feat: godot-engine-source-4.3-stable

engine/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.

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

@@ -0,0 +1,844 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  24 November 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>
+#include "clipper2/clipper.version.h"
+
+#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";
+  static const char* undefined_error =
+    "There is an undefined error in Clipper2";
+#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 undefined_error_i   = 32; // fatal 
+  const int range_error_i       = 64;
+
+#ifndef PI
+  static const double PI = 3.141592653589793238;
+#endif
+
+#ifdef CLIPPER2_MAX_PRECISION
+  const int MAX_DECIMAL_PRECISION = CLIPPER2_MAX_PRECISION;
+#else
+  const int MAX_DECIMAL_PRECISION = 8; // see Discussions #564
+#endif
+
+  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 undefined_error_i:
+      CLIPPER2_THROW(Clipper2Exception(undefined_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(const Point<T2>& p)
+    {
+      Init(p.x, p.y, p.z);
+    }
+
+    Point operator * (const double scale) const
+    {
+      return Point(x * scale, y * scale, z);
+    }
+
+    void SetZ(const int64_t z_value) { z = z_value; }
+
+    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(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>;
+
+  static const Point64 InvalidPoint64 = Point64(
+    (std::numeric_limits<int64_t>::max)(),
+    (std::numeric_limits<int64_t>::max)());
+  static const PointD InvalidPointD = PointD(
+    (std::numeric_limits<double>::max)(),
+    (std::numeric_limits<double>::max)());
+
+
+  // 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(T l, T t, T r, T b) :
+      left(l),
+      top(t),
+      right(r),
+      bottom(b) {}
+
+    Rect(bool is_valid = true)
+    {
+      if (is_valid)
+      {
+        left = right = top = bottom = 0;
+      }
+      else
+      {
+        left = top = (std::numeric_limits<T>::max)();
+        right = bottom = (std::numeric_limits<T>::lowest)();
+      }
+    }
+
+    bool IsValid() const { return left != (std::numeric_limits<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));
+    };
+
+    bool operator==(const Rect<T>& other) const {
+      return left == other.left && right == other.right && 
+        top == other.top && bottom == other.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 InvalidRect64 = Rect64(
+    (std::numeric_limits<int64_t>::max)(), 
+    (std::numeric_limits<int64_t>::max)(), 
+    (std::numeric_limits<int64_t>::lowest)(),
+    (std::numeric_limits<int64_t>::lowest)());
+  static const RectD InvalidRectD = RectD(
+    (std::numeric_limits<double>::max)(),
+    (std::numeric_limits<double>::max)(),
+    (std::numeric_limits<double>::lowest)(),
+    (std::numeric_limits<double>::lowest)());
+
+  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;
+  }
+
+  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 void StripDuplicates( Path<T>& path, bool is_closed_path)
+  {
+    //https://stackoverflow.com/questions/1041620/whats-the-most-efficient-way-to-erase-duplicates-and-sort-a-vector#:~:text=Let%27s%20compare%20three%20approaches%3A
+    path.erase(std::unique(path.begin(), path.end()), path.end());
+    if (is_closed_path)
+      while (path.size() > 1 && path.back() == path.front()) path.pop_back();
+  }
+
+  template<typename T>
+  inline void StripDuplicates( Paths<T>& paths, bool is_closed_path)
+  {
+    for (typename Paths<T>::iterator paths_citer = paths.begin();
+      paths_citer != paths.end(); ++paths_citer)
+    {
+      StripDuplicates(*paths_citer, is_closed_path);
+    }
+  }
+
+  // Miscellaneous ------------------------------------------------------------
+
+  inline void CheckPrecision(int& precision, int& error_code)
+  {
+    if (precision >= -MAX_DECIMAL_PRECISION && precision <= MAX_DECIMAL_PRECISION) return;
+    error_code |= precision_error_i; // non-fatal error
+    DoError(precision_error_i);      // does nothing unless exceptions enabled
+    precision = precision > 0 ? MAX_DECIMAL_PRECISION : -MAX_DECIMAL_PRECISION;
+  }
+
+  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 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 false;
+    double t = ((ln1a.x - ln2a.x) * dy2 - (ln1a.y - ln2a.y) * dx2) / det;
+    if (t <= 0.0) ip = ln1a;        // ?? check further (see also #568)
+    else if (t >= 1.0) ip = ln1b;   // ?? check further
+    else
+    {
+      ip.x = static_cast<int64_t>(ln1a.x + t * dx1);
+      ip.y = static_cast<int64_t>(ln1a.y + t * dy1);
+    }
+    return true;
+  }
+
+  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);
+    }
+  }
+
+  template<typename T>
+  inline Point<T> GetClosestPointOnSegment(const Point<T>& offPt,
+    const Point<T>& seg1, const Point<T>& 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;
+    if constexpr (std::numeric_limits<T>::is_integer)
+      return Point<T>(
+        seg1.x + static_cast<T>(nearbyint(q * dx)),
+        seg1.y + static_cast<T>(nearbyint(q * dy)));
+    else
+      return Point<T>(
+        seg1.x + static_cast<T>(q * dx),
+        seg1.y + static_cast<T>(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

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

@@ -0,0 +1,637 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  22 November 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
+
+#include <cstdlib>
+#include <stdint.h> //#541
+#include <iostream>
+#include <queue>
+#include <vector>
+#include <functional>
+#include <numeric>
+#include <memory>
+
+#include "clipper2/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;
+		OutRec* recursive_split = nullptr;
+		Rect64 bounds = {};
+		Path64 path;
+		bool is_open = 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;
+
+	// ReuseableDataContainer64 ------------------------------------------------
+
+	class ReuseableDataContainer64 {
+	private:
+		friend class ClipperBase;
+		LocalMinimaList minima_list_;
+		std::vector<Vertex*> vertex_lists_;
+		void AddLocMin(Vertex& vert, PathType polytype, bool is_open);
+	public:
+		virtual ~ReuseableDataContainer64();
+		void Clear();
+		void AddPaths(const Paths64& paths, PathType polytype, bool is_open);
+	};
+
+	// 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 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:
+		bool preserve_collinear_ = true;
+		bool reverse_solution_ = false;
+		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);
+		bool CheckSplitOwner(OutRec* outrec, OutRecList* splits);
+		void RecursiveCheckOwners(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() const { return error_code_; };
+		void PreserveCollinear(bool val) { preserve_collinear_ = val; };
+		bool PreserveCollinear() const { return preserve_collinear_;};
+		void ReverseSolution(bool val) { reverse_solution_ = val; };
+		bool ReverseSolution() const { return reverse_solution_; };
+		void Clear();
+		void AddReuseableData(const ReuseableDataContainer64& reuseable_data);
+#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);
+		}
+
+		PolyPath64* operator [] (size_t index) const
+		{ 
+			return childs_[index].get(); //std::unique_ptr
+		} 
+
+		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 scale_;
+		PathD polygon_;
+	public:
+		explicit PolyPathD(PolyPathD* parent = nullptr) : PolyPath(parent)
+		{
+			scale_ = parent ? parent->scale_ : 1.0;
+		}
+
+		~PolyPathD() {
+			childs_.resize(0);
+		}
+
+		PolyPathD* operator [] (size_t index) const
+		{ 
+			return childs_[index].get();
+		}
+
+		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 SetScale(double value) { scale_ = value; }
+		double Scale() const { return 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, scale_, error_code);
+			return result;
+		}
+
+		PolyPathD* AddChild(const PathD& path)
+		{
+			auto p = std::make_unique<PolyPathD>(this);
+			PolyPathD* 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 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.SetScale(invScale_);
+				open_paths.clear();
+				BuildTreeD(polytree, open_paths);
+			}
+			CleanUp();
+			return succeeded_;
+		}
+
+	};
+
+}  // namespace 
+
+#endif  // CLIPPER_ENGINE_H

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

@@ -0,0 +1,565 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  26 November 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                            *
+*******************************************************************************/
+
+
+/* 
+ Boolean clipping:
+ cliptype: None=0, Intersection=1, Union=2, Difference=3, Xor=4
+ fillrule: EvenOdd=0, NonZero=1, Positive=2, Negative=3
+
+ Polygon offsetting (inflate/deflate):
+ jointype: Square=0, Bevel=1, Round=2, Miter=3
+ endtype: Polygon=0, Joined=1, Butt=2, Square=3, Round=4
+
+The path structures used extensively in other parts of this library are all
+based on std::vector classes. Since C++ classes can't be accessed by other
+languages, these paths must be converted into simple C data structures that
+can be understood by just about any programming language. And these C style
+path structures are simple arrays of int64_t (CPath64) and double (CPathD).
+
+CPath64 and CPathD:
+These are arrays of consecutive x and y path coordinates preceeded by  
+a pair of values containing the path's length (N) and a 0 value.
+__________________________________
+|counter|coord1|coord2|...|coordN|
+|N, 0   |x1, y1|x2, y2|...|xN, yN|
+__________________________________
+
+CPaths64 and CPathsD:
+These are also arrays containing any number of consecutive CPath64 or
+CPathD  structures. But preceeding these consecutive paths, there is pair of
+values that contain the total length of the array (A) structure and 
+the number (C) of CPath64 or CPathD it contains.
+_______________________________
+|counter|path1|path2|...|pathC|
+|A  , C |                     |
+_______________________________
+
+CPolytree64 and CPolytreeD:
+These are also arrays consisting of CPolyPath structures that represent 
+individual paths in a tree structure. However, the very first (ie top)
+CPolyPath is just the tree container that won't have a path. And because
+of that, its structure will be very slightly different from the remaining
+CPolyPath. This difference will be discussed below.
+
+CPolyPath64 and CPolyPathD:
+These are simple arrays consisting of a series of path coordinates followed 
+by any number of child (ie nested) CPolyPath. Preceeding these are two values 
+indicating the length of the path (N) and the number of child CPolyPath (C).
+____________________________________________________________
+|counter|coord1|coord2|...|coordN| child1|child2|...|childC|
+|N  , C |x1, y1|x2, y2|...|xN, yN|                         |
+____________________________________________________________
+
+As mentioned above, the very first CPolyPath structure is just a container
+that owns (both directly and indirectly) every other CPolyPath in the tree. 
+Since this first CPolyPath has no path, instead of a path length, its very
+first value will contain the total length of the CPolytree array structure.
+
+All theses exported structures (CPaths64, CPathsD, CPolyTree64 & CPolyTreeD)
+are arrays of type int64_t or double. And the first value in these arrays 
+will always contain the length of that array.
+
+These array structures are allocated in heap memory which will eventually 
+need to be released. But since applications dynamically linking to these 
+functions may use different memory managers, the only safe way to free up
+this memory is to use the exported DisposeArray64 and  DisposeArrayD 
+functions below.
+*/
+
+
+#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 int64_t* CPolyPath64;
+typedef int64_t* CPolyTree64;
+typedef double* CPolyPathD;
+typedef double* 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;
+}
+
+#ifdef _WIN32
+  #define EXTERN_DLL_EXPORT extern "C" __declspec(dllexport)
+#else
+  #define EXTERN_DLL_EXPORT extern "C" 
+#endif
+
+
+//////////////////////////////////////////////////////
+// EXPORTED FUNCTION DECLARATIONS
+//////////////////////////////////////////////////////
+
+EXTERN_DLL_EXPORT const char* Version();
+
+EXTERN_DLL_EXPORT void DisposeArray64(int64_t*& p)
+{
+  delete[] p;
+}
+
+EXTERN_DLL_EXPORT void DisposeArrayD(double*& p)
+{
+  delete[] p;
+}
+
+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 BooleanOp_PolyTree64(uint8_t cliptype,
+  uint8_t fillrule, const CPaths64 subjects,
+  const CPaths64 subjects_open, const CPaths64 clips,
+  CPolyTree64& sol_tree, 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 BooleanOp_PolyTreeD(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);
+
+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);
+
+// RectClip & RectClipLines:
+EXTERN_DLL_EXPORT CPaths64 RectClip64(const CRect64& rect,
+  const CPaths64 paths);
+EXTERN_DLL_EXPORT CPathsD RectClipD(const CRectD& rect,
+  const CPathsD paths, int precision = 2);
+EXTERN_DLL_EXPORT CPaths64 RectClipLines64(const CRect64& rect,
+  const CPaths64 paths);
+EXTERN_DLL_EXPORT CPathsD RectClipLinesD(const CRectD& rect,
+  const CPathsD paths, int precision = 2);
+
+//////////////////////////////////////////////////////
+// INTERNAL FUNCTIONS
+//////////////////////////////////////////////////////
+
+template <typename T>
+static void GetPathCountAndCPathsArrayLen(const Paths<T>& paths,
+  size_t& cnt, size_t& array_len)
+{
+  array_len = 2;
+  cnt = 0;
+  for (const Path<T>& path : paths)
+    if (path.size())
+    {
+      array_len += path.size() * 2 + 2;
+      ++cnt;
+    }
+}
+
+static size_t GetPolyPath64ArrayLen(const PolyPath64& pp)
+{
+  size_t result = 2; // poly_length + child_count
+  result += pp.Polygon().size() * 2;
+  //plus nested children :)
+  for (size_t i = 0; i < pp.Count(); ++i)
+    result += GetPolyPath64ArrayLen(*pp[i]);
+  return result;
+}
+
+static void GetPolytreeCountAndCStorageSize(const PolyTree64& tree, 
+  size_t& cnt, size_t& array_len)
+{
+  cnt = tree.Count(); // nb: top level count only 
+  array_len = GetPolyPath64ArrayLen(tree);
+}
+
+template <typename T>
+static T* CreateCPaths(const Paths<T>& paths)
+{
+  size_t cnt = 0, array_len = 0;
+  GetPathCountAndCPathsArrayLen(paths, cnt, array_len);
+  T* result = new T[array_len], * v = result;
+  *v++ = array_len;
+  *v++ = cnt;
+  for (const Path<T>& path : paths)
+  {
+    if (!path.size()) continue;
+    *v++ = path.size();
+    *v++ = 0;
+    for (const Point<T>& pt : path)
+    {
+      *v++ = pt.x;
+      *v++ = pt.y;
+    }
+  }
+  return result;
+}
+
+
+CPathsD CreateCPathsDFromPaths64(const Paths64& paths, double scale)
+{
+  if (!paths.size()) return nullptr;
+  size_t cnt, array_len;
+  GetPathCountAndCPathsArrayLen(paths, cnt, array_len);
+  CPathsD result = new double[array_len], v = result;
+  *v++ = (double)array_len;
+  *v++ = (double)cnt;
+  for (const Path64& path : paths)
+  {
+    if (!path.size()) continue;
+    *v = (double)path.size();
+    ++v; *v++ = 0;
+    for (const Point64& pt : path)
+    {
+      *v++ = pt.x * scale;
+      *v++ = pt.y * scale;
+    }
+  }
+  return result;
+}
+
+template <typename T>
+static Paths<T> ConvertCPaths(T* paths)
+{
+  Paths<T> result;
+  if (!paths) return result;
+  T* v = paths; ++v;
+  size_t cnt = *v++;
+  result.reserve(cnt);
+  for (size_t i = 0; i < cnt; ++i)
+  {
+    size_t cnt2 = *v;
+    v += 2;
+    Path<T> path;
+    path.reserve(cnt2);
+    for (size_t j = 0; j < cnt2; ++j)
+    {
+      T x = *v++, y = *v++;
+      path.push_back(Point<T>(x, y));
+    }
+    result.push_back(path);
+  }
+  return result;
+}
+
+
+static Paths64 ConvertCPathsDToPaths64(const CPathsD paths, double scale)
+{
+  Paths64 result;
+  if (!paths) return result;
+  double* v = paths; 
+  ++v; // skip the first value (0)
+  int64_t cnt = (int64_t)*v++;
+  result.reserve(cnt);
+  for (int i = 0; i < cnt; ++i)
+  {
+    int64_t cnt2 = (int64_t)*v;
+    v += 2;
+    Path64 path;
+    path.reserve(cnt2);
+    for (int j = 0; j < cnt2; ++j)
+    {
+      double x = *v++ * scale;
+      double y = *v++ * scale;
+      path.push_back(Point64(x, y));
+    }
+    result.push_back(path);
+  }
+  return result;
+}
+
+template <typename T>
+static void CreateCPolyPath(const PolyPath64* pp, T*& v, T scale)
+{
+  *v++ = static_cast<T>(pp->Polygon().size());
+  *v++ = static_cast<T>(pp->Count());
+  for (const Point64& pt : pp->Polygon())
+  {
+    *v++ = static_cast<T>(pt.x * scale);
+    *v++ = static_cast<T>(pt.y * scale);
+  }
+  for (size_t i = 0; i < pp->Count(); ++i)
+    CreateCPolyPath(pp->Child(i), v, scale);
+}
+
+template <typename T>
+static T* CreateCPolyTree(const PolyTree64& tree, T scale)
+{
+  if (scale == 0) scale = 1;
+  size_t cnt, array_len;
+  GetPolytreeCountAndCStorageSize(tree, cnt, array_len);
+  if (!cnt) return nullptr;
+  // allocate storage
+  T* result = new T[array_len];
+  T* v = result;
+
+  *v++ = static_cast<T>(array_len);
+  *v++ = static_cast<T>(tree.Count());
+  for (size_t i = 0; i < tree.Count(); ++i)
+    CreateCPolyPath(tree.Child(i), v, scale);
+  return result;
+}
+
+//////////////////////////////////////////////////////
+// EXPORTED FUNCTION DEFINITIONS
+//////////////////////////////////////////////////////
+
+EXTERN_DLL_EXPORT const char* Version()
+{
+  return CLIPPER2_VERSION;
+}
+
+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       = ConvertCPaths(subjects);
+  sub_open  = ConvertCPaths(subjects_open);
+  clp       = ConvertCPaths(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 = CreateCPaths(sol);
+  solution_open = CreateCPaths(sol_open);
+  return 0; //success !!
+}
+
+EXTERN_DLL_EXPORT int BooleanOp_PolyTree64(uint8_t cliptype,
+  uint8_t fillrule, const CPaths64 subjects,
+  const CPaths64 subjects_open, const CPaths64 clips,
+  CPolyTree64& sol_tree, 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 = ConvertCPaths(subjects);
+  sub_open = ConvertCPaths(subjects_open);
+  clp = ConvertCPaths(clips);
+
+  PolyTree64 tree;
+  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), tree, sol_open))
+    return -1; // clipping bug - should never happen :)
+
+  sol_tree = CreateCPolyTree(tree, (int64_t)1);
+  solution_open = CreateCPaths(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       = ConvertCPathsDToPaths64(subjects, scale);
+  sub_open  = ConvertCPathsDToPaths64(subjects_open, scale);
+  clp       = ConvertCPathsDToPaths64(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;
+  solution = CreateCPathsDFromPaths64(sol, 1 / scale);
+  solution_open = CreateCPathsDFromPaths64(sol_open, 1 / scale);
+  return 0;
+}
+
+EXTERN_DLL_EXPORT int BooleanOp_PolyTreeD(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;
+  
+  double scale = std::pow(10, precision);
+
+  int err = 0;
+  Paths64 sub, sub_open, clp, sol_open;
+  sub = ConvertCPathsDToPaths64(subjects, scale);
+  sub_open = ConvertCPathsDToPaths64(subjects_open, scale);
+  clp = ConvertCPathsDToPaths64(clips, scale);
+
+  PolyTree64 tree;
+  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), tree, sol_open))
+    return -1; // clipping bug - should never happen :)
+
+  solution = CreateCPolyTree(tree, 1/scale);
+  solution_open = CreateCPathsDFromPaths64(sol_open, 1 / scale);
+  return 0; //success !!
+}
+
+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 = ConvertCPaths(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 CreateCPaths(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 = ConvertCPathsDToPaths64(paths, scale);
+  clip_offset.AddPaths(pp, JoinType(jointype), EndType(endtype));
+  Paths64 result;
+  clip_offset.Execute(delta * scale, result);
+
+  return CreateCPathsDFromPaths64(result, 1 / scale);
+}
+
+EXTERN_DLL_EXPORT CPaths64 RectClip64(const CRect64& rect, const CPaths64 paths)
+{
+  if (CRectIsEmpty(rect) || !paths) return nullptr;
+  Rect64 r64 = CRectToRect(rect);
+  class RectClip64 rc(r64);
+  Paths64 pp = ConvertCPaths(paths);
+  Paths64 result = rc.Execute(pp);
+  return CreateCPaths(result);
+}
+
+EXTERN_DLL_EXPORT CPathsD RectClipD(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);
+
+  RectD r = CRectToRect(rect);
+  Rect64 rec = ScaleRect<int64_t, double>(r, scale);
+  Paths64 pp = ConvertCPathsDToPaths64(paths, scale);
+  class RectClip64 rc(rec);
+  Paths64 result = rc.Execute(pp);
+
+  return CreateCPathsDFromPaths64(result, 1 / scale);
+}
+
+EXTERN_DLL_EXPORT CPaths64 RectClipLines64(const CRect64& rect,
+  const CPaths64 paths)
+{
+  if (CRectIsEmpty(rect) || !paths) return nullptr;
+  Rect64 r = CRectToRect(rect);
+  class RectClipLines64 rcl (r);
+  Paths64 pp = ConvertCPaths(paths);
+  Paths64 result = rcl.Execute(pp);
+  return CreateCPaths(result);
+}
+
+EXTERN_DLL_EXPORT CPathsD RectClipLinesD(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 RectClipLines64 rcl(r);
+  Paths64 pp = ConvertCPathsDToPaths64(paths, scale);
+  Paths64 result = rcl.Execute(pp);
+  return CreateCPathsDFromPaths64(result, 1 / scale);
+}
+
+}  // end Clipper2Lib namespace
+  
+#endif  // CLIPPER2_EXPORT_H

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

@@ -0,0 +1,781 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  18 November 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 "clipper2/clipper.core.h"
+#include "clipper2/clipper.engine.h"
+#include "clipper2/clipper.offset.h"
+#include "clipper2/clipper.minkowski.h"
+#include "clipper2/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);
+  }
+
+  template <typename T>
+  inline Path<T> TranslatePath(const Path<T>& path, T dx, T dy)
+  {
+    Path<T> result;
+    result.reserve(path.size());
+    std::transform(path.begin(), path.end(), back_inserter(result),
+      [dx, dy](const auto& pt) { return Point<T>(pt.x + dx, pt.y +dy); });
+    return result;
+  }
+
+  inline Path64 TranslatePath(const Path64& path, int64_t dx, int64_t dy)
+  {
+    return TranslatePath<int64_t>(path, dx, dy);
+  }
+
+  inline PathD TranslatePath(const PathD& path, double dx, double dy)
+  {
+    return TranslatePath<double>(path, dx, dy);
+  }
+
+  template <typename T>
+  inline Paths<T> TranslatePaths(const Paths<T>& paths, T dx, T dy)
+  {
+    Paths<T> 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 TranslatePaths(const Paths64& paths, int64_t dx, int64_t dy)
+  {
+    return TranslatePaths<int64_t>(paths, dx, dy);
+  }
+
+  inline PathsD TranslatePaths(const PathsD& paths, double dx, double dy)
+  {
+    return TranslatePaths<double>(paths, dx, dy);
+  }
+
+  inline Paths64 RectClip(const Rect64& rect, const Paths64& paths)
+  {
+    if (rect.IsEmpty() || paths.empty()) return Paths64();
+    RectClip64 rc(rect);
+    return rc.Execute(paths);
+  }
+
+  inline Paths64 RectClip(const Rect64& rect, const Path64& path)
+  {
+    if (rect.IsEmpty() || path.empty()) return Paths64();
+    RectClip64 rc(rect);
+    return rc.Execute(Paths64{ path });
+  }
+
+  inline PathsD RectClip(const RectD& rect, const PathsD& paths, 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);
+    RectClip64 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), 1 / scale, error_code);
+  }
+
+  inline PathsD RectClip(const RectD& rect, const PathD& path, int precision = 2)
+  {
+    return RectClip(rect, PathsD{ path }, precision);
+  }
+
+  inline Paths64 RectClipLines(const Rect64& rect, const Paths64& lines)
+  {
+    if (rect.IsEmpty() || lines.empty()) return Paths64();
+    RectClipLines64 rcl(rect);
+    return rcl.Execute(lines);
+  }
+
+  inline Paths64 RectClipLines(const Rect64& rect, const Path64& line)
+  {
+    return RectClipLines(rect, Paths64{ line });
+  }
+
+  inline PathsD RectClipLines(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);
+    RectClipLines64 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);
+  }
+
+  inline PathsD RectClipLines(const RectD& rect, const PathD& line, int precision = 2)
+  {
+    return RectClipLines(rect, PathsD{ line }, precision);
+  }
+
+  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
+
+        // checking for a single vertex outside is a bit too crude since 
+        // it doesn't account for rounding errors. It's better to check 
+        // for consecutive vertices found outside the parent's polygon.
+
+        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, 
+      size_t idx, bool isHole, size_t count, const std::string& preamble)
+    {
+      std::string plural = (count == 1) ? "." : "s.";
+      if (isHole)
+        os << preamble << "+- Hole (" << idx << ") contains " << count <<
+        " nested polygon" << plural << std::endl;
+      else
+        os << preamble << "+- Polygon (" << idx << ") contains " << count <<
+          " hole" << plural << std::endl;
+    }
+
+    static void OutlinePolyPath64(std::ostream& os, const PolyPath64& pp,
+      size_t idx, std::string preamble)
+    {
+      OutlinePolyPath(os, idx, pp.IsHole(), pp.Count(), preamble);
+      for (size_t i = 0; i < pp.Count(); ++i)
+        if (pp.Child(i)->Count())
+          details::OutlinePolyPath64(os, *pp.Child(i), i, preamble + "  ");
+    }
+
+    static void OutlinePolyPathD(std::ostream& os, const PolyPathD& pp,
+      size_t idx, std::string preamble)
+    {
+      OutlinePolyPath(os, idx, pp.IsHole(), pp.Count(), preamble);
+      for (size_t i = 0; i < pp.Count(); ++i)
+        if (pp.Child(i)->Count())
+          details::OutlinePolyPathD(os, *pp.Child(i), i, preamble + "  ");
+    }
+
+    template<typename T, typename U>
+    inline constexpr void MakePathGeneric(const T an_array, 
+      size_t array_size, std::vector<U>& result)
+    {
+      result.reserve(array_size / 2);
+      for (size_t i = 0; i < array_size; i +=2)
+#ifdef USINGZ
+        result.push_back( U{ an_array[i], an_array[i +1], 0} );
+#else
+        result.push_back( U{ an_array[i], an_array[i + 1]} );
+#endif
+    }
+
+  } // end details namespace 
+
+  inline std::ostream& operator<< (std::ostream& os, const PolyTree64& pp)
+  {
+    std::string plural = (pp.Count() == 1) ? " polygon." : " polygons.";
+    os << std::endl << "Polytree with " << pp.Count() << plural << std::endl;
+      for (size_t i = 0; i < pp.Count(); ++i)
+        if (pp.Child(i)->Count())
+          details::OutlinePolyPath64(os, *pp.Child(i), i, "  ");
+    os << std::endl << std::endl;
+    return os;
+  }
+
+  inline std::ostream& operator<< (std::ostream& os, const PolyTreeD& pp)
+  {
+    std::string plural = (pp.Count() == 1) ? " polygon." : " polygons.";
+    os << std::endl << "Polytree with " << pp.Count() << plural << std::endl;
+    for (size_t i = 0; i < pp.Count(); ++i)
+      if (pp.Child(i)->Count())
+        details::OutlinePolyPathD(os, *pp.Child(i), i, "  ");
+    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;
+  }
+
+  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;
+    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;
+    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;
+    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;
+    details::MakePathGeneric(list, N, result);
+    return result;
+  }
+
+#ifdef USINGZ
+  template<typename T2, std::size_t N>
+  inline Path64 MakePathZ(const T2(&list)[N])
+  {
+    static_assert(N % 3 == 0 && std::numeric_limits<T2>::is_integer,
+      "MakePathZ requires integer values in multiples of 3");
+    std::size_t size = N / 3;
+    Path64 result(size);
+    for (size_t i = 0; i < size; ++i)
+      result[i] = Point64(list[i * 3], 
+        list[i * 3 + 1], list[i * 3 + 2]);
+    return result;
+  }
+
+  template<typename T2, std::size_t N>
+  inline PathD MakePathZD(const T2(&list)[N])
+  {
+    static_assert(N % 3 == 0,
+      "MakePathZD requires values in multiples of 3");
+    std::size_t size = N / 3;
+    PathD result(size);
+    if constexpr (std::numeric_limits<T2>::is_integer)
+      for (size_t i = 0; i < size; ++i)
+        result[i] = PointD(list[i * 3],
+          list[i * 3 + 1], list[i * 3 + 2]);
+    else
+      for (size_t i = 0; i < size; ++i)
+        result[i] = PointD(list[i * 3], list[i * 3 + 1], 
+          static_cast<int64_t>(list[i * 3 + 2]));
+    return result;
+  }
+#endif
+
+  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 isClosedPath = true)
+  {
+    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;
+    if (isClosedPath)
+    {
+      distSqr[0] = PerpendicDistFromLineSqrd(path[0], path[high], path[1]);
+      distSqr[high] = PerpendicDistFromLineSqrd(path[high], path[0], path[high - 1]);
+    }
+    else 
+    {
+      distSqr[0] = MAX_DBL;
+      distSqr[high] = MAX_DBL;
+    }
+    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;
+
+      // flag for removal the smaller of adjacent 'distances'
+      if (distSqr[next] < distSqr[curr])
+      {
+        prior2 = prior;
+        prior = curr;
+        curr = next;
+        next = GetNext(next, high, flags);
+      }
+      else
+        prior2 = GetPrior(prior, high, flags);
+        
+      flags[curr] = true;
+      curr = next;
+      next = GetNext(next, high, flags);
+
+      if (isClosedPath || ((curr != high) && (curr != 0)))
+        distSqr[curr] = PerpendicDistFromLineSqrd(path[curr], path[prior], path[next]);
+      if (isClosedPath || ((prior != 0) && (prior != high)))
+        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 isClosedPath = true)
+  {
+    Paths<T> result;
+    result.reserve(paths.size());
+    for (const auto& path : paths)
+      result.push_back(SimplifyPath(path, epsilon, isClosedPath));
+    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

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

@@ -0,0 +1,120 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  1 November 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 "clipper2/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

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

@@ -0,0 +1,124 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  19 November 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, Bevel, Round, Miter };
+//Square : Joins are 'squared' at exactly the offset distance (more complex code)
+//Bevel  : Similar to Square, but the offset distance varies with angle (simple code & faster)
+
+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
+
+typedef std::function<double(const Path64& path, const PathD& path_normals, size_t curr_idx, size_t prev_idx)> DeltaCallback64;
+
+class ClipperOffset {
+private:
+
+	class Group {
+	public:
+		Paths64 paths_in;
+		std::vector<bool> is_hole_list;
+		std::vector<Rect64> bounds_list;
+		int lowest_path_idx = -1;
+		bool is_reversed = false;
+		JoinType join_type;
+		EndType end_type;
+		Group(const Paths64& _paths, JoinType _join_type, EndType _end_type);
+	};
+
+	int   error_code_ = 0;
+	double delta_ = 0.0;
+	double 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;
+	Path64 path_out;
+	Paths64 solution;
+	std::vector<Group> groups_;
+	JoinType join_type_ = JoinType::Bevel;
+	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
+	DeltaCallback64 deltaCallback64_ = nullptr;
+
+	size_t CalcSolutionCapacity();
+	bool CheckReverseOrientation();
+	void DoBevel(const Path64& path, size_t j, size_t k);
+	void DoSquare(const Path64& path, size_t j, size_t k);
+	void DoMiter(const Path64& path, size_t j, size_t k, double cos_a);
+	void DoRound(const Path64& path, size_t j, size_t k, double angle);
+	void BuildNormals(const Path64& path);
+	void OffsetPolygon(Group& group, const Path64& path);
+	void OffsetOpenJoined(Group& group, const Path64& path);
+	void OffsetOpenPath(Group& group, const Path64& path);
+	void OffsetPoint(Group& group, const 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);
+	void Execute(DeltaCallback64 delta_cb, Paths64& paths);
+
+	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
+	void SetDeltaCallback(DeltaCallback64 cb) { deltaCallback64_ = cb; }
+
+};
+
+}
+#endif /* CLIPPER_OFFSET_H_ */

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

@@ -0,0 +1,81 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  1 November 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 "clipper2/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;
+  };
+
+  //------------------------------------------------------------------------------
+  // RectClip64
+  //------------------------------------------------------------------------------
+
+  class RectClip64 {
+  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 RectClip64(const Rect64& rect) :
+      rect_(rect),
+      rect_as_path_(rect.AsPath()),
+      rect_mp_(rect.MidPoint()) {}
+    Paths64 Execute(const Paths64& paths);
+  };
+
+  //------------------------------------------------------------------------------
+  // RectClipLines64
+  //------------------------------------------------------------------------------
+
+  class RectClipLines64 : public RectClip64 {
+  private:
+    void ExecuteInternal(const Path64& path);
+    Path64 GetPath(OutPt2*& op);
+  public:
+    explicit RectClipLines64(const Rect64& rect) : RectClip64(rect) {};
+    Paths64 Execute(const Paths64& paths);
+  };
+
+} // Clipper2Lib namespace
+#endif  // CLIPPER_RECTCLIP_H

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

@@ -0,0 +1,6 @@
+#ifndef CLIPPER_VERSION_H
+#define CLIPPER_VERSION_H
+
+constexpr auto CLIPPER2_VERSION = "1.3.0";
+
+#endif  // CLIPPER_VERSION_H

engine/thirdparty/clipper2/patches/clipper2-exceptions.patch

@@ -0,0 +1,38 @@
+diff --git a/thirdparty/clipper2/include/clipper2/clipper.core.h b/thirdparty/clipper2/include/clipper2/clipper.core.h
+index b3dddeeaa2..a77cdad5f4 100644
+--- a/thirdparty/clipper2/include/clipper2/clipper.core.h
++++ b/thirdparty/clipper2/include/clipper2/clipper.core.h
+@@ -21,6 +21,8 @@
+ #include <numeric>
+ #include "clipper2/clipper.version.h"
+ 
++#define CLIPPER2_THROW(exception) std::abort()
++
+ namespace Clipper2Lib
+ {
+ 
+@@ -78,18 +80,18 @@ 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 undefined_error_i:
+-      throw Clipper2Exception(undefined_error);
++      CLIPPER2_THROW(Clipper2Exception(undefined_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
+   }
+ 

engine/thirdparty/clipper2/patches/gcc14-warning.patch

@@ -0,0 +1,22 @@
+diff --git a/thirdparty/clipper2/include/clipper2/clipper.core.h b/thirdparty/clipper2/include/clipper2/clipper.core.h
+index a77cdad5f4..0de7c3720e 100644
+--- a/thirdparty/clipper2/include/clipper2/clipper.core.h
++++ b/thirdparty/clipper2/include/clipper2/clipper.core.h
+@@ -138,7 +138,7 @@ namespace Clipper2Lib
+     }
+ 
+     template <typename T2>
+-    explicit Point<T>(const Point<T2>& p)
++    explicit Point(const Point<T2>& p)
+     {
+       Init(p.x, p.y, p.z);
+     }
+@@ -180,7 +180,7 @@ namespace Clipper2Lib
+     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); }
++    explicit Point(const Point<T2>& p) { Init(p.x, p.y); }
+ 
+     Point operator * (const double scale) const
+     {

engine/thirdparty/clipper2/src/clipper.offset.cpp

@@ -0,0 +1,723 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  28 November 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
+//------------------------------------------------------------------------------
+
+inline bool ToggleBoolIf(bool val, bool condition)
+{
+	return condition ? !val : val;
+}
+
+void GetMultiBounds(const Paths64& paths, std::vector<Rect64>& recList)
+{
+	recList.reserve(paths.size());
+	for (const Path64& path : paths)
+	{ 
+		if (path.size() < 1)
+		{
+			recList.push_back(InvalidRect64);
+			continue;
+		}
+		int64_t x = path[0].x, y = path[0].y;
+		Rect64 r = Rect64(x, y, x, y);
+		for (const Point64& pt : path)
+		{
+			if (pt.y > r.bottom) r.bottom = pt.y;
+			else if (pt.y < r.top) r.top = pt.y;
+			if (pt.x > r.right) r.right = pt.x;
+			else if (pt.x < r.left) r.left = pt.x;
+		}
+		recList.push_back(r);
+	}
+}
+
+bool ValidateBounds(std::vector<Rect64>& recList, double delta)
+{
+	int64_t int_delta = static_cast<int64_t>(delta);
+	int64_t big = MAX_COORD - int_delta;
+	int64_t small = MIN_COORD + int_delta;
+	for (const Rect64& r : recList)
+	{
+		if (!r.IsValid()) continue; // ignore invalid paths
+		else if (r.left < small || r.right > big ||
+			r.top < small || r.bottom > big) return false;
+	}
+	return true;
+}
+
+int GetLowestClosedPathIdx(std::vector<Rect64>& boundsList)
+{
+	int i = -1, result = -1;
+	Point64 botPt = Point64(INT64_MAX, INT64_MIN);
+	for (const Rect64& r : boundsList)
+	{		
+		++i;
+		if (!r.IsValid()) continue; // ignore invalid paths
+		else if (r.bottom > botPt.y || (r.bottom == botPt.y && r.left < botPt.x))
+		{
+			botPt = Point64(r.left, r.bottom);
+			result = static_cast<int>(i);
+		}
+	}
+	return result;
+}
+
+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::Group methods
+//------------------------------------------------------------------------------
+
+ClipperOffset::Group::Group(const Paths64& _paths, JoinType _join_type, EndType _end_type):
+	paths_in(_paths), join_type(_join_type), end_type(_end_type)
+{
+	bool is_joined =
+		(end_type == EndType::Polygon) ||
+		(end_type == EndType::Joined);
+	for (Path64& p: paths_in)
+	  StripDuplicates(p, is_joined);
+
+	// get bounds of each path --> bounds_list
+	GetMultiBounds(paths_in, bounds_list);
+
+	if (end_type == EndType::Polygon)
+	{
+		is_hole_list.reserve(paths_in.size());
+		for (const Path64& path : paths_in)
+			is_hole_list.push_back(Area(path) < 0);
+		lowest_path_idx = GetLowestClosedPathIdx(bounds_list);
+		// the lowermost path must be an outer path, so if its orientation is negative,
+		// then flag the whole group is 'reversed' (will negate delta etc.)
+		// as this is much more efficient than reversing every path.
+		is_reversed = (lowest_path_idx >= 0) && is_hole_list[lowest_path_idx];
+		if (is_reversed) is_hole_list.flip();
+	}
+	else
+	{
+		lowest_path_idx = -1;
+		is_reversed = false;
+		is_hole_list.resize(paths_in.size());
+	}
+}
+
+
+//------------------------------------------------------------------------------
+// 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_stop_iter = --path.cend();
+	for (path_iter = path.cbegin(); path_iter != path_stop_iter; ++path_iter)
+		norms.push_back(GetUnitNormal(*path_iter,*(path_iter +1)));
+	norms.push_back(GetUnitNormal(*path_stop_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::DoBevel(const Path64& path, size_t j, size_t k)
+{
+	PointD pt1, pt2;
+	if (j == k)
+	{
+		double abs_delta = std::abs(group_delta_);
+		pt1 = PointD(path[j].x - abs_delta * norms[j].x, path[j].y - abs_delta * norms[j].y);
+		pt2 = PointD(path[j].x + abs_delta * norms[j].x, path[j].y + abs_delta * norms[j].y);
+	} 
+	else
+	{
+		pt1 = PointD(path[j].x + group_delta_ * norms[k].x, path[j].y + group_delta_ * norms[k].y);
+		pt2 = PointD(path[j].x + group_delta_ * norms[j].x, path[j].y + group_delta_ * norms[j].y);
+	}
+	path_out.push_back(Point64(pt1));
+	path_out.push_back(Point64(pt2));
+}
+
+void ClipperOffset::DoSquare(const Path64& path, size_t j, size_t k)
+{
+	PointD vec;
+	if (j == k) 
+		vec = PointD(norms[j].y, -norms[j].x);
+	else
+		vec = GetAvgUnitVector(
+			PointD(-norms[k].y, norms[k].x),
+			PointD(norms[j].y, -norms[j].x));
+
+	double abs_delta = std::abs(group_delta_);
+
+	// now offset the original vertex delta units along unit vector
+	PointD ptQ = PointD(path[j]);
+	ptQ = TranslatePoint(ptQ, abs_delta * vec.x, abs_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
+		path_out.push_back(Point64(ReflectPoint(pt, ptQ)));
+		path_out.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
+		path_out.push_back(Point64(pt));
+		//get the second intersect point through reflecion
+		path_out.push_back(Point64(ReflectPoint(pt, ptQ)));
+	}
+}
+
+void ClipperOffset::DoMiter(const Path64& path, size_t j, size_t k, double cos_a)
+{
+	double q = group_delta_ / (cos_a + 1);
+#ifdef USINGZ
+	path_out.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
+	path_out.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(const Path64& path, size_t j, size_t k, double angle)
+{
+	if (deltaCallback64_) {
+		// when deltaCallback64_ is assigned, group_delta_ won't be constant, 
+		// so we'll need to do the following calculations for *every* vertex.
+		double abs_delta = std::fabs(group_delta_);
+		double arcTol = (arc_tolerance_ > floating_point_tolerance ?
+			std::min(abs_delta, arc_tolerance_) :
+			std::log10(2 + abs_delta) * default_arc_tolerance);
+		double steps_per_360 = std::min(PI / std::acos(1 - arcTol / abs_delta), abs_delta * PI);
+		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);
+	}
+
+	Point64 pt = path[j];
+	PointD offsetVec = PointD(norms[k].x * group_delta_, norms[k].y * group_delta_);
+
+	if (j == k) offsetVec.Negate();
+#ifdef USINGZ
+	path_out.push_back(Point64(pt.x + offsetVec.x, pt.y + offsetVec.y, pt.z));
+#else
+	path_out.push_back(Point64(pt.x + offsetVec.x, pt.y + offsetVec.y));
+#endif
+	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
+		path_out.push_back(Point64(pt.x + offsetVec.x, pt.y + offsetVec.y, pt.z));
+#else
+		path_out.push_back(Point64(pt.x + offsetVec.x, pt.y + offsetVec.y));
+#endif
+	}
+	path_out.push_back(GetPerpendic(path[j], norms[j], group_delta_));
+}
+
+void ClipperOffset::OffsetPoint(Group& group, const 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 (deltaCallback64_) {
+		group_delta_ = deltaCallback64_(path, norms, j, k);
+		if (group.is_reversed) group_delta_ = -group_delta_;
+	}
+	if (std::fabs(group_delta_) <= floating_point_tolerance)
+	{
+		path_out.push_back(path[j]);
+		return;
+	}
+
+	if (cos_a > -0.99 && (sin_a * group_delta_ < 0)) // test for concavity first (#593)
+	{
+		// is concave
+		path_out.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		
+		path_out.push_back(path[j]); // (#405)
+		path_out.push_back(GetPerpendic(path[j], norms[j], group_delta_));
+	}
+	else if (cos_a > 0.999 && join_type_ != JoinType::Round) 
+	{
+		// almost straight - less than 2.5 degree (#424, #482, #526 & #724) 
+		DoMiter(path, j, k, cos_a);
+	}
+	else if (join_type_ == JoinType::Miter)
+	{
+		// miter unless the angle is sufficiently acute to exceed ML
+		if (cos_a > temp_lim_ - 1) DoMiter(path, j, k, cos_a);
+		else DoSquare(path, j, k);
+	}
+	else if (join_type_ == JoinType::Round)
+		DoRound(path, j, k, std::atan2(sin_a, cos_a));
+	else if ( join_type_ == JoinType::Bevel)
+		DoBevel(path, j, k);
+	else
+		DoSquare(path, j, k);
+}
+
+void ClipperOffset::OffsetPolygon(Group& group, const Path64& path)
+{
+	path_out.clear();
+	for (Path64::size_type j = 0, k = path.size() -1; j < path.size(); k = j, ++j)
+		OffsetPoint(group, path, j, k);
+	solution.push_back(path_out);
+}
+
+void ClipperOffset::OffsetOpenJoined(Group& group, const Path64& path)
+{
+	OffsetPolygon(group, path);
+	Path64 reverse_path(path);
+	std::reverse(reverse_path.begin(), reverse_path.end());
+	
+	//rebuild normals // BuildNormals(path);
+	std::reverse(norms.begin(), norms.end());
+	norms.push_back(norms[0]);
+	norms.erase(norms.begin());
+	NegatePath(norms);
+
+	OffsetPolygon(group, reverse_path);
+}
+
+void ClipperOffset::OffsetOpenPath(Group& group, const Path64& path)
+{
+	// do the line start cap
+	if (deltaCallback64_) group_delta_ = deltaCallback64_(path, norms, 0, 0);
+	
+	if (std::fabs(group_delta_) <= floating_point_tolerance)
+		path_out.push_back(path[0]);
+	else
+	{
+		switch (end_type_)
+		{
+		case EndType::Butt:
+			DoBevel(path, 0, 0);
+			break;
+		case EndType::Round:
+			DoRound(path, 0, 0, PI);
+			break;
+		default:
+			DoSquare(path, 0, 0);
+			break;
+		}
+	}
+	
+	size_t highI = path.size() - 1;
+	// offset the left side going forward
+	for (Path64::size_type j = 1, k = 0; j < highI; k = j, ++j)
+		OffsetPoint(group, path, j, 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
+	if (deltaCallback64_)
+		group_delta_ = deltaCallback64_(path, norms, highI, highI);
+
+	if (std::fabs(group_delta_) <= floating_point_tolerance)
+		path_out.push_back(path[highI]);
+	else
+	{
+		switch (end_type_)
+		{
+		case EndType::Butt:
+			DoBevel(path, highI, highI);
+			break;
+		case EndType::Round:
+			DoRound(path, highI, highI, PI);
+			break;
+		default:
+			DoSquare(path, highI, highI);
+			break;
+		}
+	}
+
+	for (size_t j = highI, k = 0; j > 0; k = j, --j)
+		OffsetPoint(group, path, j, k);
+	solution.push_back(path_out);
+}
+
+void ClipperOffset::DoGroupOffset(Group& group)
+{
+	if (group.end_type == EndType::Polygon)
+	{
+		// a straight path (2 points) can now also be 'polygon' offset 
+		// where the ends will be treated as (180 deg.) joins
+		if (group.lowest_path_idx < 0) delta_ = std::abs(delta_);
+		group_delta_ = (group.is_reversed) ? -delta_ : delta_;
+	}
+	else
+		group_delta_ = std::abs(delta_);// *0.5;
+
+	double abs_delta = std::fabs(group_delta_);
+	if (!ValidateBounds(group.bounds_list, abs_delta))
+	{
+		DoError(range_error_i);
+		error_code_ |= range_error_i;
+		return;
+	}
+
+	join_type_	= group.join_type;
+	end_type_ = group.end_type;
+
+	if (group.join_type == JoinType::Round || group.end_type == EndType::Round)
+	{
+		// calculate a sensible number of steps (for 360 deg for the given offset)
+		// 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_delta, arc_tolerance_) :
+			std::log10(2 + abs_delta) * default_arc_tolerance);
+
+		double steps_per_360 = std::min(PI / std::acos(1 - arcTol / abs_delta), abs_delta * PI);
+		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);
+	}
+
+	std::vector<Rect64>::const_iterator path_rect_it = group.bounds_list.cbegin();
+	std::vector<bool>::const_iterator is_hole_it = group.is_hole_list.cbegin();
+	Paths64::const_iterator path_in_it = group.paths_in.cbegin();
+	for ( ; path_in_it != group.paths_in.cend(); ++path_in_it, ++path_rect_it, ++is_hole_it)
+	{
+		if (!path_rect_it->IsValid()) continue;
+		Path64::size_type pathLen = path_in_it->size();
+		path_out.clear();
+
+		if (pathLen == 1) // single point
+		{
+			if (group_delta_ < 1) continue;
+			const Point64& pt = (*path_in_it)[0];
+			//single vertex so build a circle or square ...
+			if (group.join_type == JoinType::Round)
+			{
+				double radius = abs_delta;
+				int steps = static_cast<int>(std::ceil(steps_per_rad_ * 2 * PI)); //#617
+				path_out = Ellipse(pt, radius, radius, steps);
+#ifdef USINGZ
+				for (auto& p : path_out) p.z = pt.z;
+#endif
+			}
+			else
+			{
+				int d = (int)std::ceil(abs_delta);
+				Rect64 r = Rect64(pt.x - d, pt.y - d, pt.x + d, pt.y + d);
+				path_out = r.AsPath();
+#ifdef USINGZ
+				for (auto& p : path_out) p.z = pt.z;
+#endif
+			}
+			solution.push_back(path_out);
+			continue;
+		} // end of offsetting a single point 
+
+		// when shrinking outer paths, make sure they can shrink this far (#593)
+		// also when shrinking holes, make sure they too can shrink this far (#715)
+		if ((group_delta_ > 0) == ToggleBoolIf(*is_hole_it, group.is_reversed) &&
+			(std::min(path_rect_it->Width(), path_rect_it->Height()) <= -group_delta_ * 2) )
+				  continue;
+
+		if ((pathLen == 2) && (group.end_type == EndType::Joined))
+			end_type_ = (group.join_type == JoinType::Round) ? 
+			  EndType::Round : 
+			  EndType::Square;
+
+		BuildNormals(*path_in_it);
+		if (end_type_ == EndType::Polygon) OffsetPolygon(group, *path_in_it);
+		else if (end_type_ == EndType::Joined) OffsetOpenJoined(group, *path_in_it);
+		else OffsetOpenPath(group, *path_in_it);
+	}
+}
+
+
+size_t ClipperOffset::CalcSolutionCapacity()
+{
+	size_t result = 0;
+	for (const Group& g : groups_)
+		result += (g.end_type == EndType::Joined) ? g.paths_in.size() * 2 : g.paths_in.size();
+	return result;
+}
+
+bool ClipperOffset::CheckReverseOrientation()
+{
+	// nb: this assumes there's consistency in orientation between groups
+	bool is_reversed_orientation = false;
+	for (const Group& g : groups_)
+		if (g.end_type == EndType::Polygon)
+		{
+			is_reversed_orientation = g.is_reversed;
+			break;
+		}
+	return is_reversed_orientation;
+}
+
+void ClipperOffset::ExecuteInternal(double delta)
+{
+	error_code_ = 0;
+	solution.clear();
+	if (groups_.size() == 0) return;
+	solution.reserve(CalcSolutionCapacity());
+
+	if (std::abs(delta) < 0.5) // ie: offset is insignificant 
+	{
+		Paths64::size_type sol_size = 0;
+		for (const Group& group : groups_) sol_size += group.paths_in.size();
+		solution.reserve(sol_size);
+		for (const Group& group : groups_)
+			copy(group.paths_in.begin(), group.paths_in.end(), back_inserter(solution));
+		return;
+	}
+
+	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;
+
+	bool paths_reversed = CheckReverseOrientation();
+	//clean up self-intersections ...
+	Clipper64 c;
+	c.PreserveCollinear(false);
+	//the solution should retain the orientation of the input
+	c.ReverseSolution(reverse_solution_ != paths_reversed);
+#ifdef USINGZ
+	if (zCallback64_) { c.SetZCallback(zCallback64_); }
+#endif
+	c.AddSubject(solution);
+	if (paths_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;
+
+	bool paths_reversed = CheckReverseOrientation();
+	//clean up self-intersections ...
+	Clipper64 c;
+	c.PreserveCollinear(false);
+	//the solution should retain the orientation of the input
+	c.ReverseSolution (reverse_solution_ != paths_reversed);
+#ifdef USINGZ
+	if (zCallback64_) {
+		c.SetZCallback(zCallback64_);
+	}
+#endif
+	c.AddSubject(solution);
+
+
+	if (paths_reversed)
+		c.Execute(ClipType::Union, FillRule::Negative, polytree);
+	else
+		c.Execute(ClipType::Union, FillRule::Positive, polytree);
+}
+
+void ClipperOffset::Execute(DeltaCallback64 delta_cb, Paths64& paths)
+{
+	deltaCallback64_ = delta_cb;
+	Execute(1.0, paths);
+}
+
+} // namespace