ENH: add clipper2 for preparing

Add clipper2 code into repo

Signed-off-by: salt.wei <salt.wei@bambulab.com>
Change-Id: Ib98ea3085055db7d125a92879c46b54e39bdc6b1
(cherry picked from commit 7398e71236a300531a172163c71f15440c37bd5e)

src/clipper2/CMakeLists.txt

@@ -0,0 +1,50 @@
+cmake_minimum_required(VERSION 3.10)
+project(Clipper2 VERSION 1.0.6 LANGUAGES C CXX)
+
+set(CMAKE_POSITION_INDEPENDENT_CODE ON)
+set(CMAKE_CXX_STANDARD 17)
+set(CMAKE_CXX_STANDARD_REQUIRED ON)
+set(CMAKE_CXX_EXTENSIONS OFF)
+set_property(GLOBAL PROPERTY USE_FOLDERS OFF)
+
+option(BUILD_SHARED_LIBS "Build shared libs" OFF)
+
+include(GNUInstallDirs)
+
+set(CLIPPER2_INC
+  Clipper2Lib/include/clipper2/clipper.h
+  Clipper2Lib/include/clipper2/clipper.core.h
+  Clipper2Lib/include/clipper2/clipper.engine.h
+  Clipper2Lib/include/clipper2/clipper.export.h
+  Clipper2Lib/include/clipper2/clipper.minkowski.h
+  Clipper2Lib/include/clipper2/clipper.offset.h
+  Clipper2Lib/include/clipper2/clipper.rectclip.h
+)
+
+set(CLIPPER2_SRC
+  Clipper2Lib/src/clipper.engine.cpp
+  Clipper2Lib/src/clipper.offset.cpp
+  Clipper2Lib/src/clipper.rectclip.cpp
+)
+
+# 2d version of Clipper2
+add_library(Clipper2 ${CLIPPER2_INC} ${CLIPPER2_SRC})
+
+target_include_directories(Clipper2
+  PUBLIC Clipper2Lib/include
+)
+
+if (WIN32)
+  target_compile_options(Clipper2 PRIVATE /W4 /WX)
+else()
+  target_compile_options(Clipper2 PRIVATE -Wall -Wextra -Wpedantic -Werror)
+  target_link_libraries(Clipper2 PUBLIC -lm)
+
+endif()
+
+set_target_properties(Clipper2 PROPERTIES FOLDER Libraries
+                                         VERSION ${PROJECT_VERSION}
+                                         SOVERSION ${PROJECT_VERSION_MAJOR}
+                                         PUBLIC_HEADER "${CLIPPER2_INC}"
+)
+

src/clipper2/Clipper2Lib/include/clipper2/clipper.core.h

@@ -0,0 +1,653 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  4 November 2022                                                 *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2022                                         *
+* 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 <cstdlib>
+#include <cmath>
+#include <vector>
+#include <string>
+#include <iostream>
+#include <algorithm>
+#include <climits>
+
+//#define NO_EXCEPTIONS
+
+namespace Clipper2Lib 
+{
+
+#ifndef NO_EXCEPTIONS
+	static const char* precision_error =
+		"Precision exceeds the permitted range";
+#endif
+
+	static double const PI = 3.141592653589793238;
+	static int64_t const MAX_COORD = LLONG_MAX / 2;
+	
+	//By far the most widely used filling rules for polygons are EvenOdd
+	//and NonZero, sometimes called Alternate and Winding respectively.
+	//https://en.wikipedia.org/wiki/Nonzero-rule
+	enum class FillRule { EvenOdd, NonZero, Positive, Negative };
+	
+// Point ------------------------------------------------------------------------
+
+template <typename T>
+struct Point {
+	T x;
+	T y;
+#ifdef USINGZ
+	int64_t z;
+
+	template <typename T2>
+	inline void Init(const T2 x_ = 0, const T2 y_ = 0, const int64_t z_ = 0)
+	{
+		if constexpr (std::numeric_limits<T>::is_integer &&
+			!std::numeric_limits<T2>::is_integer)
+		{
+			x = static_cast<T>(std::round(x_));
+			y = static_cast<T>(std::round(y_));
+			z = z_;
+		}
+		else
+		{
+			x = static_cast<T>(x_);
+			y = static_cast<T>(y_);
+			z = z_;
+		}
+	}
+
+	explicit Point() : x(0), y(0), z(0) {};
+
+	template <typename T2>
+	Point(const T2 x_, const T2 y_, const int64_t z_ = 0)
+	{
+		Init(x_, y_);
+		z = z_;
+	}
+
+	template <typename T2>
+	explicit Point<T>(const Point<T2>& p)
+	{
+		Init(p.x, p.y, p.z);
+	}
+
+	Point operator * (const double scale) const
+	{
+		return Point(x * scale, y * scale, z);
+	}
+
+
+	friend std::ostream& operator<<(std::ostream& os, const Point& point)
+	{
+		os << point.x << "," << point.y << "," << point.z;
+		return os;
+	}
+
+#else
+
+	template <typename T2>
+	inline void Init(const T2 x_ = 0, const T2 y_ = 0)
+	{
+		if constexpr (std::numeric_limits<T>::is_integer &&
+			!std::numeric_limits<T2>::is_integer)
+		{
+			x = static_cast<T>(std::round(x_));
+			y = static_cast<T>(std::round(y_));
+		}
+		else
+		{
+			x = static_cast<T>(x_);
+			y = static_cast<T>(y_);
+		}
+	}
+
+	explicit Point() : x(0), y(0) {};
+
+	template <typename T2>
+	Point(const T2 x_, const T2 y_) { Init(x_, y_); }
+
+	template <typename T2>
+	explicit Point<T>(const Point<T2>& p) { Init(p.x, p.y); }
+
+	Point operator * (const double scale) const
+	{
+		return Point(x * scale, y * scale);
+	}
+
+	friend std::ostream& operator<<(std::ostream& os, const Point& point)
+	{
+		os << point.x << "," << point.y;
+		return os;
+	}
+#endif
+
+	friend bool operator==(const Point &a, const Point &b) 
+	{
+		return a.x == b.x && a.y == b.y;
+	}
+
+	friend bool operator!=(const Point& a, const Point& b)
+	{
+		return !(a == b);
+	}
+
+	inline Point<T> operator-() const
+	{
+		return Point<T>(-x,-y);
+	}
+
+	inline Point operator+(const Point &b) const
+	{
+		return Point(x+b.x, y+b.y);
+	}
+
+	inline Point operator-(const Point &b) const
+	{
+		return Point(x-b.x, y-b.y);
+	}
+
+	inline void Negate() { x = -x; y = -y; }
+
+};
+
+//nb: using 'using' here (instead of typedef) as they can be used in templates
+using Point64 = Point<int64_t>;
+using PointD = Point<double>;
+
+template <typename T>
+using Path = std::vector<Point<T>>;
+template <typename T>
+using Paths = std::vector<Path<T>>;
+
+using Path64 = Path<int64_t>;
+using PathD = Path<double>;
+using Paths64 = std::vector< Path64>;
+using PathsD = std::vector< PathD>;
+
+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)
+{
+	Path<T1> result;
+	result.reserve(path.size());
+#ifdef USINGZ
+	for (const Point<T2>& pt : path)
+		result.push_back(Point<T1>(pt.x * scale, pt.y * scale, pt.z));
+#else
+	for (const Point<T2>& pt : path)
+		result.push_back(Point<T1>(pt.x * scale, pt.y * scale));
+#endif
+	return result;
+}
+
+template <typename T1, typename T2>
+inline Paths<T1> ScalePaths(const Paths<T2>& paths, double scale)
+{
+	Paths<T1> result;
+	result.reserve(paths.size());
+	for (const Path<T2>& path : paths)
+		result.push_back(ScalePath<T1, T2>(path, scale));
+	return result;
+}
+
+template <typename T1, typename T2>
+inline Path<T1> TransformPath(const Path<T2>& path)
+{
+	Path<T1> result;
+	result.reserve(path.size());
+	std::transform(path.cbegin(), path.cend(), std::back_inserter(result),
+		[](const Point<T2>& pt) {return Point<T1>(pt); });
+	return result;
+}
+
+template <typename T1, typename T2>
+inline Paths<T1> TransformPaths(const Paths<T2>& paths)
+{
+	Paths<T1> result;
+	std::transform(paths.cbegin(), paths.cend(), std::back_inserter(result),
+		[](const Path<T2>& path) {return TransformPath<T1, T2>(path); });
+	return result;
+}
+
+inline PathD Path64ToPathD(const Path64& path)
+{
+	return TransformPath<double, int64_t>(path);
+}
+
+inline PathsD Paths64ToPathsD(const Paths64& paths)
+{
+	return TransformPaths<double, int64_t>(paths);
+}
+
+inline Path64 PathDToPath64(const PathD& path)
+{
+	return TransformPath<int64_t, double>(path);
+}
+
+inline Paths64 PathsDToPaths64(const PathsD& paths)
+{
+	return TransformPaths<int64_t, double>(paths);
+}
+
+template<typename T>
+inline double Sqr(T val)
+{
+	return static_cast<double>(val) * static_cast<double>(val);
+}
+
+template<typename T>
+inline bool NearEqual(const Point<T>& p1,
+	const Point<T>& p2, double max_dist_sqrd)
+{
+	return Sqr(p1.x - p2.x) + Sqr(p1.y - p2.y) < max_dist_sqrd;
+}
+
+template<typename T>
+inline Path<T> StripNearEqual(const Path<T>& path, 
+	double max_dist_sqrd, bool is_closed_path)
+{
+	if (path.size() == 0) return Path<T>();
+	Path<T> result;
+	result.reserve(path.size());
+	typename Path<T>::const_iterator path_iter = path.cbegin();
+	Point<T> first_pt = *path_iter++, last_pt = first_pt;
+	result.push_back(first_pt);
+	for (; path_iter != path.cend(); ++path_iter)
+	{
+		if (!NearEqual(*path_iter, last_pt, max_dist_sqrd))
+		{
+			last_pt = *path_iter;
+			result.push_back(last_pt);
+		}
+	}
+	if (!is_closed_path) return result;
+	while (result.size() > 1 &&
+		NearEqual(result.back(), first_pt, max_dist_sqrd)) result.pop_back();
+	return result;
+}
+
+template<typename T>
+inline Paths<T> StripNearEqual(const Paths<T>& paths, 
+	double max_dist_sqrd, bool is_closed_path)
+{
+	Paths<T> result;
+	result.reserve(paths.size());
+	for (typename Paths<T>::const_iterator paths_citer = paths.cbegin();
+		paths_citer != paths.cend(); ++paths_citer)
+	{
+		result.push_back(StripNearEqual(*paths_citer, max_dist_sqrd, is_closed_path));
+	}
+	return result;
+}
+
+template<typename T>
+inline Path<T> StripDuplicates(const Path<T>& path, bool is_closed_path)
+{
+	if (path.size() == 0) return Path<T>();
+	Path<T> result;
+	result.reserve(path.size());
+	typename Path<T>::const_iterator path_iter = path.cbegin();
+	Point<T> first_pt = *path_iter++, last_pt = first_pt;
+	result.push_back(first_pt);
+	for (; path_iter != path.cend(); ++path_iter)
+	{
+		if (*path_iter != last_pt)
+		{
+			last_pt = *path_iter;
+			result.push_back(last_pt);
+		}
+	}
+	if (!is_closed_path) return result;
+	while (result.size() > 1 && result.back() == first_pt) result.pop_back();
+	return result;
+}
+
+template<typename T>
+inline Paths<T> StripDuplicates(const Paths<T>& paths, bool is_closed_path)
+{
+	Paths<T> result;
+	result.reserve(paths.size());
+	for (typename Paths<T>::const_iterator paths_citer = paths.cbegin();
+		paths_citer != paths.cend(); ++paths_citer)
+	{
+		result.push_back(StripDuplicates(*paths_citer, is_closed_path));
+	}
+	return result;
+}
+
+// Rect ------------------------------------------------------------------------
+
+template <typename T>
+struct Rect;
+
+using Rect64 = Rect<int64_t>;
+using RectD = Rect<double>;
+
+template <typename T>
+struct Rect {
+	T left;
+	T top;
+	T right;
+	T bottom;
+
+	Rect() :
+		left(0),
+		top(0),
+		right(0),
+		bottom(0) {}
+
+	Rect(T l, T t, T r, T b) :
+		left(l),
+		top(t),
+		right(r),
+		bottom(b) {}
+
+
+	T Width() const { return right - left; }
+	T Height() const { return bottom - top; }
+	void Width(T width) { right = left + width; }
+	void Height(T height) { bottom = top + height; }
+
+	Point<T> MidPoint() const
+	{
+		return Point<T>((left + right) / 2, (top + bottom) / 2);
+	}
+
+	Path<T> AsPath() const
+	{
+		Path<T> result;
+		result.reserve(4);
+		result.push_back(Point<T>(left, top));
+		result.push_back(Point<T>(right, top));
+		result.push_back(Point<T>(right, bottom));
+		result.push_back(Point<T>(left, bottom));
+		return result;
+	}
+
+	bool Contains(const Point<T>& pt) const
+	{
+		return pt.x > left && pt.x < right&& pt.y > top && pt.y < bottom;
+	}
+
+	bool Contains(const Rect<T>& rec) const
+	{
+		return rec.left >= left && rec.right <= right && 
+			rec.top >= top && rec.bottom <= bottom;
+	}
+
+	void Scale(double scale) {
+		left *= scale; 
+		top *= scale;
+		right *= scale;
+		bottom *= scale;
+	}
+
+	bool IsEmpty() const { return bottom <= top || right <= left; };
+
+	bool Intersects(const Rect<T>& rec) const 
+	{ 
+		return (std::max(left, rec.left) < std::min(right, rec.right)) &&
+			(std::max(top, rec.top) < std::min(bottom, rec.bottom));
+	};
+
+	friend std::ostream &operator<<(std::ostream &os, const Rect<T> &rect) {
+		os << "("
+		   << rect.left << "," << rect.top << "," << rect.right << "," << rect.bottom
+		   << ")";
+		return os;
+	}
+};
+
+template <typename T1, typename T2>
+inline Rect<T1> ScaleRect(const Rect<T2>& rect, double scale)
+{
+	Rect<T1> result;
+
+	if constexpr (std::numeric_limits<T1>::is_integer &&
+		!std::numeric_limits<T2>::is_integer)
+	{
+		result.left = static_cast<T1>(std::round(rect.left * scale));
+		result.top = static_cast<T1>(std::round(rect.top * scale));
+		result.right = static_cast<T1>(std::round(rect.right * scale));
+		result.bottom = static_cast<T1>(std::round(rect.bottom * scale));
+	}
+	else
+	{
+		result.left = rect.left * scale;
+		result.top = rect.top * scale;
+		result.right = rect.right * scale;
+		result.bottom = rect.bottom * scale;
+	}
+	return result;
+}
+
+// clipper2Exception ---------------------------------------------------------
+
+#ifndef NO_EXCEPTIONS
+class Clipper2Exception : public std::exception {
+public:
+	explicit Clipper2Exception(const char *description) :
+		m_descr(description) {}
+	virtual const char *what() const throw() { return m_descr.c_str(); }
+
+private:
+	std::string m_descr;
+};
+#endif
+
+// Miscellaneous ------------------------------------------------------------
+
+inline void CheckPrecision(int& precision)
+{
+	if (precision >= -8 && precision <= 8) return;
+#ifdef NO_EXCEPTIONS
+	precision = precision > 8 ? 8 : -8;
+#else
+	throw Clipper2Exception(precision_error);
+#endif
+}
+
+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 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 {
+		double dx1 = static_cast<double>(seg1a.x - seg1b.x);
+		double dy1 = static_cast<double>(seg1a.y - seg1b.y);
+		double dx2 = static_cast<double>(seg2a.x - seg2b.x);
+		double dy2 = static_cast<double>(seg2a.y - seg2b.y);
+		return (((dy1 * (seg2a.x - seg1a.x) - dx1 * (seg2a.y - seg1a.y)) *
+			(dy1 * (seg2b.x - seg1a.x) - dx1 * (seg2b.y - seg1a.y)) < 0) &&
+			((dy2 * (seg1a.x - seg2a.x) - dx2 * (seg1a.y - seg2a.y)) *
+				(dy2 * (seg1b.x - seg2a.x) - dx2 * (seg1b.y - seg2a.y)) < 0));
+	}
+}
+
+
+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 start = polygon.cbegin(), cit = start;
+	typename Path<T>::const_iterator cend = polygon.cend(), pit = cend - 1;
+
+	while (pit->y == pt.y)
+	{
+		if (pit == start) return PointInPolygonResult::IsOutside;
+		--pit;
+	}
+	bool is_above = pit->y < pt.y;
+
+	while (cit != cend)
+	{
+		if (is_above)
+		{
+			while (cit != cend && cit->y < pt.y) ++cit;
+			if (cit == cend) break;
+		}
+		else
+		{
+			while (cit != cend && cit->y > pt.y) ++cit;
+			if (cit == cend) break;
+		}
+
+		if (cit == start) pit = cend - 1;
+		else  pit = cit - 1;
+
+		if (cit->y == pt.y)
+		{
+			if (cit->x == pt.x || (cit->y == pit->y &&
+				((pt.x < pit->x) != (pt.x < cit->x))))
+				return PointInPolygonResult::IsOn;
+			++cit;
+			continue;
+		}
+
+		if (pt.x < cit->x && pt.x < pit->x)
+		{
+			// we're only interested in edges crossing on the left
+		}
+		else if (pt.x > pit->x && pt.x > cit->x)
+			val = 1 - val; // toggle val
+		else
+		{
+			double d = CrossProduct(*pit, *cit, pt);
+			if (d == 0) return PointInPolygonResult::IsOn;
+			if ((d < 0) == is_above) val = 1 - val;
+		}
+		is_above = !is_above;
+		++cit;
+	}
+	return (val == 0) ? 
+		PointInPolygonResult::IsOutside :
+		PointInPolygonResult::IsInside;
+}
+
+}  // namespace
+
+#endif  // CLIPPER_CORE_H

src/clipper2/Clipper2Lib/include/clipper2/clipper.engine.h

@@ -0,0 +1,586 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  4 November 2022                                                 *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2022                                         *
+* Purpose   :  This is the main polygon clipping module                        *
+* License   :  http://www.boost.org/LICENSE_1_0.txt                            *
+*******************************************************************************/
+
+#ifndef CLIPPER_ENGINE_H
+#define CLIPPER_ENGINE_H
+
+constexpr auto CLIPPER2_VERSION = "1.0.6";
+
+#include <cstdlib>
+#include <queue>
+#include <stdexcept>
+#include <vector>
+#include <functional>
+#include "clipper.core.h"
+
+namespace Clipper2Lib {
+
+	struct Scanline;
+	struct IntersectNode;
+	struct Active;
+	struct Vertex;
+	struct LocalMinima;
+	struct OutRec;
+	struct Joiner;
+
+	//Note: all clipping operations except for Difference are commutative.
+	enum class ClipType { None, Intersection, Union, Difference, Xor };
+	
+	enum class PathType { Subject, Clip };
+
+	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;
+		Joiner* joiner = 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;
+		OutRecList* splits = nullptr;
+		Active* front_edge = nullptr;
+		Active* back_edge = nullptr;
+		OutPt* pts = nullptr;
+		PolyPath* polypath = nullptr;
+		Rect64 bounds = {};
+		Path64 path;
+		bool is_open = false;
+		~OutRec() { if (splits) delete splits; };
+	};
+
+	///////////////////////////////////////////////////////////////////
+	//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;
+	};
+
+	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)
+		{
+		}
+	};
+
+#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
+
+	// 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;
+		Joiner *horz_joiners_ = nullptr;
+		std::vector<LocalMinima*> minima_list_;		//pointers in case of memory reallocs
+		std::vector<LocalMinima*>::iterator current_locmin_iter_;
+		std::vector<Vertex*> vertex_lists_;
+		std::priority_queue<int64_t> scanline_list_;
+		std::vector<IntersectNode> intersect_nodes_; 
+		std::vector<Joiner*> joiner_list_;				//pointers in case of memory reallocs
+		void Reset();
+		void InsertScanline(int64_t y);
+		bool PopScanline(int64_t &y);
+		bool PopLocalMinima(int64_t y, LocalMinima *&local_minima);
+		void DisposeAllOutRecs();
+		void DisposeVerticesAndLocalMinima();
+		void DeleteEdges(Active*& e);
+		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);
+		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 Active *max_pair,
+			int64_t &horz_left, int64_t &horz_right);
+		void DoTopOfScanbeam(const int64_t top_y);
+		Active *DoMaxima(Active &e);
+		void JoinOutrecPaths(Active &e1, Active &e2);
+		void CompleteSplit(OutPt* op1, OutPt* op2, OutRec& outrec);
+		bool ValidateClosedPathEx(OutPt*& outrec);
+		void CleanCollinear(OutRec* outrec);
+		void FixSelfIntersects(OutRec* outrec);
+		void DoSplitOp(OutRec* outRec, OutPt* splitOp);
+		Joiner* GetHorzTrialParent(const OutPt* op);
+		bool OutPtInTrialHorzList(OutPt* op);
+		void SafeDisposeOutPts(OutPt*& op);
+		void SafeDeleteOutPtJoiners(OutPt* op);
+		void AddTrialHorzJoin(OutPt* op);
+		void DeleteTrialHorzJoin(OutPt* op);
+		void ConvertHorzTrialsToJoins();
+		void AddJoin(OutPt* op1, OutPt* op2);
+		void DeleteJoin(Joiner* joiner);
+		void ProcessJoinerList();
+		OutRec* ProcessJoin(Joiner* joiner);
+	protected:
+		bool has_open_paths_ = false;
+		bool succeeded_ = true;
+		std::vector<OutRec*> outrec_list_; //pointers in case list memory reallocated
+		bool ExecuteInternal(ClipType ct, FillRule ft, bool use_polytrees);
+		bool DeepCheckOwner(OutRec* outrec, OutRec* owner);
+#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();
+		bool PreserveCollinear = true;
+		bool ReverseSolution = false;
+		void Clear();
+	};
+
+	// 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() { Clear(); };		
+		//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() {};
+		virtual size_t Count() const { return 0; }
+
+		const PolyPath* Parent() const { return parent_; }
+
+		bool IsHole() const 
+		{
+			const PolyPath* pp = parent_;
+			bool is_hole = pp;
+			while (pp) {
+				is_hole = !is_hole;
+				pp = pp->parent_;
+			}
+			return is_hole;
+		}
+	};
+
+	class PolyPath64 : public PolyPath {
+	private:
+		std::vector<PolyPath64*> childs_;
+		Path64 polygon_;
+		typedef typename std::vector<PolyPath64*>::const_iterator pp64_itor;
+	public:
+		PolyPath64(PolyPath64* parent = nullptr) : PolyPath(parent) {}
+		PolyPath64* operator [] (size_t index) { return static_cast<PolyPath64*>(childs_[index]); }
+		pp64_itor begin() const { return childs_.cbegin(); }
+		pp64_itor end() const { return childs_.cend(); }
+
+		PolyPath64* AddChild(const Path64& path) override
+		{
+			PolyPath64* result = new PolyPath64(this);
+			childs_.push_back(result);
+			result->polygon_ = path;
+			return result;
+		}
+
+		void Clear() override
+		{
+			for (const PolyPath64* child : childs_) delete child;
+			childs_.resize(0);
+		}
+
+		size_t Count() const  override
+		{
+			return childs_.size();
+		}
+
+		const Path64& Polygon() const { return polygon_; };
+
+		double Area() const
+		{
+			double result = Clipper2Lib::Area<int64_t>(polygon_);
+			for (const PolyPath64* child : childs_)
+				result += child->Area();
+			return result;
+		}
+
+		friend std::ostream& operator << (std::ostream& outstream, const PolyPath64& polypath)
+		{
+			const size_t level_indent = 4;
+			const size_t coords_per_line = 4;
+			const size_t last_on_line = coords_per_line - 1;
+			unsigned level = polypath.Level();
+			if (level > 0)
+			{
+				std::string level_padding;
+				level_padding.insert(0, (level - 1) * level_indent, ' ');
+				std::string caption = polypath.IsHole() ? "Hole " : "Outer Polygon ";
+				std::string childs = polypath.Count() == 1 ? " child" : " children";
+				outstream << level_padding.c_str() << caption << "with " << polypath.Count() << childs << std::endl;
+				outstream << level_padding;
+				size_t i = 0, highI = polypath.Polygon().size() - 1;
+				for (; i < highI; ++i)
+				{
+					outstream << polypath.Polygon()[i] << ' ';
+					if ((i % coords_per_line) == last_on_line)
+						outstream << std::endl << level_padding;
+				}
+				if (highI > 0) outstream << polypath.Polygon()[i];
+				outstream << std::endl;
+			}
+			for (auto child : polypath)
+				outstream << *child;
+			return outstream;
+		}
+
+	};
+
+	class PolyPathD : public PolyPath {
+	private:
+		std::vector<PolyPathD*> childs_;
+		double inv_scale_;
+		PathD polygon_;
+		typedef typename std::vector<PolyPathD*>::const_iterator ppD_itor;
+	public:
+		PolyPathD(PolyPathD* parent = nullptr) : PolyPath(parent) 
+		{
+			inv_scale_ = parent ? parent->inv_scale_ : 1.0;
+		}
+		PolyPathD* operator [] (size_t index) 
+		{ 
+			return static_cast<PolyPathD*>(childs_[index]); 
+		}
+		ppD_itor begin() const { return childs_.cbegin(); }
+		ppD_itor end() const { return childs_.cend(); }
+
+		void SetInvScale(double value) { inv_scale_ = value; }
+		double InvScale() { return inv_scale_; }
+		PolyPathD* AddChild(const Path64& path) override
+		{
+			PolyPathD* result = new PolyPathD(this);
+			childs_.push_back(result);
+			result->polygon_ = ScalePath<double, int64_t>(path, inv_scale_);
+			return result;
+		}
+
+		void Clear() override
+		{
+			for (const PolyPathD* child : childs_) delete child;
+			childs_.resize(0);
+		}
+
+		size_t Count() const  override
+		{
+			return childs_.size();
+		}
+
+		const PathD& Polygon() const { return polygon_; };
+
+		double Area() const
+		{
+			double result = Clipper2Lib::Area<double>(polygon_);
+			for (const PolyPathD* child : childs_)
+				result += child->Area();
+			return result;
+		}
+	};
+
+	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 zCallback_ = nullptr;
+#endif
+		void BuildPathsD(PathsD& solutionClosed, PathsD* solutionOpen);
+		void BuildTreeD(PolyPathD& polytree, PathsD& open_paths);
+	public:
+		explicit ClipperD(int precision = 2) : ClipperBase()
+		{
+			CheckPrecision(precision);
+			// 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) { zCallback_ = 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_;
+			zCallback_(e1b,e1t, e2b, e2t, tmp);
+			pt.z = tmp.z; // only update 'z'
+		};
+
+		void CheckCallback()
+		{
+			if(zCallback_)
+				// 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_), PathType::Subject, false);
+		}
+
+		void AddOpenSubject(const PathsD& open_subjects)
+		{
+			AddPaths(ScalePaths<int64_t, double>(open_subjects, scale_), PathType::Subject, true);
+		}
+
+		void AddClip(const PathsD& clips)
+		{
+			AddPaths(ScalePaths<int64_t, double>(clips, scale_), PathType::Clip, false);
+		}
+
+		bool Execute(ClipType clip_type, FillRule fill_rule, PathsD& closed_paths)
+		{
+			PathsD dummy;
+			return Execute(clip_type, fill_rule, closed_paths, dummy);
+		}
+
+		bool Execute(ClipType clip_type,
+			FillRule fill_rule, PathsD& closed_paths, PathsD& open_paths)
+		{
+#ifdef USINGZ
+			CheckCallback();
+#endif
+			if (ExecuteInternal(clip_type, fill_rule, false))
+			{
+				BuildPathsD(closed_paths, &open_paths);
+			}
+			CleanUp();
+			return succeeded_;
+		}
+
+		bool Execute(ClipType clip_type, FillRule fill_rule, PolyTreeD& polytree)
+		{
+			PathsD dummy;
+			return Execute(clip_type, fill_rule, polytree, dummy);
+		}
+
+		bool Execute(ClipType clip_type,
+			FillRule fill_rule, PolyTreeD& polytree, PathsD& open_paths)
+		{
+#ifdef USINGZ
+			CheckCallback();
+#endif
+			if (ExecuteInternal(clip_type, fill_rule, true))
+			{
+				polytree.Clear();
+				polytree.SetInvScale(invScale_);
+				open_paths.clear();
+				BuildTreeD(polytree, open_paths);
+			}
+			CleanUp();
+			return succeeded_;
+		}
+
+	};
+
+}  // namespace 
+
+#endif  // CLIPPER_ENGINE_H

src/clipper2/Clipper2Lib/include/clipper2/clipper.export.h

@@ -0,0 +1,830 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  30 October 2022                                                 *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2022                                         *
+* Purpose   :  This module exports the Clipper2 Library (ie DLL/so)            *
+* License   :  http://www.boost.org/LICENSE_1_0.txt                            *
+*******************************************************************************/
+
+// The exported functions below refer to simple structures that
+// can be understood across multiple languages. Consequently
+// Path64, PathD, Polytree64 etc are converted from C++ classes
+// (std::vector<> etc) into the following data structures:
+//
+// CPath64 (int64_t*) & CPathD (double_t*):
+// Path64 and PathD are converted into arrays of x,y coordinates.
+// However in these arrays the first x,y coordinate pair is a
+// counter with 'x' containing the number of following coordinate
+// pairs. ('y' should be 0, with one exception explained below.)
+// __________________________________
+// |counter|coord1|coord2|...|coordN|
+// |N ,0   |x1, y1|x2, y2|...|xN, yN|
+// __________________________________
+//
+// CPaths64 (int64_t**) & CPathsD (double_t**):
+// These are arrays of pointers to CPath64 and CPathD where
+// the first pointer is to a 'counter path'. This 'counter
+// path' has a single x,y coord pair with 'y' (not 'x')
+// containing the number of paths that follow. ('x' = 0).
+// _______________________________
+// |counter|path1|path2|...|pathN|
+// |addr0  |addr1|addr2|...|addrN| (*addr0[0]=0; *addr0[1]=N)
+// _______________________________
+//
+// The structures of CPolytree64 and CPolytreeD are defined
+// below and these structures don't need to be explained here.
+
+#ifndef CLIPPER2_EXPORT_H
+#define CLIPPER2_EXPORT_H
+
+#include <cstdlib>
+#include <vector>
+
+#include "clipper2/clipper.core.h"
+#include "clipper2/clipper.engine.h"
+#include "clipper2/clipper.offset.h"
+#include "clipper2/clipper.rectclip.h"
+
+namespace Clipper2Lib {
+
+typedef int64_t* CPath64;
+typedef int64_t** CPaths64;
+typedef double* CPathD;
+typedef double** CPathsD;
+
+typedef struct CPolyPath64 {
+  CPath64       polygon;
+  uint32_t      is_hole;
+  uint32_t      child_count;
+  CPolyPath64*  childs;
+}
+CPolyTree64;
+
+typedef struct CPolyPathD {
+  CPathD        polygon;
+  uint32_t      is_hole;
+  uint32_t      child_count;
+  CPolyPathD*   childs;
+}
+CPolyTreeD;
+
+template <typename T>
+struct CRect {
+  T left;
+  T top;
+  T right;
+  T bottom;
+};
+
+typedef CRect<int64_t> CRect64;
+typedef CRect<double> CRectD;
+
+template <typename T>
+inline bool CRectIsEmpty(const CRect<T>& rect)
+{
+  return (rect.right <= rect.left) || (rect.bottom <= rect.top);
+}
+
+template <typename T>
+inline Rect<T> CRectToRect(const CRect<T>& rect)
+{
+  Rect<T> result;
+  result.left = rect.left;
+  result.top = rect.top;
+  result.right = rect.right;
+  result.bottom = rect.bottom;
+  return result;
+}
+
+#define EXTERN_DLL_EXPORT extern "C" __declspec(dllexport)
+
+//////////////////////////////////////////////////////
+// EXPORTED FUNCTION DEFINITIONS
+//////////////////////////////////////////////////////
+
+EXTERN_DLL_EXPORT const char* Version();
+
+// Some of the functions below will return data in the various CPath
+// and CPolyTree structures which are pointers to heap allocated
+// memory. Eventually this memory will need to be released with one
+// of the following 'DisposeExported' functions.  (This may be the
+// only safe way to release this memory since the executable
+// accessing these exported functions may use a memory manager that
+// allocates and releases heap memory in a different way. Also,
+// CPath structures that have been constructed by the executable
+// should not be destroyed using these 'DisposeExported' functions.)
+EXTERN_DLL_EXPORT void DisposeExportedCPath64(CPath64 p);
+EXTERN_DLL_EXPORT void DisposeExportedCPaths64(CPaths64& pp);
+EXTERN_DLL_EXPORT void DisposeExportedCPathD(CPathD p);
+EXTERN_DLL_EXPORT void DisposeExportedCPathsD(CPathsD& pp);
+EXTERN_DLL_EXPORT void DisposeExportedCPolyTree64(CPolyTree64*& cpt);
+EXTERN_DLL_EXPORT void DisposeExportedCPolyTreeD(CPolyTreeD*& cpt);
+
+// Boolean clipping:
+// cliptype: None=0, Intersection=1, Union=2, Difference=3, Xor=4
+// fillrule: EvenOdd=0, NonZero=1, Positive=2, Negative=3
+EXTERN_DLL_EXPORT int BooleanOp64(uint8_t cliptype,
+  uint8_t fillrule, const CPaths64 subjects,
+  const CPaths64 subjects_open, const CPaths64 clips,
+  CPaths64& solution, CPaths64& solution_open,
+  bool preserve_collinear = true, bool reverse_solution = false);
+EXTERN_DLL_EXPORT int BooleanOpPt64(uint8_t cliptype,
+  uint8_t fillrule, const CPaths64 subjects,
+  const CPaths64 subjects_open, const CPaths64 clips,
+  CPolyTree64*& solution, CPaths64& solution_open,
+  bool preserve_collinear = true, bool reverse_solution = false);
+EXTERN_DLL_EXPORT int BooleanOpD(uint8_t cliptype,
+  uint8_t fillrule, const CPathsD subjects,
+  const CPathsD subjects_open, const CPathsD clips,
+  CPathsD& solution, CPathsD& solution_open, int precision = 2,
+  bool preserve_collinear = true, bool reverse_solution = false);
+EXTERN_DLL_EXPORT int BooleanOpPtD(uint8_t cliptype,
+  uint8_t fillrule, const CPathsD subjects,
+  const CPathsD subjects_open, const CPathsD clips,
+  CPolyTreeD*& solution, CPathsD& solution_open, int precision = 2,
+  bool preserve_collinear = true, bool reverse_solution = false);
+
+// Polygon offsetting (inflate/deflate):
+// jointype: Square=0, Round=1, Miter=2
+// endtype: Polygon=0, Joined=1, Butt=2, Square=3, Round=4
+EXTERN_DLL_EXPORT CPaths64 InflatePaths64(const CPaths64 paths,
+  double delta, uint8_t jointype, uint8_t endtype, 
+  double miter_limit = 2.0, double arc_tolerance = 0.0, 
+  bool reverse_solution = false);
+EXTERN_DLL_EXPORT CPathsD InflatePathsD(const CPathsD paths,
+  double delta, uint8_t jointype, uint8_t endtype,
+  int precision = 2, double miter_limit = 2.0,
+  double arc_tolerance = 0.0, bool reverse_solution = false);
+
+// 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
+//////////////////////////////////////////////////////
+
+inline CPath64 CreateCPath64(size_t cnt1, size_t cnt2);
+inline CPath64 CreateCPath64(const Path64& p);
+inline CPaths64 CreateCPaths64(const Paths64& pp);
+inline Path64 ConvertCPath64(const CPath64& p);
+inline Paths64 ConvertCPaths64(const CPaths64& pp);
+
+inline CPathD CreateCPathD(size_t cnt1, size_t cnt2);
+inline CPathD CreateCPathD(const PathD& p);
+inline CPathsD CreateCPathsD(const PathsD& pp);
+inline PathD ConvertCPathD(const CPathD& p);
+inline PathsD ConvertCPathsD(const CPathsD& pp);
+
+// the following function avoid multiple conversions
+inline CPathD CreateCPathD(const Path64& p, double scale);
+inline CPathsD CreateCPathsD(const Paths64& pp, double scale);
+inline Path64 ConvertCPathD(const CPathD& p, double scale);
+inline Paths64 ConvertCPathsD(const CPathsD& pp, double scale);
+
+inline CPolyTree64* CreateCPolyTree64(const PolyTree64& pt);
+inline CPolyTreeD* CreateCPolyTreeD(const PolyTree64& pt, double scale);
+
+EXTERN_DLL_EXPORT const char* Version()
+{
+  return CLIPPER2_VERSION;
+}
+
+EXTERN_DLL_EXPORT void DisposeExportedCPath64(CPath64 p)
+{
+  if (p) delete[] p;
+}
+
+EXTERN_DLL_EXPORT void DisposeExportedCPaths64(CPaths64& pp)
+{
+  if (!pp) return;
+  CPaths64 v = pp;
+  CPath64 cnts = *v;
+  const size_t cnt = static_cast<size_t>(cnts[1]);
+  for (size_t i = 0; i <= cnt; ++i) //nb: cnt +1
+    DisposeExportedCPath64(*v++);
+  delete[] pp;
+  pp = nullptr;
+}
+
+EXTERN_DLL_EXPORT void DisposeExportedCPathD(CPathD p)
+{
+  if (p) delete[] p;
+}
+
+EXTERN_DLL_EXPORT void DisposeExportedCPathsD(CPathsD& pp)
+{
+  if (!pp) return;
+  CPathsD v = pp;
+  CPathD cnts = *v;
+  size_t cnt = static_cast<size_t>(cnts[1]);
+  for (size_t i = 0; i <= cnt; ++i) //nb: cnt +1
+    DisposeExportedCPathD(*v++);
+  delete[] pp;
+  pp = nullptr;
+}
+
+EXTERN_DLL_EXPORT int BooleanOp64(uint8_t cliptype, 
+  uint8_t fillrule, const CPaths64 subjects,
+  const CPaths64 subjects_open, const CPaths64 clips,
+  CPaths64& solution, CPaths64& solution_open,
+  bool preserve_collinear, bool reverse_solution)
+{
+  if (cliptype > static_cast<uint8_t>(ClipType::Xor)) return -4;
+  if (fillrule > static_cast<uint8_t>(FillRule::Negative)) return -3;
+  
+  Paths64 sub, sub_open, clp, sol, sol_open;
+  sub       = ConvertCPaths64(subjects);
+  sub_open  = ConvertCPaths64(subjects_open);
+  clp       = ConvertCPaths64(clips);
+
+  Clipper64 clipper;
+  clipper.PreserveCollinear = preserve_collinear;
+  clipper.ReverseSolution = reverse_solution;
+  if (sub.size() > 0) clipper.AddSubject(sub);
+  if (sub_open.size() > 0) clipper.AddOpenSubject(sub_open);
+  if (clp.size() > 0) clipper.AddClip(clp);
+  if (!clipper.Execute(ClipType(cliptype), FillRule(fillrule), sol, sol_open)) 
+    return -1; // clipping bug - should never happen :)
+  solution = CreateCPaths64(sol);
+  solution_open = CreateCPaths64(sol_open);
+  return 0; //success !!
+}
+
+EXTERN_DLL_EXPORT int BooleanOpPt64(uint8_t cliptype,
+  uint8_t fillrule, const CPaths64 subjects,
+  const CPaths64 subjects_open, const CPaths64 clips,
+  CPolyTree64*& solution, CPaths64& solution_open,
+  bool preserve_collinear, bool reverse_solution)
+{
+  if (cliptype > static_cast<uint8_t>(ClipType::Xor)) return -4;
+  if (fillrule > static_cast<uint8_t>(FillRule::Negative)) return -3;
+  Paths64 sub, sub_open, clp, sol_open;
+  sub = ConvertCPaths64(subjects);
+  sub_open = ConvertCPaths64(subjects_open);
+  clp = ConvertCPaths64(clips);
+
+  PolyTree64 pt;
+  Clipper64 clipper;
+  clipper.PreserveCollinear = preserve_collinear;
+  clipper.ReverseSolution = reverse_solution;
+  if (sub.size() > 0) clipper.AddSubject(sub);
+  if (sub_open.size() > 0) clipper.AddOpenSubject(sub_open);
+  if (clp.size() > 0) clipper.AddClip(clp);
+  if (!clipper.Execute(ClipType(cliptype), FillRule(fillrule), pt, sol_open))
+    return -1; // clipping bug - should never happen :)
+
+  solution = CreateCPolyTree64(pt);
+  solution_open = CreateCPaths64(sol_open);
+  return 0; //success !!
+}
+
+EXTERN_DLL_EXPORT int BooleanOpD(uint8_t cliptype,
+  uint8_t fillrule, const CPathsD subjects,
+  const CPathsD subjects_open, const CPathsD clips,
+  CPathsD& solution, CPathsD& solution_open, int precision,
+  bool preserve_collinear, bool reverse_solution)
+{
+  if (precision < -8 || precision > 8) return -5;
+  if (cliptype > static_cast<uint8_t>(ClipType::Xor)) return -4;
+  if (fillrule > static_cast<uint8_t>(FillRule::Negative)) return -3;
+  const double scale = std::pow(10, precision);
+
+  Paths64 sub, sub_open, clp, sol, sol_open;
+  sub       = ConvertCPathsD(subjects, scale);
+  sub_open  = ConvertCPathsD(subjects_open, scale);
+  clp       = ConvertCPathsD(clips, scale);
+
+  Clipper64 clipper;
+  clipper.PreserveCollinear = preserve_collinear;
+  clipper.ReverseSolution = reverse_solution;
+  if (sub.size() > 0) clipper.AddSubject(sub);
+  if (sub_open.size() > 0)
+    clipper.AddOpenSubject(sub_open);
+  if (clp.size() > 0) clipper.AddClip(clp);
+  if (!clipper.Execute(ClipType(cliptype),
+    FillRule(fillrule), sol, sol_open)) return -1;
+
+  if (sol.size() > 0) solution = CreateCPathsD(sol, 1 / scale);
+  if (sol_open.size() > 0)
+    solution_open = CreateCPathsD(sol_open, 1 / scale);
+  return 0;
+}
+
+EXTERN_DLL_EXPORT int BooleanOpPtD(uint8_t cliptype,
+  uint8_t fillrule, const CPathsD subjects,
+  const CPathsD subjects_open, const CPathsD clips,
+  CPolyTreeD*& solution, CPathsD& solution_open, int precision,
+  bool preserve_collinear, bool reverse_solution)
+{
+  if (precision < -8 || precision > 8) return -5;
+  if (cliptype > static_cast<uint8_t>(ClipType::Xor)) return -4;
+  if (fillrule > static_cast<uint8_t>(FillRule::Negative)) return -3;
+  
+  const double scale = std::pow(10, precision);
+  Paths64 sub, sub_open, clp, sol_open;
+  sub       = ConvertCPathsD(subjects, scale);
+  sub_open  = ConvertCPathsD(subjects_open, scale);
+  clp       = ConvertCPathsD(clips, scale);
+
+  PolyTree64 sol;
+  Clipper64 clipper;
+  clipper.PreserveCollinear = preserve_collinear;
+  clipper.ReverseSolution = reverse_solution;
+  if (sub.size() > 0) clipper.AddSubject(sub);
+  if (sub_open.size() > 0)
+    clipper.AddOpenSubject(sub_open);
+  if (clp.size() > 0) clipper.AddClip(clp);
+  if (!clipper.Execute(ClipType(cliptype),
+    FillRule(fillrule), sol, sol_open)) return -1;
+
+  solution = CreateCPolyTreeD(sol, 1 / scale);
+  if (sol_open.size() > 0)
+    solution_open = CreateCPathsD(sol_open, 1 / scale);
+  return 0;
+}
+
+EXTERN_DLL_EXPORT CPaths64 InflatePaths64(const CPaths64 paths,
+  double delta, uint8_t jointype, uint8_t endtype, double miter_limit,
+  double arc_tolerance, bool reverse_solution)
+{
+  Paths64 pp;
+  pp = ConvertCPaths64(paths);
+
+  ClipperOffset clip_offset( miter_limit, 
+    arc_tolerance, reverse_solution);
+  clip_offset.AddPaths(pp, JoinType(jointype), EndType(endtype));
+  Paths64 result = clip_offset.Execute(delta);
+  return CreateCPaths64(result);
+}
+
+EXTERN_DLL_EXPORT CPathsD InflatePathsD(const CPathsD paths,
+  double delta, uint8_t jointype, uint8_t endtype,
+  int precision, double miter_limit,
+  double arc_tolerance, bool reverse_solution)
+{
+  if (precision < -8 || precision > 8 || !paths) return nullptr;
+  const double scale = std::pow(10, precision);
+  ClipperOffset clip_offset(miter_limit, arc_tolerance, reverse_solution);
+  Paths64 pp = ConvertCPathsD(paths, scale);
+  clip_offset.AddPaths(pp, JoinType(jointype), EndType(endtype));
+  Paths64 result = clip_offset.Execute(delta * scale);
+  return CreateCPathsD(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 RectClip rc(r64);
+  Paths64 pp = ConvertCPaths64(paths);
+  Paths64 result;
+  result.reserve(pp.size());
+  for (const Path64& p : pp)
+  {
+    Rect64 pathRec = Bounds(p);
+    if (!r64.Intersects(pathRec)) continue;
+    
+    if (r64.Contains(pathRec))
+      result.push_back(p);
+    else
+    {
+      Path64 p2 = rc.Execute(p);
+      if (!p2.empty()) result.push_back(std::move(p2));
+    }
+  }
+  return CreateCPaths64(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);
+  Rect64 r = ScaleRect<int64_t, double>(CRectToRect(rect), scale);
+  Paths64 pp = ConvertCPathsD(paths, scale);
+  class RectClip rc(r);
+  Paths64 result;
+  result.reserve(pp.size());
+  for (const Path64& p : pp)
+  {
+    Rect64 pathRec = Bounds(p);
+    if (!r.Intersects(pathRec)) continue;
+    
+    if (r.Contains(pathRec))
+      result.push_back(p);
+    else
+    {
+      Path64 p2 = rc.Execute(p);
+      if (!p2.empty()) result.push_back(std::move(p2));
+    }
+  }
+  return CreateCPathsD(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 RectClipLines rcl (r);
+  Paths64 pp = ConvertCPaths64(paths);
+  Paths64 result;
+  result.reserve(pp.size());
+
+  for (const Path64& p : pp)
+  {
+    Rect64 pathRec = Bounds(p);
+    if (!r.Intersects(pathRec)) continue;
+    
+    if (r.Contains(pathRec))
+      result.push_back(p);
+    else
+    {
+      Paths64 pp2 = rcl.Execute(p);
+      if (!pp2.empty())
+        result.insert(result.end(), pp2.begin(), pp2.end());
+    }
+  }
+  return CreateCPaths64(result);
+}
+
+EXTERN_DLL_EXPORT CPathsD RectClipLinesD(const CRectD& rect, 
+  const CPathsD paths, int precision)
+{
+  Paths64 result;
+  if (CRectIsEmpty(rect) || !paths) return nullptr;
+  if (precision < -8 || precision > 8) return nullptr;
+  const double scale = std::pow(10, precision);
+  Rect64 r = ScaleRect<int64_t, double>(CRectToRect(rect), scale);
+  class RectClipLines rcl(r);
+  Paths64 pp = ConvertCPathsD(paths, scale);
+
+  result.reserve(pp.size());
+  for (const Path64& p : pp)
+  {
+    Rect64 pathRec = Bounds(p);
+    if (!r.Intersects(pathRec)) continue;
+    
+    if (r.Contains(pathRec))
+      result.push_back(p);
+    else
+    {
+      Paths64 pp2 = rcl.Execute(p);
+      if (pp2.empty()) continue;
+      result.insert(result.end(), pp2.begin(), pp2.end());
+    }
+  }
+  return CreateCPathsD(result, 1/scale);
+}
+
+inline CPath64 CreateCPath64(size_t cnt1, size_t cnt2)
+{
+  // allocates memory for CPath64, fills in the counter, and
+  // returns the structure ready to be filled with path data
+  CPath64 result = new int64_t[2 + cnt1 *2];
+  result[0] = cnt1;
+  result[1] = cnt2;
+  return result;
+}
+
+inline CPath64 CreateCPath64(const Path64& p)
+{
+  // allocates memory for CPath64, fills the counter
+  // and returns the memory filled with path data
+  size_t cnt = p.size();
+  if (!cnt) return nullptr;
+  CPath64 result = CreateCPath64(cnt, 0);
+  CPath64 v = result;
+  v += 2; // skip counters
+  for (const Point64& pt : p)
+  {
+    *v++ = pt.x;
+    *v++ = pt.y;
+  }
+  return result;
+}
+
+inline Path64 ConvertCPath64(const CPath64& p)
+{
+  Path64 result;
+  if (p && *p)
+  {
+    CPath64 v = p;
+    const size_t cnt = static_cast<size_t>(p[0]);
+    v += 2; // skip counters
+    result.reserve(cnt);
+    for (size_t i = 0; i < cnt; ++i)
+    {
+      // x,y here avoids right to left function evaluation
+      // result.push_back(Point64(*v++, *v++));
+      int64_t x = *v++;
+      int64_t y = *v++;
+      result.push_back(Point64(x, y));
+    }
+  }
+  return result;
+}
+
+inline CPaths64 CreateCPaths64(const Paths64& pp)
+{
+  // allocates memory for multiple CPath64 and
+  // and returns this memory filled with path data
+  size_t cnt = pp.size(), cnt2 = cnt;
+
+  // don't allocate space for empty paths
+  for (size_t i = 0; i < cnt; ++i)
+    if (!pp[i].size()) --cnt2;
+  if (!cnt2) return nullptr;
+
+  CPaths64 result = new int64_t* [cnt2 + 1];
+  CPaths64 v = result;
+  *v++ = CreateCPath64(0, cnt2); // assign a counter path
+  for (const Path64& p : pp)
+  {
+    *v = CreateCPath64(p);
+    if (*v) ++v;
+  }
+  return result;
+}
+
+inline Paths64 ConvertCPaths64(const CPaths64& pp)
+{
+  Paths64 result;
+  if (pp) 
+  {
+    CPaths64 v = pp;
+    CPath64 cnts = pp[0];
+    const size_t cnt = static_cast<size_t>(cnts[1]); // nb 2nd cnt
+    ++v; // skip cnts
+    result.reserve(cnt);
+    for (size_t i = 0; i < cnt; ++i)
+      result.push_back(ConvertCPath64(*v++));
+  }
+  return result;
+}
+
+inline CPathD CreateCPathD(size_t cnt1, size_t cnt2)
+{
+  // allocates memory for CPathD, fills in the counter, and
+  // returns the structure ready to be filled with path data
+  CPathD result = new double[2 + cnt1 * 2];
+  result[0] = static_cast<double>(cnt1);
+  result[1] = static_cast<double>(cnt2);
+  return result;
+}
+
+inline CPathD CreateCPathD(const PathD& p)
+{
+  // allocates memory for CPath, fills the counter
+  // and returns the memory fills with path data
+  size_t cnt = p.size();
+  if (!cnt) return nullptr; 
+  CPathD result = CreateCPathD(cnt, 0);
+  CPathD v = result;
+  v += 2; // skip counters
+  for (const PointD& pt : p)
+  {
+    *v++ = pt.x;
+    *v++ = pt.y;
+  }
+  return result;
+}
+
+inline PathD ConvertCPathD(const CPathD& p)
+{
+  PathD result;
+  if (p)
+  {
+    CPathD v = p;
+    size_t cnt = static_cast<size_t>(v[0]);
+    v += 2; // skip counters
+    result.reserve(cnt);
+    for (size_t i = 0; i < cnt; ++i)
+    {
+      // x,y here avoids right to left function evaluation
+      // result.push_back(PointD(*v++, *v++));
+      double x = *v++;
+      double y = *v++;
+      result.push_back(PointD(x, y));
+    }
+  }
+  return result;
+}
+
+inline CPathsD CreateCPathsD(const PathsD& pp)
+{
+  size_t cnt = pp.size(), cnt2 = cnt;
+  // don't allocate space for empty paths
+  for (size_t i = 0; i < cnt; ++i)
+    if (!pp[i].size()) --cnt2;
+  if (!cnt2) return nullptr;
+  CPathsD result = new double * [cnt2 + 1];
+  CPathsD v = result;
+  *v++ = CreateCPathD(0, cnt2); // assign counter path
+  for (const PathD& p : pp)
+  {
+    *v = CreateCPathD(p);
+    if (*v) { ++v; }
+  }
+  return result;
+}
+
+inline PathsD ConvertCPathsD(const CPathsD& pp)
+{
+  PathsD result;
+  if (pp)
+  {
+    CPathsD v = pp;
+    CPathD cnts = v[0];
+    size_t cnt = static_cast<size_t>(cnts[1]);
+    ++v; // skip cnts path
+    result.reserve(cnt);
+    for (size_t i = 0; i < cnt; ++i)
+      result.push_back(ConvertCPathD(*v++));
+  }
+  return result;
+}
+
+inline Path64 ConvertCPathD(const CPathD& p, double scale)
+{
+  Path64 result;
+  if (p)
+  {
+    CPathD v = p;
+    size_t cnt = static_cast<size_t>(*v);
+    v += 2; // skip counters
+    result.reserve(cnt);
+    for (size_t i = 0; i < cnt; ++i)
+    {
+      // x,y here avoids right to left function evaluation
+      // result.push_back(PointD(*v++, *v++));
+      double x = *v++ * scale;
+      double y = *v++ * scale;
+      result.push_back(Point64(x, y));
+    }
+  }
+  return result;
+}
+
+inline Paths64 ConvertCPathsD(const CPathsD& pp, double scale)
+{
+  Paths64 result;
+  if (pp)
+  {
+    CPathsD v = pp;
+    CPathD cnts = v[0];
+    size_t cnt = static_cast<size_t>(cnts[1]);
+    result.reserve(cnt);
+    ++v; // skip cnts path
+    for (size_t i = 0; i < cnt; ++i)
+      result.push_back(ConvertCPathD(*v++, scale));
+  }
+  return result;
+}
+
+inline CPathD CreateCPathD(const Path64& p, double scale)
+{
+  // allocates memory for CPathD, fills in the counter, and
+  // returns the structure filled with *scaled* path data
+  size_t cnt = p.size();
+  if (!cnt) return nullptr;
+  CPathD result = CreateCPathD(cnt, 0);
+  CPathD v = result;
+  v += 2; // skip cnts 
+  for (const Point64& pt : p)
+  {
+    *v++ = pt.x * scale;
+    *v++ = pt.y * scale;
+  }
+  return result;
+}
+
+inline CPathsD CreateCPathsD(const Paths64& pp, double scale)
+{
+  // allocates memory for *multiple* CPathD, and
+  // returns the structure filled with scaled path data
+  size_t cnt = pp.size(), cnt2 = cnt;
+  // don't allocate space for empty paths
+  for (size_t i = 0; i < cnt; ++i)
+    if (!pp[i].size()) --cnt2;
+  if (!cnt2) return nullptr;
+  CPathsD result = new double* [cnt2 + 1];
+  CPathsD v = result;
+  *v++ = CreateCPathD(0, cnt2);
+  for (const Path64& p : pp)
+  {
+    *v = CreateCPathD(p, scale);
+    if (*v) ++v;
+  }
+  return result;
+}
+
+inline void InitCPolyPath64(CPolyTree64* cpt, 
+  bool is_hole, const PolyPath64* pp)
+{
+  cpt->polygon = CreateCPath64(pp->Polygon());
+  cpt->is_hole = is_hole;
+  size_t child_cnt = pp->Count();
+  cpt->child_count = static_cast<uint32_t>(child_cnt);
+  cpt->childs = nullptr;
+  if (!child_cnt) return;
+  cpt->childs = new CPolyPath64[child_cnt];
+  CPolyPath64* child = cpt->childs;
+  for (const PolyPath64* pp_child : *pp)
+    InitCPolyPath64(child++, !is_hole, pp_child);  
+}
+
+inline CPolyTree64* CreateCPolyTree64(const PolyTree64& pt)
+{
+  CPolyTree64* result = new CPolyTree64();
+  result->polygon = nullptr;
+  result->is_hole = false;
+  size_t child_cnt = pt.Count();
+  result->childs = nullptr;
+  result->child_count = static_cast<uint32_t>(child_cnt);
+  if (!child_cnt) return result;
+  result->childs = new CPolyPath64[child_cnt];
+  CPolyPath64* child = result->childs;
+  for (const PolyPath64* pp : pt)
+    InitCPolyPath64(child++, true, pp);
+  return result;
+}
+
+inline void DisposeCPolyPath64(CPolyPath64* cpp) 
+{
+  if (!cpp->child_count) return;
+  CPolyPath64* child = cpp->childs;
+  for (size_t i = 0; i < cpp->child_count; ++i)
+    DisposeCPolyPath64(child);
+  delete[] cpp->childs;
+}
+
+EXTERN_DLL_EXPORT void DisposeExportedCPolyTree64(CPolyTree64*& cpt)
+{
+  if (!cpt) return;
+  DisposeCPolyPath64(cpt);
+  delete cpt;
+  cpt = nullptr;
+}
+
+inline void InitCPolyPathD(CPolyTreeD* cpt,
+  bool is_hole, const PolyPath64* pp, double scale)
+{
+  cpt->polygon = CreateCPathD(pp->Polygon(), scale);
+  cpt->is_hole = is_hole;
+  size_t child_cnt = pp->Count();
+  cpt->child_count = static_cast<uint32_t>(child_cnt);
+  cpt->childs = nullptr;
+  if (!child_cnt) return;
+  cpt->childs = new CPolyPathD[child_cnt];
+  CPolyPathD* child = cpt->childs;
+  for (const PolyPath64* pp_child : *pp)
+    InitCPolyPathD(child++, !is_hole, pp_child, scale);
+}
+
+inline CPolyTreeD* CreateCPolyTreeD(const PolyTree64& pt, double scale)
+{
+  CPolyTreeD* result = new CPolyTreeD();
+  result->polygon = nullptr;
+  result->is_hole = false;
+  size_t child_cnt = pt.Count();
+  result->child_count = static_cast<uint32_t>(child_cnt);
+  result->childs = nullptr;
+  if (!child_cnt) return result;
+  result->childs = new CPolyPathD[child_cnt];
+  CPolyPathD* child = result->childs;
+  for (const PolyPath64* pp : pt)
+    InitCPolyPathD(child++, true, pp, scale);
+  return result;
+}
+
+inline void DisposeCPolyPathD(CPolyPathD* cpp)
+{
+  if (!cpp->child_count) return;
+  CPolyPathD* child = cpp->childs;
+  for (size_t i = 0; i < cpp->child_count; ++i)
+    DisposeCPolyPathD(child++);
+  delete[] cpp->childs;
+}
+
+EXTERN_DLL_EXPORT void DisposeExportedCPolyTreeD(CPolyTreeD*& cpt)
+{
+  if (!cpt) return;
+  DisposeCPolyPathD(cpt);
+  delete cpt;
+  cpt = nullptr;
+}
+
+}  // end Clipper2Lib namespace
+  
+#endif  // CLIPPER2_EXPORT_H

src/clipper2/Clipper2Lib/include/clipper2/clipper.h

@@ -0,0 +1,762 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  29 October 2022                                                 *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2022                                         *
+* 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 <vector>
+
+#include "clipper.core.h"
+#include "clipper.engine.h"
+#include "clipper.offset.h"
+#include "clipper.minkowski.h"
+#include "clipper.rectclip.h"
+
+namespace Clipper2Lib {
+
+  static const Rect64 MaxInvalidRect64 = 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 MaxInvalidRectD = RectD(
+      (std::numeric_limits<double>::max)(),
+      (std::numeric_limits<double>::max)(),
+      (std::numeric_limits<double>::lowest)(),
+      (std::numeric_limits<double>::lowest)());
+
+  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 decimal_prec = 2)
+  {
+    CheckPrecision(decimal_prec);
+    PathsD result;
+    ClipperD clipper(decimal_prec);
+    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 decimal_prec = 2)
+  {
+    CheckPrecision(decimal_prec);
+    PathsD result;
+    ClipperD clipper(decimal_prec);
+    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 decimal_prec = 2)
+  {
+    CheckPrecision(decimal_prec);
+    PathsD result;
+    ClipperD clipper(decimal_prec);
+    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)
+  {
+    ClipperOffset clip_offset(miter_limit);
+    clip_offset.AddPaths(paths, jt, et);
+    return clip_offset.Execute(delta);
+  }
+
+  inline PathsD InflatePaths(const PathsD& paths, double delta,
+    JoinType jt, EndType et, double miter_limit = 2.0, int precision = 2)
+  {
+    CheckPrecision(precision);
+    const double scale = std::pow(10, precision);
+    ClipperOffset clip_offset(miter_limit);
+    clip_offset.AddPaths(ScalePaths<int64_t,double>(paths, scale), jt, et);
+    Paths64 tmp = clip_offset.Execute(delta * scale);
+    return ScalePaths<double, int64_t>(tmp, 1 / scale);
+  }
+
+  inline Path64 TranslatePath(const Path64& path, int64_t dx, int64_t dy)
+  {
+    Path64 result;
+    result.reserve(path.size());
+    for (const Point64& pt : path)
+      result.push_back(Point64(pt.x + dx, pt.y + dy));
+    return result;
+  }
+
+  inline PathD TranslatePath(const PathD& path, double dx, double dy)
+  {
+    PathD result;
+    result.reserve(path.size());
+    for (const PointD& pt : path)
+      result.push_back(PointD(pt.x + dx, pt.y + dy));
+    return result;
+  }
+
+  inline Paths64 TranslatePaths(const Paths64& paths, int64_t dx, int64_t dy)
+  {
+    Paths64 result;
+    result.reserve(paths.size());
+    for (const Path64& path : paths)
+      result.push_back(TranslatePath(path, dx, dy));
+    return result;
+  }
+
+  inline PathsD TranslatePaths(const PathsD& paths, double dx, double dy)
+  {
+    PathsD result;
+    result.reserve(paths.size());
+    for (const PathD& path : paths)
+      result.push_back(TranslatePath(path, dx, dy));
+    return result;
+  }
+
+  inline Rect64 Bounds(const Path64& path)
+  {
+    Rect64 rec = MaxInvalidRect64;
+    for (const Point64& pt : path)
+    {
+      if (pt.x < rec.left) rec.left = pt.x;
+      if (pt.x > rec.right) rec.right = pt.x;
+      if (pt.y < rec.top) rec.top = pt.y;
+      if (pt.y > rec.bottom) rec.bottom = pt.y;
+    }
+    if (rec.IsEmpty()) return Rect64();
+    return rec;
+  }
+  
+  inline Rect64 Bounds(const Paths64& paths)
+  {
+    Rect64 rec = MaxInvalidRect64;
+    for (const Path64& path : paths)
+      for (const Point64& pt : path)
+      {
+        if (pt.x < rec.left) rec.left = pt.x;
+        if (pt.x > rec.right) rec.right = pt.x;
+        if (pt.y < rec.top) rec.top = pt.y;
+        if (pt.y > rec.bottom) rec.bottom = pt.y;
+      }
+    if (rec.IsEmpty()) return Rect64();
+    return rec;
+  }
+
+  inline RectD Bounds(const PathD& path)
+  {
+    RectD rec = MaxInvalidRectD;
+    for (const PointD& pt : path)
+    {
+      if (pt.x < rec.left) rec.left = pt.x;
+      if (pt.x > rec.right) rec.right = pt.x;
+      if (pt.y < rec.top) rec.top = pt.y;
+      if (pt.y > rec.bottom) rec.bottom = pt.y;
+    }
+    if (rec.IsEmpty()) return RectD();
+    return rec;
+  }
+
+  inline RectD Bounds(const PathsD& paths)
+  {
+    RectD rec = MaxInvalidRectD;
+    for (const PathD& path : paths)
+      for (const PointD& pt : path)
+      {
+        if (pt.x < rec.left) rec.left = pt.x;
+        if (pt.x > rec.right) rec.right = pt.x;
+        if (pt.y < rec.top) rec.top = pt.y;
+        if (pt.y > rec.bottom) rec.bottom = pt.y;
+      }
+    if (rec.IsEmpty()) return RectD();
+    return rec;
+  }
+
+  inline Path64 RectClip(const Rect64& rect, const Path64& path)
+  {
+    if (rect.IsEmpty() || path.empty()) return Path64();
+    Rect64 pathRec = Bounds(path);
+    if (!rect.Intersects(pathRec)) return Path64();
+    if (rect.Contains(pathRec)) return path;
+    class RectClip rc(rect);
+    return rc.Execute(path);
+  }
+  
+  inline Paths64 RectClip(const Rect64& rect, const Paths64& paths)
+  {
+    if (rect.IsEmpty() || paths.empty()) return Paths64();
+    class RectClip rc(rect);
+    Paths64 result;
+    result.reserve(paths.size());
+
+    for (const Path64& p : paths)
+    {
+      Rect64 pathRec = Bounds(p);
+      if (!rect.Intersects(pathRec)) 
+        continue;
+      else if (rect.Contains(pathRec))
+        result.push_back(p);
+      else
+      {
+        Path64 p2 = rc.Execute(p);
+        if (!p2.empty()) result.push_back(std::move(p2));
+      }
+    }
+    return result;
+  }
+
+  inline PathD RectClip(const RectD& rect, const PathD& path, int precision = 2)
+  {
+    if (rect.IsEmpty() || path.empty() ||
+      !rect.Contains(Bounds(path))) return PathD();
+    CheckPrecision(precision);
+    const double scale = std::pow(10, precision);
+    Rect64 r = ScaleRect<int64_t, double>(rect, scale);
+    class RectClip rc(r);
+    Path64 p = ScalePath<int64_t, double>(path, scale);
+    return ScalePath<double, int64_t>(rc.Execute(p), 1 / scale);
+  }
+
+  inline PathsD RectClip(const RectD& rect, const PathsD& paths, int precision = 2)
+  {
+    if (rect.IsEmpty() || paths.empty()) return PathsD();
+    CheckPrecision(precision);
+    const double scale = std::pow(10, precision);
+    Rect64 r = ScaleRect<int64_t, double>(rect, scale);
+    class RectClip rc(r);
+    PathsD result;
+    result.reserve(paths.size());
+    for (const PathD& path : paths) 
+    {
+      RectD pathRec = Bounds(path);
+      if (!rect.Intersects(pathRec))
+        continue;
+      else if (rect.Contains(pathRec))
+        result.push_back(path);
+      else
+      {
+        Path64 p = ScalePath<int64_t, double>(path, scale);
+        p = rc.Execute(p);
+        if (!p.empty()) 
+          result.push_back(ScalePath<double, int64_t>(p, 1 / scale));
+      }
+    }
+    return result;
+  }
+
+  inline Paths64 RectClipLines(const Rect64& rect, const Path64& path)
+  {
+    Paths64 result;
+    if (rect.IsEmpty() || path.empty()) return result;
+    Rect64 pathRec = Bounds(path);
+    if (!rect.Intersects(pathRec)) return result;
+    if (rect.Contains(pathRec)) 
+    {
+      result.push_back(path);
+      return result;
+    }
+    class RectClipLines rcl(rect);
+    return rcl.Execute(path);
+  }
+
+  inline Paths64 RectClipLines(const Rect64& rect, const Paths64& paths)
+  {
+    Paths64 result;
+    if (rect.IsEmpty() || paths.empty()) return result;
+    class RectClipLines rcl(rect);
+    for (const Path64& p : paths)
+    {
+      Rect64 pathRec = Bounds(p);
+      if (!rect.Intersects(pathRec))
+        continue;
+      else if (rect.Contains(pathRec))
+        result.push_back(p);
+      else
+      {
+        Paths64 pp = rcl.Execute(p);
+        if (!pp.empty()) 
+          result.insert(result.end(), pp.begin(), pp.end());
+      }
+    }
+    return result;
+  }
+
+  inline PathsD RectClipLines(const RectD& rect, const PathD& path, int precision = 2)
+  {
+    if (rect.IsEmpty() || path.empty() ||
+      !rect.Contains(Bounds(path))) return PathsD();
+    CheckPrecision(precision);
+    const double scale = std::pow(10, precision);
+    Rect64 r = ScaleRect<int64_t, double>(rect, scale);
+    class RectClipLines rcl(r);
+    Path64 p = ScalePath<int64_t, double>(path, scale);
+    return ScalePaths<double, int64_t>(rcl.Execute(p), 1 / scale);
+  }
+
+  inline PathsD RectClipLines(const RectD& rect, const PathsD& paths, int precision = 2)
+  {
+    PathsD result;
+    if (rect.IsEmpty() || paths.empty()) return result;
+    CheckPrecision(precision);
+    const double scale = std::pow(10, precision);
+    Rect64 r = ScaleRect<int64_t, double>(rect, scale);
+    class RectClipLines rcl(r);
+    result.reserve(paths.size());
+    for (const PathD& path : paths)
+    {
+      RectD pathRec = Bounds(path);
+      if (!rect.Intersects(pathRec))
+        continue;
+      else if (rect.Contains(pathRec))
+        result.push_back(path);
+      else
+      {
+        Path64 p = ScalePath<int64_t, double>(path, scale);
+        Paths64 pp = rcl.Execute(p);
+        if (pp.empty()) continue;
+        PathsD ppd = ScalePaths<double, int64_t>(pp, 1 / scale);
+        result.insert(result.end(), ppd.begin(), ppd.end());
+      }
+    }
+    return result;
+  }
+
+  namespace details
+  {
+
+    inline void PolyPathToPaths64(const PolyPath64& polypath, Paths64& paths)
+    {
+      paths.push_back(polypath.Polygon());
+      for (const PolyPath* child : polypath)
+        PolyPathToPaths64(*(PolyPath64*)(child), paths);
+    }
+
+    inline void PolyPathToPathsD(const PolyPathD& polypath, PathsD& paths)
+    {
+      paths.push_back(polypath.Polygon());
+      for (const PolyPath* child : polypath)
+        PolyPathToPathsD(*(PolyPathD*)(child), paths);
+    }
+
+    inline bool PolyPath64ContainsChildren(const PolyPath64& pp)
+    {
+      for (auto ch : pp)
+      {
+        PolyPath64* child = (PolyPath64*)ch;
+        for (const Point64& pt : child->Polygon())
+          if (PointInPolygon(pt, pp.Polygon()) == PointInPolygonResult::IsOutside)
+            return false;
+        if (child->Count() > 0 && !PolyPath64ContainsChildren(*child))
+          return false;
+      }
+      return true;
+    }
+
+    inline bool GetInt(std::string::const_iterator& iter, const
+      std::string::const_iterator& end_iter, int64_t& val)
+    {
+      val = 0;
+      bool is_neg = *iter == '-';
+      if (is_neg) ++iter;
+      std::string::const_iterator start_iter = iter;
+      while (iter != end_iter &&
+        ((*iter >= '0') && (*iter <= '9')))
+      {
+        val = val * 10 + (static_cast<int64_t>(*iter++) - '0');
+      }
+      if (is_neg) val = -val;
+      return (iter != start_iter);
+    }
+
+    inline bool GetFloat(std::string::const_iterator& iter, const 
+      std::string::const_iterator& end_iter, double& val)
+    {
+      val = 0;
+      bool is_neg = *iter == '-';
+      if (is_neg) ++iter;
+      int dec_pos = 1;
+      const std::string::const_iterator start_iter = iter;
+      while (iter != end_iter && (*iter == '.' ||
+        ((*iter >= '0') && (*iter <= '9'))))
+      {
+        if (*iter == '.')
+        {
+          if (dec_pos != 1) break;
+          dec_pos = 0;
+          ++iter;
+          continue;
+        }
+        if (dec_pos != 1) --dec_pos;
+        val = val * 10 + ((int64_t)(*iter++) - '0');
+      }
+      if (iter == start_iter || dec_pos == 0) return false;
+      if (dec_pos < 0)
+        val *= std::pow(10, dec_pos);
+      if (is_neg)
+        val *= -1;
+      return true;
+    }
+
+    inline void SkipWhiteSpace(std::string::const_iterator& iter, 
+      const std::string::const_iterator& end_iter)
+    {
+      while (iter != end_iter && *iter <= ' ') ++iter;
+    }
+
+    inline void SkipSpacesWithOptionalComma(std::string::const_iterator& iter, 
+      const std::string::const_iterator& end_iter)
+    {
+      bool comma_seen = false;
+      while (iter != end_iter)
+      {
+        if (*iter == ' ') ++iter;
+        else if (*iter == ',')
+        {
+          if (comma_seen) return; // don't skip 2 commas!
+          comma_seen = true;
+          ++iter;
+        }
+        else return;                
+      }
+    }
+
+    inline bool has_one_match(const char c, char* chrs)
+    {
+      while (*chrs > 0 && c != *chrs) ++chrs;
+      if (!*chrs) return false;
+      *chrs = ' '; // only match once per char
+      return true;
+    }
+
+
+    inline void SkipUserDefinedChars(std::string::const_iterator& iter,
+      const std::string::const_iterator& end_iter, const std::string& skip_chars)
+    {
+      const size_t MAX_CHARS = 16;
+      char buff[MAX_CHARS] = {0};
+      std::copy(skip_chars.cbegin(), skip_chars.cend(), &buff[0]);
+      while (iter != end_iter && 
+        (*iter <= ' ' || has_one_match(*iter, buff))) ++iter;
+      return;
+    }
+
+  } // end details namespace 
+
+  inline Paths64 PolyTreeToPaths64(const PolyTree64& polytree)
+  {
+    Paths64 result;
+    for (auto child : polytree)
+      details::PolyPathToPaths64(*(PolyPath64*)(child), result);
+    return result;
+  }
+
+  inline PathsD PolyTreeToPathsD(const PolyTreeD& polytree)
+  {
+    PathsD result;
+    for (auto child : polytree)
+      details::PolyPathToPathsD(*(PolyPathD*)(child), result);
+    return result;
+  }
+
+  inline bool CheckPolytreeFullyContainsChildren(const PolyTree64& polytree)
+  {
+    for (auto child : polytree)
+      if (child->Count() > 0 && 
+        !details::PolyPath64ContainsChildren(*(PolyPath64*)(child)))
+          return false;
+    return true;
+  }
+
+  inline Path64 MakePath(const std::string& s)
+  {
+    const std::string skip_chars = " ,(){}[]";
+    Path64 result;
+    std::string::const_iterator s_iter = s.cbegin();
+    details::SkipUserDefinedChars(s_iter, s.cend(), skip_chars);
+    while (s_iter != s.cend())
+    {
+      int64_t y = 0, x = 0;
+      if (!details::GetInt(s_iter, s.cend(), x)) break;
+      details::SkipSpacesWithOptionalComma(s_iter, s.cend());
+      if (!details::GetInt(s_iter, s.cend(), y)) break;
+      result.push_back(Point64(x, y));
+      details::SkipUserDefinedChars(s_iter, s.cend(), skip_chars);
+    }
+    return result;
+  }
+  
+  inline PathD MakePathD(const std::string& s)
+  {
+    const std::string skip_chars = " ,(){}[]";
+    PathD result;
+    std::string::const_iterator s_iter = s.cbegin();
+    details::SkipUserDefinedChars(s_iter, s.cend(), skip_chars);
+    while (s_iter != s.cend())
+    {
+      double y = 0, x = 0;
+      if (!details::GetFloat(s_iter, s.cend(), x)) break;
+      details::SkipSpacesWithOptionalComma(s_iter, s.cend());
+      if (!details::GetFloat(s_iter, s.cend(), y)) break;
+      result.push_back(PointD(x, y));
+      details::SkipUserDefinedChars(s_iter, s.cend(), skip_chars);
+    }
+    return result;
+  }
+
+  inline Path64 TrimCollinear(const Path64& p, bool is_open_path = false)
+  {
+    size_t len = p.size();
+    if (len < 3)
+    {
+      if (!is_open_path || len < 2 || p[0] == p[1]) return Path64();
+      else return p;
+    }
+
+    Path64 dst;
+    dst.reserve(len);
+    Path64::const_iterator srcIt = p.cbegin(), prevIt, stop = p.cend() - 1;
+
+    if (!is_open_path)
+    {
+      while (srcIt != stop && !CrossProduct(*stop, *srcIt, *(srcIt + 1)))
+        ++srcIt;
+      while (srcIt != stop && !CrossProduct(*(stop - 1), *stop, *srcIt))
+        --stop;
+      if (srcIt == stop) return Path64();
+    }
+
+    prevIt = srcIt++;
+    dst.push_back(*prevIt);
+    for (; srcIt != stop; ++srcIt)
+    {
+      if (CrossProduct(*prevIt, *srcIt, *(srcIt + 1)))
+      {
+        prevIt = srcIt;
+        dst.push_back(*prevIt);
+      }
+    }
+
+    if (is_open_path)
+      dst.push_back(*srcIt);
+    else if (CrossProduct(*prevIt, *stop, dst[0]))
+      dst.push_back(*stop);
+    else
+    {
+      while (dst.size() > 2 &&
+        !CrossProduct(dst[dst.size() - 1], dst[dst.size() - 2], dst[0]))
+          dst.pop_back();
+      if (dst.size() < 3) return Path64();
+    }
+    return dst;
+  }
+
+  inline PathD TrimCollinear(const PathD& path, int precision, bool is_open_path = false)
+  {
+    CheckPrecision(precision);
+    const double scale = std::pow(10, precision);
+    Path64 p = ScalePath<int64_t, double>(path, scale);
+    p = TrimCollinear(p, is_open_path);
+    return ScalePath<double, int64_t>(p, 1/scale);
+  }
+
+  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);
+  }
+
+  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());
+    for (const Path<T>& path : paths)
+      result.push_back(RamerDouglasPeucker<T>(path, epsilon));
+    return result;
+  }
+
+}  // end Clipper2Lib namespace
+
+#endif  // CLIPPER_H

src/clipper2/Clipper2Lib/include/clipper2/clipper.minkowski.h

@@ -0,0 +1,118 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  15 October 2022                                                 *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2022                                         *
+* Purpose   :  Minkowski Sum and Difference                                    *
+* License   :  http://www.boost.org/LICENSE_1_0.txt                            *
+*******************************************************************************/
+
+#ifndef CLIPPER_MINKOWSKI_H
+#define CLIPPER_MINKOWSKI_H
+
+#include <cstdlib>
+#include <vector>
+#include <string>
+#include "clipper.core.h"
+
+namespace Clipper2Lib 
+{
+
+  namespace detail
+  {
+    inline Paths64 Minkowski(const Path64& pattern, const Path64& path, bool isSum, bool isClosed)
+    {
+      size_t delta = isClosed ? 0 : 1;
+      size_t patLen = pattern.size(), pathLen = path.size();
+      if (patLen == 0 || pathLen == 0) return Paths64();
+      Paths64 tmp;
+      tmp.reserve(pathLen);
+
+      if (isSum)
+      {
+        for (const Point64& p : path)
+        {
+          Path64 path2(pattern.size());
+          std::transform(pattern.cbegin(), pattern.cend(),
+            path2.begin(), [p](const Point64& pt2) {return p + pt2; });
+          tmp.push_back(path2);
+        }
+      }
+      else
+      {
+        for (const Point64& p : path)
+        {
+          Path64 path2(pattern.size());
+          std::transform(pattern.cbegin(), pattern.cend(),
+            path2.begin(), [p](const Point64& pt2) {return p - pt2; });
+          tmp.push_back(path2);
+        }
+      }
+
+      Paths64 result;
+      result.reserve((pathLen - delta) * patLen);
+      size_t g = isClosed ? pathLen - 1 : 0;
+      for (size_t h = patLen - 1, i = delta; i < pathLen; ++i)
+      {
+        for (size_t j = 0; j < patLen; j++)
+        {
+          Path64 quad;
+          quad.reserve(4);
+          {
+            quad.push_back(tmp[g][h]);
+            quad.push_back(tmp[i][h]);
+            quad.push_back(tmp[i][j]);
+            quad.push_back(tmp[g][j]);
+          };
+          if (!IsPositive(quad))
+            std::reverse(quad.begin(), quad.end());
+          result.push_back(quad);
+          h = j;
+        }
+        g = i;
+      }
+      return result;
+    }
+
+    inline Paths64 Union(const Paths64& subjects, FillRule fillrule)
+    {
+      Paths64 result;
+      Clipper64 clipper;
+      clipper.AddSubject(subjects);
+      clipper.Execute(ClipType::Union, fillrule, result);
+      return result;
+    }
+
+  } // namespace internal
+
+  inline Paths64 MinkowskiSum(const Path64& pattern, const Path64& path, bool isClosed)
+  {
+    return detail::Union(detail::Minkowski(pattern, path, true, isClosed), FillRule::NonZero);
+  }
+
+  inline PathsD MinkowskiSum(const PathD& pattern, const PathD& path, bool isClosed, int decimalPlaces = 2)
+  {
+    double scale = pow(10, decimalPlaces);
+    Path64 pat64 = ScalePath<int64_t, double>(pattern, scale);
+    Path64 path64 = ScalePath<int64_t, double>(path, scale);
+    Paths64 tmp = detail::Union(detail::Minkowski(pat64, path64, true, isClosed), FillRule::NonZero);
+    return ScalePaths<double, int64_t>(tmp, 1 / scale);
+  }
+
+  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)
+  {
+    double scale = pow(10, decimalPlaces);
+    Path64 pat64 = ScalePath<int64_t, double>(pattern, scale); 
+    Path64 path64 = ScalePath<int64_t, double>(path, scale);
+    Paths64 tmp = detail::Union(detail::Minkowski(pat64, path64, false, isClosed), FillRule::NonZero);
+    return ScalePaths<double, int64_t>(tmp, 1 / scale);
+  }
+
+} // Clipper2Lib namespace
+
+#endif  // CLIPPER_MINKOWSKI_H

src/clipper2/Clipper2Lib/include/clipper2/clipper.offset.h

@@ -0,0 +1,107 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  15 October 2022                                                 *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2022                                         *
+* 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"
+
+namespace Clipper2Lib {
+
+enum class JoinType { Square, Round, Miter };
+
+enum class EndType {Polygon, Joined, Butt, Square, Round};
+//Butt   : offsets both sides of a path, with square blunt ends
+//Square : offsets both sides of a path, with square extended ends
+//Round  : offsets both sides of a path, with round extended ends
+//Joined : offsets both sides of a path, with joined ends
+//Polygon: offsets only one side of a closed path
+
+class ClipperOffset {
+private:
+
+	class Group {
+	public:
+		Paths64 paths_in_;
+		Paths64 paths_out_;
+		Path64 path_;
+		bool is_reversed_ = false;
+		JoinType join_type_;
+		EndType end_type_;
+		Group(const Paths64& paths, JoinType join_type, EndType end_type) :
+			paths_in_(paths), join_type_(join_type), end_type_(end_type) {}
+	};
+
+	double group_delta_ = 0.0;
+	double abs_group_delta_ = 0.0;
+	double temp_lim_ = 0.0;
+	double steps_per_rad_ = 0.0;
+	PathD norms;
+	Paths64 solution;
+	std::vector<Group> groups_;
+	JoinType join_type_ = JoinType::Square;
+	
+	double miter_limit_ = 0.0;
+	double arc_tolerance_ = 0.0;
+	bool merge_groups_ = true;
+	bool preserve_collinear_ = false;
+	bool reverse_solution_ = false;
+
+	void DoSquare(Group& group, const Path64& path, size_t j, size_t k);
+	void DoMiter(Group& group, const Path64& path, size_t j, size_t k, double cos_a);
+	void DoRound(Group& group, const Path64& path, size_t j, size_t k, double angle);
+	void BuildNormals(const Path64& path);
+	void OffsetPolygon(Group& group, Path64& path);
+	void OffsetOpenJoined(Group& group, Path64& path);
+	void OffsetOpenPath(Group& group, Path64& path, EndType endType);
+	void OffsetPoint(Group& group, Path64& path, size_t j, size_t& k);
+	void DoGroupOffset(Group &group, double delta);
+public:
+	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(); };
+
+	void AddPath(const Path64& path, JoinType jt_, EndType et_);
+	void AddPaths(const Paths64& paths, JoinType jt_, EndType et_);
+	void AddPath(const PathD &p, JoinType jt_, EndType et_);
+	void AddPaths(const PathsD &p, JoinType jt_, EndType et_);
+	void Clear() { groups_.clear(); norms.clear(); };
+	
+	Paths64 Execute(double delta);
+
+	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; }
+
+	//MergeGroups: A path group is one or more paths added via the AddPath or
+	//AddPaths methods. By default these path groups will be offset
+	//independently of other groups and this may cause overlaps (intersections).
+	//However, when MergeGroups is enabled, any overlapping offsets will be
+	//merged (via a clipping union operation) to remove overlaps.
+	bool MergeGroups() const { return merge_groups_; }
+	void MergeGroups(bool merge_groups) { merge_groups_ = merge_groups; }
+
+	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;}
+};
+
+}
+#endif /* CLIPPER_OFFSET_H_ */

src/clipper2/Clipper2Lib/include/clipper2/clipper.rectclip.h

@@ -0,0 +1,50 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  26 October 2022                                                 *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2022                                         *
+* 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 "clipper.h"
+#include "clipper.core.h"
+
+namespace Clipper2Lib 
+{
+
+  enum class Location { Left, Top, Right, Bottom, Inside };
+
+  class RectClip {
+  protected:
+    const Rect64 rect_;
+    const Point64 mp_;
+    const Path64 rectPath_;
+    Path64 result_;
+    std::vector<Location> start_locs_;
+
+    void GetNextLocation(const Path64& path,
+      Location& loc, int& i, int highI);
+    void AddCorner(Location prev, Location curr);
+    void AddCorner(Location& loc, bool isClockwise);
+  public:
+    RectClip(const Rect64& rect) :
+      rect_(rect),
+      mp_(rect.MidPoint()),
+      rectPath_(rect.AsPath()) {}
+    Path64 Execute(const Path64& path);
+  };
+
+  class RectClipLines : public RectClip {
+  public:
+    RectClipLines(const Rect64& rect) : RectClip(rect) {};
+    Paths64 Execute(const Path64& path);
+  };
+
+} // Clipper2Lib namespace
+#endif  // CLIPPER_RECTCLIP_H

src/clipper2/Clipper2Lib/src/clipper.offset.cpp

@@ -0,0 +1,485 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  15 October 2022                                                 *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2022                                         *
+* 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
+//------------------------------------------------------------------------------
+
+Paths64::size_type GetLowestPolygonIdx(const Paths64& paths)
+{
+	Paths64::size_type result = 0;
+	Point64 lp = Point64(static_cast<int64_t>(0), 
+		std::numeric_limits<int64_t>::min());
+
+	for (Paths64::size_type i = 0 ; i < paths.size(); ++i)
+		for (const Point64& p : paths[i])
+		{ 
+			if (p.y < lp.y || (p.y == lp.y && p.x >= lp.x)) continue;
+			result = i;
+			lp = p;
+		}	
+	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)
+{
+	return Point64(pt.x + norm.x * delta, pt.y + norm.y * delta);
+}
+
+inline PointD GetPerpendicD(const Point64& pt, const PointD& norm, double delta)
+{
+	return PointD(pt.x + norm.x * delta, pt.y + norm.y * delta);
+}
+
+//------------------------------------------------------------------------------
+// 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::AddPath(const Clipper2Lib::PathD& path, JoinType jt_, EndType et_)
+{
+	PathsD paths;
+	paths.push_back(path);
+	AddPaths(paths, jt_, et_);
+}
+
+void ClipperOffset::AddPaths(const PathsD& paths, JoinType jt_, EndType et_)
+{
+	if (paths.size() == 0) return;
+	groups_.push_back(Group(PathsDToPaths64(paths), jt_, et_));
+}
+
+void ClipperOffset::BuildNormals(const Path64& path)
+{
+	norms.clear();
+	norms.reserve(path.size());
+	if (path.size() == 0) return;
+	Path64::const_iterator path_iter, path_last_iter = --path.cend();
+	for (path_iter = path.cbegin(); path_iter != path_last_iter; ++path_iter)
+		norms.push_back(GetUnitNormal(*path_iter,*(path_iter +1)));
+	norms.push_back(GetUnitNormal(*path_last_iter, *(path.cbegin())));
+}
+
+inline PointD TranslatePoint(const PointD& pt, double dx, double dy)
+{
+	return PointD(pt.x + dx, pt.y + dy);
+}
+
+inline PointD ReflectPoint(const PointD& pt, const PointD& pivot)
+{
+	return PointD(pivot.x + (pivot.x - pt.x), pivot.y + (pivot.y - pt.y));
+}
+
+PointD IntersectPoint(const PointD& pt1a, const PointD& pt1b,
+	const PointD& pt2a, const PointD& pt2b)
+{
+	if (pt1a.x == pt1b.x) //vertical
+	{
+		if (pt2a.x == pt2b.x) return PointD(0, 0);
+
+		double m2 = (pt2b.y - pt2a.y) / (pt2b.x - pt2a.x);
+		double b2 = pt2a.y - m2 * pt2a.x;
+		return PointD(pt1a.x, m2 * pt1a.x + b2);
+	}
+	else if (pt2a.x == pt2b.x) //vertical
+	{
+		double m1 = (pt1b.y - pt1a.y) / (pt1b.x - pt1a.x);
+		double b1 = pt1a.y - m1 * pt1a.x;
+		return PointD(pt2a.x, m1 * pt2a.x + b1);
+	}
+	else
+	{
+		double m1 = (pt1b.y - pt1a.y) / (pt1b.x - pt1a.x);
+		double b1 = pt1a.y - m1 * pt1a.x;
+		double m2 = (pt2b.y - pt2a.y) / (pt2b.x - pt2a.x);
+		double b2 = pt2a.y - m2 * pt2a.x;
+		if (m1 == m2) return PointD(0, 0);
+		double x = (b2 - b1) / (m1 - m2);
+		return PointD(x, m1 * x + b1);
+	}
+}
+
+void ClipperOffset::DoSquare(Group& group, const Path64& path, size_t j, size_t k)
+{
+	PointD vec;
+	if (j == k) 
+		vec = PointD(norms[0].y, -norms[0].x);
+	else
+		vec = GetAvgUnitVector(
+			PointD(-norms[k].y, norms[k].x),
+			PointD(norms[j].y, -norms[j].x));
+
+	// now offset the original vertex delta units along unit vector
+	PointD ptQ = PointD(path[j]);
+	ptQ = TranslatePoint(ptQ, abs_group_delta_ * vec.x, abs_group_delta_ * vec.y);
+	// get perpendicular vertices
+	PointD pt1 = TranslatePoint(ptQ, group_delta_ * vec.y, group_delta_ * -vec.x);
+	PointD pt2 = TranslatePoint(ptQ, group_delta_ * -vec.y, group_delta_ * vec.x);
+	// get 2 vertices along one edge offset
+	PointD pt3 = GetPerpendicD(path[k], norms[k], group_delta_);
+	if (j == k)
+	{
+		PointD pt4 = PointD(pt3.x + vec.x * group_delta_, pt3.y + vec.y * group_delta_);
+		PointD pt = IntersectPoint(pt1, pt2, pt3, pt4);
+		//get the second intersect point through reflecion
+		group.path_.push_back(Point64(ReflectPoint(pt, ptQ)));
+		group.path_.push_back(Point64(pt));
+	}
+	else
+	{
+		PointD pt4 = GetPerpendicD(path[j], norms[k], group_delta_);
+		PointD pt = IntersectPoint(pt1, pt2, pt3, pt4);
+		group.path_.push_back(Point64(pt));
+		//get the second intersect point through reflecion
+		group.path_.push_back(Point64(ReflectPoint(pt, ptQ)));
+	}
+}
+
+void ClipperOffset::DoMiter(Group& group, const Path64& path, size_t j, size_t k, double cos_a)
+{
+	double q = group_delta_ / (cos_a + 1);
+	group.path_.push_back(Point64(
+		path[j].x + (norms[k].x + norms[j].x) * q,
+		path[j].y + (norms[k].y + norms[j].y) * q));
+}
+
+void ClipperOffset::DoRound(Group& group, const Path64& path, size_t j, size_t k, double angle)
+{
+	//even though angle may be negative this is a convex join
+	Point64 pt = path[j];
+	int steps = static_cast<int>(std::ceil(steps_per_rad_ * std::abs(angle)));
+	double step_sin = std::sin(angle / steps);
+	double step_cos = std::cos(angle / steps);
+	
+	PointD pt2 = PointD(norms[k].x * group_delta_, norms[k].y * group_delta_);
+	if (j == k) pt2.Negate();
+
+	group.path_.push_back(Point64(pt.x + pt2.x, pt.y + pt2.y));
+	for (int i = 0; i < steps; i++)
+	{
+		pt2 = PointD(pt2.x * step_cos - step_sin * pt2.y,
+			pt2.x * step_sin + pt2.y * step_cos);
+		group.path_.push_back(Point64(pt.x + pt2.x, pt.y + pt2.y));
+	}
+	group.path_.push_back(GetPerpendic(path[j], norms[j], group_delta_));
+}
+
+void ClipperOffset::OffsetPoint(Group& group, Path64& path, size_t j, size_t& k)
+{
+	// Let A = change in angle where edges join
+	// A == 0: ie no change in angle (flat join)
+	// A == PI: edges 'spike'
+	// sin(A) < 0: right turning
+	// cos(A) < 0: change in angle is more than 90 degree
+
+	if (path[j] == path[k]) { k = j; return; }
+
+	double sin_a = CrossProduct(norms[j], norms[k]);
+	double cos_a = DotProduct(norms[j], norms[k]);
+	if (sin_a > 1.0) sin_a = 1.0;
+	else if (sin_a < -1.0) sin_a = -1.0;
+
+	bool almostNoAngle = AlmostZero(sin_a) && cos_a > 0;
+	// when there's almost no angle of deviation or it's concave
+	if (almostNoAngle || (sin_a * group_delta_ < 0))
+	{
+		Point64 p1 = Point64(
+			path[j].x + norms[k].x * group_delta_,
+			path[j].y + norms[k].y * group_delta_);
+		Point64 p2 = Point64(
+			path[j].x + norms[j].x * group_delta_,
+			path[j].y + norms[j].y * group_delta_);
+		group.path_.push_back(p1);
+		if (p1 != p2)
+		{
+			// when concave add an extra vertex to ensure neat clipping
+			if (!almostNoAngle) group.path_.push_back(path[j]);
+			group.path_.push_back(p2);
+		}
+	}
+	else // it's convex 
+	{
+		if (join_type_ == JoinType::Round)
+			DoRound(group, path, j, k, std::atan2(sin_a, cos_a));
+		else if (join_type_ == JoinType::Miter)
+		{
+			// miter unless the angle is so acute the miter would exceeds ML
+			if (cos_a > temp_lim_ - 1) DoMiter(group, path, j, k, cos_a);
+			else DoSquare(group, path, j, k);
+		}
+		// don't bother squaring angles that deviate < ~20 degrees because
+		// squaring will be indistinguishable from mitering and just be a lot slower
+		else if (cos_a > 0.9)
+			DoMiter(group, path, j, k, cos_a);			
+		else
+			DoSquare(group, path, j, k);			
+	}
+	k = j;
+}
+
+void ClipperOffset::OffsetPolygon(Group& group, Path64& path)
+{
+	group.path_.clear();
+	for (Path64::size_type i = 0, j = path.size() -1; i < path.size(); j = i, ++i)
+		OffsetPoint(group, path, i, j);
+	group.paths_out_.push_back(group.path_);
+}
+
+void ClipperOffset::OffsetOpenJoined(Group& group, Path64& path)
+{
+	OffsetPolygon(group, path);
+	std::reverse(path.begin(), path.end());
+	BuildNormals(path);
+	OffsetPolygon(group, path);
+}
+
+void ClipperOffset::OffsetOpenPath(Group& group, Path64& path, EndType end_type)
+{
+	group.path_.clear();
+
+	// do the line start cap
+	switch (end_type)
+	{
+	case EndType::Butt:
+		group.path_.push_back(Point64(
+			path[0].x - norms[0].x * group_delta_,
+			path[0].y - norms[0].y * group_delta_));
+		group.path_.push_back(GetPerpendic(path[0], norms[0], group_delta_));
+		break;
+	case EndType::Round:
+		DoRound(group, path, 0,0, PI);
+		break;
+	default:
+		DoSquare(group, path, 0, 0);
+		break;
+	}
+
+	size_t highI = path.size() - 1;
+
+	// offset the left side going forward
+	for (Path64::size_type i = 1, k = 0; i < highI; ++i)
+		OffsetPoint(group, path, i, k);
+
+	// reverse normals 
+	for (size_t i = highI; i > 0; --i)
+		norms[i] = PointD(-norms[i - 1].x, -norms[i - 1].y);
+	norms[0] = norms[highI];
+
+	// do the line end cap
+	switch (end_type)
+	{
+	case EndType::Butt:
+		group.path_.push_back(Point64(
+			path[highI].x - norms[highI].x * group_delta_,
+			path[highI].y - norms[highI].y * group_delta_));
+		group.path_.push_back(GetPerpendic(path[highI], norms[highI], group_delta_));
+		break;
+	case EndType::Round:
+		DoRound(group, path, highI, highI, PI);
+		break;
+	default:
+		DoSquare(group, path, highI, highI);
+		break;
+	}
+
+	for (size_t i = highI, k = 0; i > 0; --i)
+		OffsetPoint(group, path, i, k);
+	group.paths_out_.push_back(group.path_);
+}
+
+void ClipperOffset::DoGroupOffset(Group& group, double delta)
+{
+	if (group.end_type_ != EndType::Polygon) delta = std::abs(delta) * 0.5;
+	bool isClosedPaths = IsClosedPath(group.end_type_);
+
+	if (isClosedPaths)
+	{
+		//the lowermost polygon must be an outer polygon. So we can use that as the
+		//designated orientation for outer polygons (needed for tidy-up clipping)
+		Paths64::size_type lowestIdx = GetLowestPolygonIdx(group.paths_in_);
+    // nb: don't use the default orientation here ...
+		double area = Area(group.paths_in_[lowestIdx]);
+		if (area == 0) return;	
+		group.is_reversed_ = (area < 0);
+		if (group.is_reversed_) delta = -delta;
+	} 
+	else
+		group.is_reversed_ = false;
+
+	group_delta_ = delta;
+	abs_group_delta_ = std::abs(group_delta_);
+	join_type_ = group.join_type_;
+
+	double arcTol = (arc_tolerance_ > floating_point_tolerance ? arc_tolerance_
+		: std::log10(2 + abs_group_delta_) * default_arc_tolerance); // empirically derived
+
+//calculate a sensible number of steps (for 360 deg for the given offset
+	if (group.join_type_ == JoinType::Round || group.end_type_ == EndType::Round)
+	{
+		steps_per_rad_ = PI / std::acos(1 - arcTol / abs_group_delta_) / (PI *2);
+	}
+
+	bool is_closed_path = IsClosedPath(group.end_type_);
+	Paths64::const_iterator path_iter;
+	for(path_iter = group.paths_in_.cbegin(); path_iter != group.paths_in_.cend(); ++path_iter)
+	{
+		Path64 path = StripDuplicates(*path_iter, is_closed_path);
+		Path64::size_type cnt = path.size();
+		if (cnt == 0) continue;
+
+		if (cnt == 1) // single point - only valid with open paths
+		{
+			group.path_ = Path64();
+			//single vertex so build a circle or square ...
+			if (group.join_type_ == JoinType::Round)
+			{
+				double radius = abs_group_delta_;
+				group.path_ = Ellipse(path[0], radius, radius);
+			}
+			else
+			{
+				int d = (int)std::ceil(abs_group_delta_);
+				Rect64 r = Rect64(path[0].x - d, path[0].y - d, path[0].x + d, path[0].y + d);
+				group.path_ = r.AsPath();
+			}
+			group.paths_out_.push_back(group.path_);
+		}
+		else
+		{
+			BuildNormals(path);
+			if (group.end_type_ == EndType::Polygon) OffsetPolygon(group, path);
+			else if (group.end_type_ == EndType::Joined) OffsetOpenJoined(group, path);
+			else OffsetOpenPath(group, path, group.end_type_);
+		}
+	}
+
+	if (!merge_groups_)
+	{
+		//clean up self-intersections ...
+		Clipper64 c;
+		c.PreserveCollinear = false;
+		//the solution should retain the orientation of the input
+		c.ReverseSolution = reverse_solution_ != group.is_reversed_;
+		c.AddSubject(group.paths_out_);
+		if (group.is_reversed_)
+			c.Execute(ClipType::Union, FillRule::Negative, group.paths_out_);
+		else
+			c.Execute(ClipType::Union, FillRule::Positive, group.paths_out_);
+	}
+
+	solution.reserve(solution.size() + group.paths_out_.size());
+	copy(group.paths_out_.begin(), group.paths_out_.end(), back_inserter(solution));
+	group.paths_out_.clear();
+}
+
+Paths64 ClipperOffset::Execute(double delta)
+{
+	solution.clear();
+	if (std::abs(delta) < default_arc_tolerance)
+	{
+		for (const Group& group : groups_)
+		{
+			solution.reserve(solution.size() + group.paths_in_.size());
+			copy(group.paths_in_.begin(), group.paths_in_.end(), back_inserter(solution));
+		}
+		return solution;
+	}
+
+	temp_lim_ = (miter_limit_ <= 1) ? 
+		2.0 : 
+		2.0 / (miter_limit_ * miter_limit_);
+
+	std::vector<Group>::iterator groups_iter;
+	for (groups_iter = groups_.begin(); 
+		groups_iter != groups_.end(); ++groups_iter)
+	{
+		DoGroupOffset(*groups_iter, delta);
+	}
+
+	if (merge_groups_ && groups_.size() > 0)
+	{
+		//clean up self-intersections ...
+		Clipper64 c;
+		c.PreserveCollinear = false;
+		//the solution should retain the orientation of the input
+		c.ReverseSolution = reverse_solution_ != groups_[0].is_reversed_;
+
+		c.AddSubject(solution);
+		if (groups_[0].is_reversed_)
+			c.Execute(ClipType::Union, FillRule::Negative, solution);
+		else
+			c.Execute(ClipType::Union, FillRule::Positive, solution);
+	}
+	return solution;
+}
+
+} // namespace

src/clipper2/Clipper2Lib/src/clipper.rectclip.cpp

@@ -0,0 +1,547 @@
+/*******************************************************************************
+* Author    :  Angus Johnson                                                   *
+* Date      :  26 October 2022                                                 *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2022                                         *
+* Purpose   :  FAST rectangular clipping                                       *
+* License   :  http://www.boost.org/LICENSE_1_0.txt                            *
+*******************************************************************************/
+
+#include <cmath>
+#include "clipper2/clipper.h"
+#include "clipper2/clipper.rectclip.h"
+
+namespace Clipper2Lib {
+
+  //------------------------------------------------------------------------------
+  // Miscellaneous methods
+  //------------------------------------------------------------------------------
+
+  inline PointInPolygonResult Path1ContainsPath2(Path64 path1, Path64 path2)
+  {
+    PointInPolygonResult result = PointInPolygonResult::IsOn;
+    for(const Point64& pt : path2)
+    {
+      result = PointInPolygon(pt, path1);
+      if (result != PointInPolygonResult::IsOn) break;
+    }
+    return result;
+  }
+
+  inline bool GetLocation(const Rect64& rec,
+    const Point64& pt, Location& loc)
+  {
+    if (pt.x == rec.left && pt.y >= rec.top && pt.y <= rec.bottom)
+    {
+      loc = Location::Left;
+      return false;
+    }
+    else if (pt.x == rec.right && pt.y >= rec.top && pt.y <= rec.bottom)
+    {
+      loc = Location::Right;
+      return false;
+    }
+    else if (pt.y == rec.top && pt.x >= rec.left && pt.x <= rec.right)
+    {
+      loc = Location::Top;
+      return false;
+    }
+    else if (pt.y == rec.bottom && pt.x >= rec.left && pt.x <= rec.right)
+    {
+      loc = Location::Bottom;
+      return false;
+    }
+    else if (pt.x < rec.left) loc = Location::Left;
+    else if (pt.x > rec.right) loc = Location::Right;
+    else if (pt.y < rec.top) loc = Location::Top;
+    else if (pt.y > rec.bottom) loc = Location::Bottom;
+    else loc = Location::Inside;
+    return true;
+  }
+
+  Point64 GetIntersectPoint64(const Point64& ln1a, const Point64& ln1b,
+    const Point64& ln2a, const Point64& ln2b)
+  {
+    // see http://astronomy.swin.edu.au/~pbourke/geometry/lineline2d/
+    if (ln1b.x == ln1a.x) 
+    {
+      if (ln2b.x == ln2a.x) return Point64(); // parallel lines
+      double m2 = static_cast<double>(ln2b.y - ln2a.y) / (ln2b.x - ln2a.x);
+      double b2 = ln2a.y - m2 * ln2a.x;
+      return Point64(ln1a.x, static_cast<int64_t>(std::round(m2 * ln1a.x + b2)));
+    }
+    else if (ln2b.x == ln2a.x)
+    {
+      double m1  = static_cast<double>(ln1b.y - ln1a.y) / (ln1b.x - ln1a.x);
+      double b1 = ln1a.y - m1 * ln1a.x;
+      return Point64(ln2a.x, static_cast<int64_t>(std::round(m1 * ln2a.x + b1)));
+    }
+    else
+    {
+      double m1 = static_cast<double>(ln1b.y - ln1a.y) / (ln1b.x - ln1a.x);
+      double b1 = ln1a.y - m1 * ln1a.x;
+      double m2 = static_cast<double>(ln2b.y - ln2a.y) / (ln2b.x - ln2a.x);
+      double b2 = ln2a.y - m2 * ln2a.x;
+      if (std::fabs(m1 - m2) > 1.0E-15)
+      {
+        double x = (b2 - b1) / (m1 - m2);
+        return Point64(x, m1 * x + b1);
+      }
+      else
+        return Point64((ln1a.x + ln1b.x) * 0.5, (ln1a.y + ln1b.y) * 0.5);
+    }
+  }
+
+  inline bool GetIntersection(const Path64& rectPath,
+    const Point64& p, const Point64& p2, Location& loc, Point64& ip)
+  {
+    // gets the intersection closest to 'p'
+    // when Result = false, loc will remain unchanged
+    switch (loc)
+    {
+    case Location::Left:
+      if (SegmentsIntersect(p, p2, rectPath[0], rectPath[3], true))
+        ip = GetIntersectPoint64(p, p2, rectPath[0], rectPath[3]);
+      else if (p.y < rectPath[0].y &&
+        SegmentsIntersect(p, p2, rectPath[0], rectPath[1], true))
+      {
+        ip = GetIntersectPoint64(p, p2, rectPath[0], rectPath[1]);
+        loc = Location::Top;
+      }
+      else if (SegmentsIntersect(p, p2, rectPath[2], rectPath[3], true))
+      {
+        ip = GetIntersectPoint64(p, p2, rectPath[2], rectPath[3]);
+        loc = Location::Bottom;
+      }
+      else return false;
+      break;
+
+    case Location::Top:
+      if (SegmentsIntersect(p, p2, rectPath[0], rectPath[1], true))
+        ip = GetIntersectPoint64(p, p2, rectPath[0], rectPath[1]);
+      else if (p.x < rectPath[0].x &&
+        SegmentsIntersect(p, p2, rectPath[0], rectPath[3], true))
+      {
+        ip = GetIntersectPoint64(p, p2, rectPath[0], rectPath[3]);
+        loc = Location::Left;
+      }
+      else if (p.x > rectPath[1].x &&
+        SegmentsIntersect(p, p2, rectPath[1], rectPath[2], true))
+      {
+        ip = GetIntersectPoint64(p, p2, rectPath[1], rectPath[2]);
+        loc = Location::Right;
+      }
+      else return false;
+        break;
+
+    case Location::Right:
+      if (SegmentsIntersect(p, p2, rectPath[1], rectPath[2], true))
+        ip = GetIntersectPoint64(p, p2, rectPath[1], rectPath[2]);
+      else if (p.y < rectPath[0].y &&
+        SegmentsIntersect(p, p2, rectPath[0], rectPath[1], true))
+      {
+        ip = GetIntersectPoint64(p, p2, rectPath[0], rectPath[1]);
+        loc = Location::Top;
+      }
+      else if (SegmentsIntersect(p, p2, rectPath[2], rectPath[3], true))
+      {
+        ip = GetIntersectPoint64(p, p2, rectPath[2], rectPath[3]);
+        loc = Location::Bottom;
+      }
+      else return false;
+      break;
+
+    case Location::Bottom:
+      if (SegmentsIntersect(p, p2, rectPath[2], rectPath[3], true))
+        ip = GetIntersectPoint64(p, p2, rectPath[2], rectPath[3]);
+      else if (p.x < rectPath[3].x &&
+        SegmentsIntersect(p, p2, rectPath[0], rectPath[3], true))
+      {
+        ip = GetIntersectPoint64(p, p2, rectPath[0], rectPath[3]);
+        loc = Location::Left;
+      }
+      else if (p.x > rectPath[2].x &&
+        SegmentsIntersect(p, p2, rectPath[1], rectPath[2], true))
+      {
+        ip = GetIntersectPoint64(p, p2, rectPath[1], rectPath[2]);
+        loc = Location::Right;
+      }
+      else return false;
+      break;
+
+    default: // loc == rInside
+      if (SegmentsIntersect(p, p2, rectPath[0], rectPath[3], true))
+      {
+        ip = GetIntersectPoint64(p, p2, rectPath[0], rectPath[3]);
+        loc = Location::Left;
+      }
+      else if (SegmentsIntersect(p, p2, rectPath[0], rectPath[1], true))
+      {
+        ip = GetIntersectPoint64(p, p2, rectPath[0], rectPath[1]);
+        loc = Location::Top;
+      }
+      else if (SegmentsIntersect(p, p2, rectPath[1], rectPath[2], true))
+      {
+        ip = GetIntersectPoint64(p, p2, rectPath[1], rectPath[2]);
+        loc = Location::Right;
+      }
+      else if (SegmentsIntersect(p, p2, rectPath[2], rectPath[3], true))
+      {
+        ip = GetIntersectPoint64(p, p2, rectPath[2], rectPath[3]);
+        loc = Location::Bottom;
+      }
+      else return false;
+      break;
+    }
+
+    return true;
+  }
+
+  inline Location GetAdjacentLocation(Location loc, bool isClockwise)
+  {
+    int delta = (isClockwise) ? 1 : 3;
+    return static_cast<Location>((static_cast<int>(loc) + delta) % 4);
+  }
+
+  inline bool HeadingClockwise(Location prev, Location curr)
+  {
+    return (static_cast<int>(prev) + 1) % 4 == static_cast<int>(curr);
+  }
+
+  inline bool AreOpposites(Location prev, Location curr)
+  {
+    return abs(static_cast<int>(prev) - static_cast<int>(curr)) == 2;
+  }
+
+  inline bool IsClockwise(Location prev, Location curr,
+    Point64 prev_pt, Point64 curr_pt, Point64 rect_mp)
+  {
+    if (AreOpposites(prev, curr))
+      return CrossProduct(prev_pt, rect_mp, curr_pt) < 0;
+    else
+      return HeadingClockwise(prev, curr);
+  }
+
+  //----------------------------------------------------------------------------
+  // RectClip64
+  //----------------------------------------------------------------------------
+
+  void RectClip::AddCorner(Location prev, Location curr)
+  {
+    if (HeadingClockwise(prev, curr))
+      result_.push_back(rectPath_[static_cast<int>(prev)]);
+    else
+      result_.push_back(rectPath_[static_cast<int>(curr)]);
+  }
+
+  void RectClip::AddCorner(Location& loc, bool isClockwise)
+  {
+    if (isClockwise)
+    {
+      result_.push_back(rectPath_[static_cast<int>(loc)]);
+      loc = GetAdjacentLocation(loc, true);
+    }
+    else
+    {
+      loc = GetAdjacentLocation(loc, false);
+      result_.push_back(rectPath_[static_cast<int>(loc)]);
+    }
+  }
+
+  void RectClip::GetNextLocation(const Path64& path,
+      Location& loc, int& i, int highI)
+  {
+    switch (loc)
+    {
+    case Location::Left:
+      while (i <= highI && path[i].x <= rect_.left) ++i;
+      if (i > highI) break;
+      else if (path[i].x >= rect_.right) loc = Location::Right;
+      else if (path[i].y <= rect_.top) loc = Location::Top;
+      else if (path[i].y >= rect_.bottom) loc = Location::Bottom;
+      else loc = Location::Inside;
+      break;
+
+    case Location::Top:
+      while (i <= highI && path[i].y <= rect_.top) ++i;
+      if (i > highI) break;
+      else if (path[i].y >= rect_.bottom) loc = Location::Bottom;
+      else if (path[i].x <= rect_.left) loc = Location::Left;
+      else if (path[i].x >= rect_.right) loc = Location::Right;
+      else loc = Location::Inside;
+      break;
+
+    case Location::Right:
+      while (i <= highI && path[i].x >= rect_.right) ++i;
+      if (i > highI) break;
+      else if (path[i].x <= rect_.left) loc = Location::Left;
+      else if (path[i].y <= rect_.top) loc = Location::Top;
+      else if (path[i].y >= rect_.bottom) loc = Location::Bottom;
+      else loc = Location::Inside;
+      break;
+
+    case Location::Bottom:
+      while (i <= highI && path[i].y >= rect_.bottom) ++i;
+      if (i > highI) break;
+      else if (path[i].y <= rect_.top) loc = Location::Top;
+      else if (path[i].x <= rect_.left) loc = Location::Left;
+      else if (path[i].x >= rect_.right) loc = Location::Right;
+      else loc = Location::Inside;
+      break;
+
+    case Location::Inside:
+      while (i <= highI)
+      {
+        if (path[i].x < rect_.left) loc = Location::Left;
+        else if (path[i].x > rect_.right) loc = Location::Right;
+        else if (path[i].y > rect_.bottom) loc = Location::Bottom;
+        else if (path[i].y < rect_.top) loc = Location::Top;
+        else { result_.push_back(path[i]); ++i; continue; }
+        break; //inner loop
+      }
+      break;
+    } //switch          
+  }
+
+  Path64 RectClip::Execute(const Path64& path)
+  {
+    if (rect_.IsEmpty() || path.size() < 3) return Path64();
+
+    result_.clear();
+    start_locs_.clear();
+    int i = 0, highI = static_cast<int>(path.size()) - 1;
+    Location prev = Location::Inside, loc;
+    Location crossing_loc = Location::Inside;
+    Location first_cross_ = Location::Inside;
+    if (!GetLocation(rect_, path[highI], loc))
+    {
+      i = highI - 1;
+      while (i >= 0 && !GetLocation(rect_, path[i], prev)) --i;
+      if (i < 0) return path;
+      if (prev == Location::Inside) loc = Location::Inside;
+      i = 0;
+    }
+    Location starting_loc = loc;
+
+    ///////////////////////////////////////////////////
+    while (i <= highI)
+    {
+      prev = loc;
+      Location crossing_prev = crossing_loc;
+
+      GetNextLocation(path, loc, i, highI);
+
+      if (i > highI) break;
+      Point64 ip, ip2;
+      Point64 prev_pt = (i) ? path[static_cast<size_t>(i - 1)] : path[highI];
+
+      crossing_loc = loc;
+      if (!GetIntersection(rectPath_, path[i], prev_pt, crossing_loc, ip))
+      {
+        // ie remaining outside
+
+        if (crossing_prev == Location::Inside)
+        {
+          bool isClockw = IsClockwise(prev, loc, prev_pt, path[i], mp_);
+          do {
+            start_locs_.push_back(prev);
+            prev = GetAdjacentLocation(prev, isClockw);
+          } while (prev != loc);
+          crossing_loc = crossing_prev; // still not crossed 
+        }
+        else if (prev != Location::Inside && prev != loc)
+        {
+          bool isClockw = IsClockwise(prev, loc, prev_pt, path[i], mp_);
+          do {
+            AddCorner(prev, isClockw);
+          } while (prev != loc);
+        }
+        ++i;
+        continue;
+      }
+
+      ////////////////////////////////////////////////////
+      // we must be crossing the rect boundary to get here
+      ////////////////////////////////////////////////////
+
+      if (loc == Location::Inside) // path must be entering rect
+      {
+        if (first_cross_ == Location::Inside)
+        {
+          first_cross_ = crossing_loc;
+          start_locs_.push_back(prev);
+        }
+        else if (prev != crossing_loc)
+        {
+          bool isClockw = IsClockwise(prev, crossing_loc, prev_pt, path[i], mp_);
+          do {
+            AddCorner(prev, isClockw);
+          } while (prev != crossing_loc);
+        }
+      }
+      else if (prev != Location::Inside)
+      {
+        // passing right through rect. 'ip' here will be the second 
+        // intersect pt but we'll also need the first intersect pt (ip2)
+        loc = prev;
+        GetIntersection(rectPath_, prev_pt, path[i], loc, ip2);
+        if (crossing_prev != Location::Inside)
+          AddCorner(crossing_prev, loc);
+
+        if (first_cross_ == Location::Inside)
+        {
+          first_cross_ = loc;
+          start_locs_.push_back(prev);
+        }
+
+        loc = crossing_loc;
+        result_.push_back(ip2);
+        if (ip == ip2)
+        {
+          // it's very likely that path[i] is on rect
+          GetLocation(rect_, path[i], loc);
+          AddCorner(crossing_loc, loc);
+          crossing_loc = loc;
+          continue;
+        }
+      }
+      else // path must be exiting rect
+      {
+        loc = crossing_loc;
+        if (first_cross_ == Location::Inside)
+          first_cross_ = crossing_loc;
+      }
+
+      result_.push_back(ip);
+
+    } //while i <= highI
+    ///////////////////////////////////////////////////
+
+    if (first_cross_ == Location::Inside)
+    {
+      if (starting_loc == Location::Inside) return path;
+      Rect64 tmp_rect = Bounds(path);
+      if (tmp_rect.Contains(rect_) &&
+        Path1ContainsPath2(path, rectPath_) !=
+        PointInPolygonResult::IsOutside) return rectPath_;
+      else
+        return Path64();
+    }
+
+    if (loc != Location::Inside &&
+      (loc != first_cross_ || start_locs_.size() > 2))
+    {
+      if (start_locs_.size() > 0)
+      {
+        prev = loc;
+        for (auto loc2 : start_locs_)
+        {
+          if (prev == loc2) continue;
+          AddCorner(prev, HeadingClockwise(prev, loc2));
+          prev = loc2;
+        }
+        loc = prev;
+      }
+      if (loc != first_cross_)
+        AddCorner(loc, HeadingClockwise(loc, first_cross_));
+    }
+
+    if (result_.size() < 3) return Path64();
+
+    // tidy up duplicates and collinear segments
+    Path64 res;
+    res.reserve(result_.size());
+    size_t k = 0; highI = static_cast<int>(result_.size()) - 1;
+    Point64 prev_pt = result_[highI];
+    res.push_back(result_[0]);
+    Path64::const_iterator cit;
+    for (cit = result_.cbegin() + 1; cit != result_.cend(); ++cit)
+    {
+      if (CrossProduct(prev_pt, res[k], *cit))
+      {
+        prev_pt = res[k++];
+        res.push_back(*cit);
+      }
+      else
+        res[k] = *cit;
+    }
+
+    if (k < 2) return Path64();
+    // and a final check for collinearity
+    else if (!CrossProduct(res[0], res[k - 1], res[k])) res.pop_back();
+    return res;
+  }
+
+  Paths64 RectClipLines::Execute(const Path64& path)
+  {
+    result_.clear();
+    Paths64 result;
+    if (rect_.IsEmpty() || path.size() == 0) return result;
+
+    int i = 1, highI = static_cast<int>(path.size()) - 1;
+
+    Location prev = Location::Inside, loc;
+    Location crossing_loc = Location::Inside;
+    if (!GetLocation(rect_, path[0], loc))
+    {
+      while (i <= highI && !GetLocation(rect_, path[i], prev)) ++i;
+      if (i > highI) {
+        result.push_back(path);
+        return result;
+      }
+      if (prev == Location::Inside) loc = Location::Inside;
+      i = 1;
+    }
+    if (loc == Location::Inside) result_.push_back(path[0]);
+
+    ///////////////////////////////////////////////////
+    while (i <= highI)
+    {
+      prev = loc;
+      GetNextLocation(path, loc, i, highI);
+      if (i > highI) break;
+      Point64 ip, ip2;
+      Point64 prev_pt = path[static_cast<size_t>(i - 1)];
+
+      crossing_loc = loc;
+      if (!GetIntersection(rectPath_, path[i], prev_pt, crossing_loc, ip))
+      {
+        // ie remaining outside
+        ++i;
+        continue;
+      }
+
+      ////////////////////////////////////////////////////
+      // we must be crossing the rect boundary to get here
+      ////////////////////////////////////////////////////
+
+      if (loc == Location::Inside) // path must be entering rect
+      {
+        result_.push_back(ip);
+      }
+      else if (prev != Location::Inside)
+      {
+        // passing right through rect. 'ip' here will be the second 
+        // intersect pt but we'll also need the first intersect pt (ip2)
+        crossing_loc = prev;
+        GetIntersection(rectPath_, prev_pt, path[i], crossing_loc, ip2);
+        result_.push_back(ip2);
+        result_.push_back(ip);
+        result.push_back(result_);
+        result_.clear();
+      }
+      else // path must be exiting rect
+      {
+        result_.push_back(ip);
+        result.push_back(result_);
+        result_.clear();
+      }
+    } //while i <= highI
+    ///////////////////////////////////////////////////
+
+    if (result_.size() > 1)
+      result.push_back(result_);
+    return result;
+  }
+
+} // namespace