (prev != Location::Inside)
+      {
+        // passing right through rect. 'ip' here will be the second 
+        // intersect pt but we'll also need the first intersect pt (ip2)
+        loc = prev;
+        GetIntersection(rect_as_path_, prev_pt, path[i], loc, ip2);
+        if (crossing_prev != Location::Inside)
+          AddCorner(crossing_prev, loc);
+
+        if (first_cross_ == Location::Inside)
+        {
+          first_cross_ = loc;
+          start_locs_.push_back(prev);
+        }
+
+        loc = crossing_loc;
+        Add(ip2);
+        if (ip == ip2)
+        {
+          // it's very likely that path[i] is on rect
+          GetLocation(rect_, path[i], loc);
+          AddCorner(crossing_loc, loc);
+          crossing_loc = loc;
+          continue;
+        }
+      }
+      else // path must be exiting rect
+      {
+        loc = crossing_loc;
+        if (first_cross_ == Location::Inside)
+          first_cross_ = crossing_loc;
+      }
+
+      Add(ip);
+
+    } //while i <= highI
+    ///////////////////////////////////////////////////
+
+    if (first_cross_ == Location::Inside)
+    {
+      // path never intersects
+      if (startingLoc != Location::Inside)
+      {
+        // path is outside rect
+        // but being outside, it still may not contain rect
+        if (path_bounds_.Contains(rect_) &&
+          Path1ContainsPath2(path, rect_as_path_))
+        {
+          // yep, the path does fully contain rect
+          // so add rect to the solution
+          for (size_t j = 0; j < 4; ++j)
+          {
+            Add(rect_as_path_[j]);
+            // we may well need to do some splitting later, so
+            AddToEdge(edges_[j * 2], results_[0]);
+          }
+        }
+      }
+    }
+    else if (loc != Location::Inside &&
+      (loc != first_cross_ || start_locs_.size() > 2))
+    {
+      if (start_locs_.size() > 0)
+      {
+        prev = loc;
+        for (auto loc2 : start_locs_)
+        {
+          if (prev == loc2) continue;
+          AddCorner(prev, HeadingClockwise(prev, loc2));
+          prev = loc2;
+        }
+        loc = prev;
+      }
+      if (loc != first_cross_)
+        AddCorner(loc, HeadingClockwise(loc, first_cross_));
+    }
+  }
+
+  void RectClip::CheckEdges()
+  {
+    for (size_t i = 0; i < results_.size(); ++i)
+    {
+      OutPt2* op = results_[i];
+      if (!op) continue;
+      OutPt2* op2 = op;
+      do
+      {
+        if (!CrossProduct(op2->prev->pt,
+          op2->pt, op2->next->pt))
+        {
+          if (op2 == op)
+          {
+            op2 = UnlinkOpBack(op2);
+            if (!op2) break;
+            op = op2->prev;
+          }
+          else
+          {
+            op2 = UnlinkOpBack(op2);
+            if (!op2) break;
+          }
+        }
+        else
+          op2 = op2->next;
+      } while (op2 != op);
+
+      if (!op2)
+      {
+        results_[i] = nullptr;
+        continue;
+      }
+      results_[i] = op; // safety first
+
+      uint32_t edgeSet1 = GetEdgesForPt(op->prev->pt, rect_);
+      op2 = op;
+      do
+      {
+        uint32_t edgeSet2 = GetEdgesForPt(op2->pt, rect_);
+        if (edgeSet2 && !op2->edge)
+        {
+          uint32_t combinedSet = (edgeSet1 & edgeSet2);
+          for (int j = 0; j < 4; ++j)
+          {
+            if (combinedSet & (1 << j))
+            {
+              if (IsHeadingClockwise(op2->prev->pt, op2->pt, j))
+                AddToEdge(edges_[j * 2], op2);
+              else
+                AddToEdge(edges_[j * 2 + 1], op2);
+            }
+          }
+        }
+        edgeSet1 = edgeSet2;
+        op2 = op2->next;
+      } while (op2 != op);
+    }
+  }
+
+  void RectClip::TidyEdges(int idx, OutPt2List& cw, OutPt2List& ccw)
+  {
+    if (ccw.empty()) return;
+    bool isHorz = ((idx == 1) || (idx == 3));
+    bool cwIsTowardLarger = ((idx == 1) || (idx == 2));
+    size_t i = 0, j = 0;
+    OutPt2* p1, * p2, * p1a, * p2a, * op, * op2;
+
+    while (i < cw.size()) 
+    {
+      p1 = cw[i];
+      if (!p1 || p1->next == p1->prev)
+      {
+        cw[i++]->edge = nullptr;
+        j = 0;
+        continue;
+      }
+
+      size_t jLim = ccw.size();
+      while (j < jLim &&
+        (!ccw[j] || ccw[j]->next == ccw[j]->prev)) ++j;
+
+      if (j == jLim)
+      {
+        ++i;
+        j = 0;
+        continue;
+      }
+
+      if (cwIsTowardLarger)
+      {
+        // p1 >>>> p1a;
+        // p2 <<<< p2a;
+        p1 = cw[i]->prev;
+        p1a = cw[i];
+        p2 = ccw[j];
+        p2a = ccw[j]->prev;
+      }
+      else
+      {
+        // p1 <<<< p1a;
+        // p2 >>>> p2a;
+        p1 = cw[i];
+        p1a = cw[i]->prev;
+        p2 = ccw[j]->prev;
+        p2a = ccw[j];
+      }
+
+      if ((isHorz && !HasHorzOverlap(p1->pt, p1a->pt, p2->pt, p2a->pt)) ||
+        (!isHorz && !HasVertOverlap(p1->pt, p1a->pt, p2->pt, p2a->pt)))
+      {
+        ++j;
+        continue;
+      }
+
+      // to get here we're either splitting or rejoining
+      bool isRejoining = cw[i]->owner_idx != ccw[j]->owner_idx;
+
+      if (isRejoining)
+      {
+        results_[p2->owner_idx] = nullptr;
+        SetNewOwner(p2, p1->owner_idx);
+      }
+
+      // do the split or re-join
+      if (cwIsTowardLarger)
+      {
+        // p1 >> | >> p1a;
+        // p2 << | << p2a;
+        p1->next = p2;
+        p2->prev = p1;
+        p1a->prev = p2a;
+        p2a->next = p1a;
+      }
+      else
+      {
+        // p1 << | << p1a;
+        // p2 >> | >> p2a;
+        p1->prev = p2;
+        p2->next = p1;
+        p1a->next = p2a;
+        p2a->prev = p1a;
+      }
+
+      if (!isRejoining)
+      {
+        size_t new_idx = results_.size();
+        results_.push_back(p1a);
+        SetNewOwner(p1a, new_idx);
+      }
+
+      if (cwIsTowardLarger)
+      {
+        op = p2;
+        op2 = p1a;
+      }
+      else
+      {
+        op = p1;
+        op2 = p2a;
+      }
+      results_[op->owner_idx] = op;
+      results_[op2->owner_idx] = op2;
+
+      // and now lots of work to get ready for the next loop
+
+      bool opIsLarger, op2IsLarger;
+      if (isHorz) // X
+      {
+        opIsLarger = op->pt.x > op->prev->pt.x;
+        op2IsLarger = op2->pt.x > op2->prev->pt.x;
+      }
+      else       // Y
+      {
+        opIsLarger = op->pt.y > op->prev->pt.y;
+        op2IsLarger = op2->pt.y > op2->prev->pt.y;
+      }
+
+      if ((op->next == op->prev) ||
+        (op->pt == op->prev->pt))
+      {
+        if (op2IsLarger == cwIsTowardLarger)
+        {
+          cw[i] = op2;
+          ccw[j++] = nullptr;
+        }
+        else
+        {
+          ccw[j] = op2;
+          cw[i++] = nullptr;
+        }
+      }
+      else if ((op2->next == op2->prev) ||
+        (op2->pt == op2->prev->pt))
+      {
+        if (opIsLarger == cwIsTowardLarger)
+        {
+          cw[i] = op;
+          ccw[j++] = nullptr;
+        }
+        else
+        {
+          ccw[j] = op;
+          cw[i++] = nullptr;
+        }
+      }
+      else if (opIsLarger == op2IsLarger)
+      {
+        if (opIsLarger == cwIsTowardLarger)
+        {
+          cw[i] = op;
+          UncoupleEdge(op2);
+          AddToEdge(cw, op2);
+          ccw[j++] = nullptr;
+        }
+        else
+        {
+          cw[i++] = nullptr;
+          ccw[j] = op2;
+          UncoupleEdge(op);
+          AddToEdge(ccw, op);
+          j = 0;
+        }
+      }
+      else
+      {
+        if (opIsLarger == cwIsTowardLarger)
+          cw[i] = op;
+        else
+          ccw[j] = op;
+        if (op2IsLarger == cwIsTowardLarger)
+          cw[i] = op2;
+        else
+          ccw[j] = op2;
+      }
+    }
+  }
+
+  Path64 RectClip::GetPath(OutPt2*& op)
+  {
+    if (!op || op->next == op->prev) return Path64();
+
+    OutPt2* op2 = op->next;
+    while (op2 && op2 != op)
+    {
+      if (CrossProduct(op2->prev->pt, 
+        op2->pt, op2->next->pt) == 0)
+      {
+        op = op2->prev;
+        op2 = UnlinkOp(op2);
+      }
+      else
+        op2 = op2->next;
+    }
+    op = op2; // needed for op cleanup
+    if (!op2) return Path64();
+
+    Path64 result;
+    result.push_back(op->pt);
+    op2 = op->next;
+    while (op2 != op)
+    {
+      result.push_back(op2->pt);
+      op2 = op2->next;
+    }
+    return result;
+  }
+
+  Paths64 RectClip::Execute(const Paths64& paths, bool convex_only)
+  {
+    Paths64 result;
+    if (rect_.IsEmpty()) return result;
+
+    for (const auto& path : paths)
+    {
+      if (path.size() < 3) continue;
+      path_bounds_ = GetBounds(path);
+      if (!rect_.Intersects(path_bounds_))
+        continue; // the path must be completely outside rect_
+      else if (rect_.Contains(path_bounds_))
+      {
+        // the path must be completely inside rect_
+        result.push_back(path);
+        continue;
+      }
+
+      ExecuteInternal(path);
+      if (!convex_only)
+      {
+        CheckEdges();
+        for (int i = 0; i < 4; ++i)
+          TidyEdges(i, edges_[i * 2], edges_[i * 2 + 1]);
+      }
+
+      for (OutPt2*& op :  results_)
+      {
+        Path64 tmp = GetPath(op);
+        if (!tmp.empty())
+          result.emplace_back(tmp);
+      }
+
+      //clean up after every loop
+      op_container_ = std::deque<OutPt2>();
+      results_.clear();
+      for (OutPt2List edge : edges_) edge.clear();
+      start_locs_.clear();
+    }
+    return result;
+  }
+
+  //------------------------------------------------------------------------------
+  // RectClipLines
+  //------------------------------------------------------------------------------
+
+  Paths64 RectClipLines::Execute(const Paths64& paths)
+  {
+    Paths64 result;
+    if (rect_.IsEmpty()) return result;
+
+    for (const auto& path : paths)
+    {
+      if (path.size() < 2) continue;
+      Rect64 pathrec = GetBounds(path);
+
+      if (!rect_.Intersects(pathrec)) continue;
+
+      ExecuteInternal(path);
+
+      for (OutPt2*& op : results_)
+      {
+        Path64 tmp = GetPath(op);
+        if (!tmp.empty())
+          result.emplace_back(tmp);
+      }
+      results_.clear();
+
+      op_container_ = std::deque<OutPt2>();
+      start_locs_.clear();
+    }
+    return result;
+  }
+
+  void RectClipLines::ExecuteInternal(const Path64& path)
+  {
+    if (rect_.IsEmpty() || path.size() < 2) return;
+
+    results_.clear();
+    op_container_ = std::deque<OutPt2>();
+    start_locs_.clear();
+
+    int i = 1, highI = static_cast<int>(path.size()) - 1;
+
+    Location prev = Location::Inside, loc;
+    Location crossing_loc;
+    if (!GetLocation(rect_, path[0], loc))
+    {
+      while (i <= highI && !GetLocation(rect_, path[i], prev)) ++i;
+      if (i > highI) 
+      {
+        // all of path must be inside fRect
+        for (const auto& pt : path) Add(pt);
+        return;
+      }
+      if (prev == Location::Inside) loc = Location::Inside;
+      i = 1;
+    }
+    if (loc == Location::Inside) Add(path[0]);
+
+    ///////////////////////////////////////////////////
+    while (i <= highI)
+    {
+      prev = loc;
+      GetNextLocation(path, loc, i, highI);
+      if (i > highI) break;
+      Point64 ip, ip2;
+      Point64 prev_pt = path[static_cast<size_t>(i - 1)];
+
+      crossing_loc = loc;
+      if (!GetIntersection(rect_as_path_, 
+        path[i], prev_pt, crossing_loc, ip))
+      {
+        // ie remaining outside
+        ++i;
+        continue;
+      }
+
+      ////////////////////////////////////////////////////
+      // we must be crossing the rect boundary to get here
+      ////////////////////////////////////////////////////
+
+      if (loc == Location::Inside) // path must be entering rect
+      {
+        Add(ip, true);
+      }
+      else if (prev != Location::Inside)
+      {
+        // passing right through rect. 'ip' here will be the second 
+        // intersect pt but we'll also need the first intersect pt (ip2)
+        crossing_loc = prev;
+        GetIntersection(rect_as_path_, 
+          prev_pt, path[i], crossing_loc, ip2);
+        Add(ip2, true);
+        Add(ip);
+      }
+      else // path must be exiting rect
+      {
+        Add(ip);
+      }
+    } //while i <= highI
+    ///////////////////////////////////////////////////
+  }
+
+  Path64 RectClipLines::GetPath(OutPt2*& op)
+  {
+    Path64 result;
+    if (!op || op == op->next) return result;
+    op = op->next; // starting at path beginning 
+    result.push_back(op->pt);
+    OutPt2 *op2 = op->next;
+    while (op2 != op)
+    {
+      result.push_back(op2->pt);
+      op2 = op2->next;
+    }        
+    return result;
+  }
+
+} // namespace