clipper.offset.cpp

/*******************************************************************************
* Author    :  Angus Johnson                                                   *
* Date      :  4 May 2025                                                      *
* Website   :  https://www.angusj.com                                          *
* Copyright :  Angus Johnson 2010-2025                                         *
* Purpose   :  Path Offset (Inflate/Shrink)                                    *
* License   :  https://www.boost.org/LICENSE_1_0.txt                           *
*******************************************************************************/

#include "clipper2/clipper.h"
#include "clipper2/clipper.offset.h"

namespace Clipper2Lib {

const double floating_point_tolerance = 1e-12;

// Clipper2 approximates arcs by using series of relatively short straight
//line segments. And logically, shorter line segments will produce better arc
// approximations. But very short segments can degrade performance, usually
// with little or no discernable improvement in curve quality. Very short
// segments can even detract from curve quality, due to the effects of integer
// rounding. Since there isn't an optimal number of line segments for any given
// arc radius (that perfectly balances curve approximation with performance),
// arc tolerance is user defined. Nevertheless, when the user doesn't define
// an arc tolerance (ie leaves alone the 0 default value), the calculated
// default arc tolerance (offset_radius / 500) generally produces good (smooth)
// arc approximations without producing excessively small segment lengths.
// See also: https://www.angusj.com/clipper2/Docs/Trigonometry.htm
const double arc_const = 0.002; // <-- 1/500


//------------------------------------------------------------------------------
// Miscellaneous methods
//------------------------------------------------------------------------------

void GetLowestClosedPathInfo(const Paths64& paths, std::optional<size_t>& idx, bool& is_neg_area)
{
	idx.reset();
	Point64 botPt = Point64(INT64_MAX, INT64_MIN);
	for (size_t i = 0; i < paths.size(); ++i)
	{
		double a = MAX_DBL;
		for (const Point64& pt : paths[i])
		{
			if ((pt.y < botPt.y) ||
				((pt.y == botPt.y) && (pt.x >= botPt.x))) continue;
			if (a == MAX_DBL) 
			{
				a = Area(paths[i]);
				if (a == 0) break; // invalid closed path, so break from inner loop
				is_neg_area = a < 0;
			}
      idx = i;
			botPt.x = pt.x;
			botPt.y = pt.y;
		}
	}
}

inline double Hypot(double x, double y)
{
	// given that this is an internal function, and given the x and y parameters
	// will always be coordinate values (or the difference between coordinate values),
	// x and y should always be within INT64_MIN to INT64_MAX. Consequently, 
	// there should be no risk that the following computation will overflow
	// see https://stackoverflow.com/a/32436148/359538
	return std::sqrt(x * x + y * y);
}

static PointD GetUnitNormal(const Point64& pt1, const Point64& pt2)
{
	if (pt1 == pt2) return PointD(0.0, 0.0);
	double dx = static_cast<double>(pt2.x - pt1.x);
	double dy = static_cast<double>(pt2.y - pt1.y);
	double 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 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;
}

static inline Point64 GetPerpendic(const Point64& pt, const PointD& norm, double delta)
{
#ifdef USINGZ
	return Point64(pt.x + norm.x * delta, pt.y + norm.y * delta, pt.z);
#else
	return Point64(pt.x + norm.x * delta, pt.y + norm.y * delta);
#endif
}

inline PointD GetPerpendicD(const Point64& pt, const PointD& norm, double delta)
{
#ifdef USINGZ
	return PointD(pt.x + norm.x * delta, pt.y + norm.y * delta, pt.z);
#else
	return PointD(pt.x + norm.x * delta, pt.y + norm.y * delta);
#endif
}

inline void NegatePath(PathD& path)
{
	for (PointD& pt : path)
	{
		pt.x = -pt.x;
		pt.y = -pt.y;
#ifdef USINGZ
		pt.z = pt.z;
#endif
	}
}


//------------------------------------------------------------------------------
// ClipperOffset::Group methods
//------------------------------------------------------------------------------

ClipperOffset::Group::Group(const Paths64& _paths, JoinType _join_type, EndType _end_type):
	paths_in(_paths), join_type(_join_type), end_type(_end_type)
{
	bool is_joined =
		(end_type == EndType::Polygon) ||
		(end_type == EndType::Joined);
	for (Path64& p: paths_in)
	  StripDuplicates(p, is_joined);

	if (end_type == EndType::Polygon)
	{
		bool is_neg_area;
		GetLowestClosedPathInfo(paths_in, lowest_path_idx, is_neg_area);
		// the lowermost path must be an outer path, so if its orientation is negative,
		// then flag the whole group is 'reversed' (will negate delta etc.)
		// as this is much more efficient than reversing every path.
    is_reversed = lowest_path_idx.has_value() && is_neg_area;
	}
	else
	{
    lowest_path_idx.reset();
		is_reversed = false;
	}
}

//------------------------------------------------------------------------------
// ClipperOffset methods
//------------------------------------------------------------------------------

void ClipperOffset::AddPath(const Path64& path, JoinType jt_, EndType et_)
{
    groups_.emplace_back(Paths64(1, path), jt_, et_);
}

void ClipperOffset::AddPaths(const Paths64 &paths, JoinType jt_, EndType et_)
{
	if (paths.size() == 0) return;
    groups_.emplace_back(paths, jt_, et_);
}

void ClipperOffset::BuildNormals(const Path64& path)
{
	norms.clear();
	norms.reserve(path.size());
	if (path.size() == 0) return;
	Path64::const_iterator path_iter, path_stop_iter = --path.cend();
	for (path_iter = path.cbegin(); path_iter != path_stop_iter; ++path_iter)
        norms.emplace_back(GetUnitNormal(*path_iter,*(path_iter +1)));
    norms.emplace_back(GetUnitNormal(*path_stop_iter, *(path.cbegin())));
}

void ClipperOffset::DoBevel(const Path64& path, size_t j, size_t k)
{
	PointD pt1, pt2;
	if (j == k)
	{
		double abs_delta = std::abs(group_delta_);
#ifdef USINGZ
		pt1 = PointD(path[j].x - abs_delta * norms[j].x, path[j].y - abs_delta * norms[j].y, path[j].z);
		pt2 = PointD(path[j].x + abs_delta * norms[j].x, path[j].y + abs_delta * norms[j].y, path[j].z);
#else
		pt1 = PointD(path[j].x - abs_delta * norms[j].x, path[j].y - abs_delta * norms[j].y);
		pt2 = PointD(path[j].x + abs_delta * norms[j].x, path[j].y + abs_delta * norms[j].y);
#endif
	}
	else
	{
#ifdef USINGZ
		pt1 = PointD(path[j].x + group_delta_ * norms[k].x, path[j].y + group_delta_ * norms[k].y, path[j].z);
		pt2 = PointD(path[j].x + group_delta_ * norms[j].x, path[j].y + group_delta_ * norms[j].y, path[j].z);
#else
		pt1 = PointD(path[j].x + group_delta_ * norms[k].x, path[j].y + group_delta_ * norms[k].y);
		pt2 = PointD(path[j].x + group_delta_ * norms[j].x, path[j].y + group_delta_ * norms[j].y);
#endif
	}
    path_out.emplace_back(pt1);
    path_out.emplace_back(pt2);
}

void ClipperOffset::DoSquare(const Path64& path, size_t j, size_t k)
{
	PointD vec;
	if (j == k)
		vec = PointD(norms[j].y, -norms[j].x);
	else
		vec = GetAvgUnitVector(
			PointD(-norms[k].y, norms[k].x),
			PointD(norms[j].y, -norms[j].x));

	double abs_delta = std::abs(group_delta_);

	// now offset the original vertex delta units along unit vector
	PointD ptQ = PointD(path[j]);
	ptQ = TranslatePoint(ptQ, abs_delta * vec.x, abs_delta * vec.y);
	// get perpendicular vertices
	PointD pt1 = TranslatePoint(ptQ, group_delta_ * vec.y, group_delta_ * -vec.x);
	PointD pt2 = TranslatePoint(ptQ, group_delta_ * -vec.y, group_delta_ * vec.x);
	// get 2 vertices along one edge offset
	PointD pt3 = GetPerpendicD(path[k], norms[k], group_delta_);
	if (j == k)
	{
		PointD pt4 = PointD(pt3.x + vec.x * group_delta_, pt3.y + vec.y * group_delta_);
		PointD pt = ptQ;
		GetSegmentIntersectPt(pt1, pt2, pt3, pt4, pt);
		//get the second intersect point through reflecion
        path_out.emplace_back(ReflectPoint(pt, ptQ));
        path_out.emplace_back(pt);
	}
	else
	{
		PointD pt4 = GetPerpendicD(path[j], norms[k], group_delta_);
		PointD pt = ptQ;
		GetSegmentIntersectPt(pt1, pt2, pt3, pt4, pt);
        path_out.emplace_back(pt);
		//get the second intersect point through reflecion
        path_out.emplace_back(ReflectPoint(pt, ptQ));
	}
}

void ClipperOffset::DoMiter(const Path64& path, size_t j, size_t k, double cos_a)
{
	double q = group_delta_ / (cos_a + 1);
#ifdef USINGZ
    path_out.emplace_back(
		path[j].x + (norms[k].x + norms[j].x) * q,
		path[j].y + (norms[k].y + norms[j].y) * q,
        path[j].z);
#else
    path_out.emplace_back(
		path[j].x + (norms[k].x + norms[j].x) * q,
        path[j].y + (norms[k].y + norms[j].y) * q);
#endif
}

void ClipperOffset::DoRound(const Path64& path, size_t j, size_t k, double angle)
{
	if (deltaCallback64_) {
		// when deltaCallback64_ is assigned, group_delta_ won't be constant,
		// so we'll need to do the following calculations for *every* vertex.
		double abs_delta = std::fabs(group_delta_);
		double arcTol = (arc_tolerance_ > floating_point_tolerance ?
			std::min(abs_delta, arc_tolerance_) : abs_delta * arc_const);
		double steps_per_360 = std::min(PI / std::acos(1 - arcTol / abs_delta), abs_delta * PI);
		step_sin_ = std::sin(2 * PI / steps_per_360);
		step_cos_ = std::cos(2 * PI / steps_per_360);
		if (group_delta_ < 0.0) step_sin_ = -step_sin_;
		steps_per_rad_ = steps_per_360 / (2 * PI);
	}

	Point64 pt = path[j];
	PointD offsetVec = PointD(norms[k].x * group_delta_, norms[k].y * group_delta_);

	if (j == k) offsetVec.Negate();
#ifdef USINGZ
    path_out.emplace_back(pt.x + offsetVec.x, pt.y + offsetVec.y, pt.z);
#else
    path_out.emplace_back(pt.x + offsetVec.x, pt.y + offsetVec.y);
#endif
	int steps = static_cast<int>(std::ceil(steps_per_rad_ * std::abs(angle))); // #448, #456
	for (int i = 1; i < steps; ++i) // ie 1 less than steps
	{
		offsetVec = PointD(offsetVec.x * step_cos_ - step_sin_ * offsetVec.y,
			offsetVec.x * step_sin_ + offsetVec.y * step_cos_);
#ifdef USINGZ
        path_out.emplace_back(pt.x + offsetVec.x, pt.y + offsetVec.y, pt.z);
#else
        path_out.emplace_back(pt.x + offsetVec.x, pt.y + offsetVec.y);
#endif
	}
    path_out.emplace_back(GetPerpendic(path[j], norms[j], group_delta_));
}

void ClipperOffset::OffsetPoint(Group& group, const Path64& path, size_t j, size_t k)
{
	// Let A = change in angle where edges join
	// A == 0: ie no change in angle (flat join)
	// A == PI: edges 'spike'
	// sin(A) < 0: right turning
	// cos(A) < 0: change in angle is more than 90 degree

	if (path[j] == path[k]) return;

	double sin_a = CrossProduct(norms[j], norms[k]);
	double cos_a = DotProduct(norms[j], norms[k]);
	if (sin_a > 1.0) sin_a = 1.0;
	else if (sin_a < -1.0) sin_a = -1.0;

	if (deltaCallback64_) {
		group_delta_ = deltaCallback64_(path, norms, j, k);
		if (group.is_reversed) group_delta_ = -group_delta_;
	}
	if (std::fabs(group_delta_) <= floating_point_tolerance)
	{
        path_out.emplace_back(path[j]);
		return;
	}

	if (cos_a > -0.999 && (sin_a * group_delta_ < 0)) // test for concavity first (#593)
	{
		// is concave
		// by far the simplest way to construct concave joins, especially those joining very 
		// short segments, is to insert 3 points that produce negative regions. These regions 
		// will be removed later by the finishing union operation. This is also the best way 
		// to ensure that path reversals (ie over-shrunk paths) are removed.
#ifdef USINGZ
        path_out.emplace_back(GetPerpendic(path[j], norms[k], group_delta_), path[j].z);
        path_out.emplace_back(path[j]); // (#405, #873, #916)
        path_out.emplace_back(GetPerpendic(path[j], norms[j], group_delta_), path[j].z);
#else
        path_out.emplace_back(GetPerpendic(path[j], norms[k], group_delta_));
        path_out.emplace_back(path[j]); // (#405, #873, #916)
        path_out.emplace_back(GetPerpendic(path[j], norms[j], group_delta_));
#endif
	}
	else if (cos_a > 0.999 && join_type_ != JoinType::Round)
	{
		// almost straight - less than 2.5 degree (#424, #482, #526 & #724)
		DoMiter(path, j, k, cos_a);
	}
	else if (join_type_ == JoinType::Miter)
	{
		// miter unless the angle is sufficiently acute to exceed ML
		if (cos_a > temp_lim_ - 1) DoMiter(path, j, k, cos_a);
		else DoSquare(path, j, k);
	}
	else if (join_type_ == JoinType::Round)
		DoRound(path, j, k, std::atan2(sin_a, cos_a));
	else if ( join_type_ == JoinType::Bevel)
		DoBevel(path, j, k);
	else
		DoSquare(path, j, k);
}

void ClipperOffset::OffsetPolygon(Group& group, const Path64& path)
{
	path_out.clear();
	for (Path64::size_type j = 0, k = path.size() - 1; j < path.size(); k = j, ++j)
		OffsetPoint(group, path, j, k);	
    solution->emplace_back(path_out);
}

void ClipperOffset::OffsetOpenJoined(Group& group, const Path64& path)
{
	OffsetPolygon(group, path);
	Path64 reverse_path(path);
	std::reverse(reverse_path.begin(), reverse_path.end());

	//rebuild normals 
	std::reverse(norms.begin(), norms.end());
    norms.emplace_back(norms[0]);
	norms.erase(norms.begin());
	NegatePath(norms);

	OffsetPolygon(group, reverse_path);
}

void ClipperOffset::OffsetOpenPath(Group& group, const Path64& path)
{
	// do the line start cap
	if (deltaCallback64_) group_delta_ = deltaCallback64_(path, norms, 0, 0);

	if (std::fabs(group_delta_) <= floating_point_tolerance)
        path_out.emplace_back(path[0]);
	else
	{
		switch (end_type_)
		{
		case EndType::Butt:
			DoBevel(path, 0, 0);
			break;
		case EndType::Round:
			DoRound(path, 0, 0, PI);
			break;
		default:
			DoSquare(path, 0, 0);
			break;
		}
	}

	size_t highI = path.size() - 1;
	// offset the left side going forward
	for (Path64::size_type j = 1, k = 0; j < highI; k = j, ++j)
		OffsetPoint(group, path, j, k);

	// reverse normals
	for (size_t i = highI; i > 0; --i)
		norms[i] = PointD(-norms[i - 1].x, -norms[i - 1].y);
	norms[0] = norms[highI];

	// do the line end cap
	if (deltaCallback64_)
		group_delta_ = deltaCallback64_(path, norms, highI, highI);

	if (std::fabs(group_delta_) <= floating_point_tolerance)
        path_out.emplace_back(path[highI]);
	else
	{
		switch (end_type_)
		{
		case EndType::Butt:
			DoBevel(path, highI, highI);
			break;
		case EndType::Round:
			DoRound(path, highI, highI, PI);
			break;
		default:
			DoSquare(path, highI, highI);
			break;
		}
	}

	for (size_t j = highI -1, k = highI; j > 0; k = j, --j)
		OffsetPoint(group, path, j, k);
    solution->emplace_back(path_out);
}

void ClipperOffset::DoGroupOffset(Group& group)
{
	if (group.end_type == EndType::Polygon)
	{
		// a straight path (2 points) can now also be 'polygon' offset
		// where the ends will be treated as (180 deg.) joins
        if (!group.lowest_path_idx.has_value()) delta_ = std::abs(delta_);
		group_delta_ = (group.is_reversed) ? -delta_ : delta_;
	}
	else
		group_delta_ = std::abs(delta_);// *0.5;

	double abs_delta = std::fabs(group_delta_);
	join_type_	= group.join_type;
	end_type_ = group.end_type;

	if (group.join_type == JoinType::Round || group.end_type == EndType::Round)
	{
		// calculate the number of steps required to approximate a circle
		// (see https://www.angusj.com/clipper2/Docs/Trigonometry.htm)
		// arcTol - when arc_tolerance_ is undefined (0) then curve imprecision
		// will be relative to the size of the offset (delta). Obviously very
		//large offsets will almost always require much less precision.
		double arcTol = (arc_tolerance_ > floating_point_tolerance) ?
			std::min(abs_delta, arc_tolerance_) : abs_delta * arc_const;

		double steps_per_360 = std::min(PI / std::acos(1 - arcTol / abs_delta), abs_delta * PI);
		step_sin_ = std::sin(2 * PI / steps_per_360);
		step_cos_ = std::cos(2 * PI / steps_per_360);
		if (group_delta_ < 0.0) step_sin_ = -step_sin_;
		steps_per_rad_ = steps_per_360 / (2 * PI);
	}

	//double min_area = PI * Sqr(group_delta_);
	Paths64::const_iterator path_in_it = group.paths_in.cbegin();
	for ( ; path_in_it != group.paths_in.cend(); ++path_in_it)
	{
		Path64::size_type pathLen = path_in_it->size();
		path_out.clear();

		if (pathLen == 1) // single point
		{
			if (deltaCallback64_)
			{
				group_delta_ = deltaCallback64_(*path_in_it, norms, 0, 0);
				if (group.is_reversed) group_delta_ = -group_delta_;
				abs_delta = std::fabs(group_delta_);
			}

			if (group_delta_ < 1) continue;
			const Point64& pt = (*path_in_it)[0];
			//single vertex so build a circle or square ...
			if (group.join_type == JoinType::Round)
			{
				double radius = abs_delta;
                size_t steps = steps_per_rad_ > 0 ? static_cast<size_t>(std::ceil(steps_per_rad_ * 2 * PI)) : 0; //#617
				path_out = Ellipse(pt, radius, radius, steps);
#ifdef USINGZ
				for (auto& p : path_out) p.z = pt.z;
#endif
			}
			else
			{
				int d = (int)std::ceil(abs_delta);
				Rect64 r = Rect64(pt.x - d, pt.y - d, pt.x + d, pt.y + d);
				path_out = r.AsPath();
#ifdef USINGZ
				for (auto& p : path_out) p.z = pt.z;
#endif
			}

            solution->emplace_back(path_out);
			continue;
		} // end of offsetting a single point

		if ((pathLen == 2) && (group.end_type == EndType::Joined))
			end_type_ = (group.join_type == JoinType::Round) ?
			  EndType::Round :
			  EndType::Square;

		BuildNormals(*path_in_it);
		if (end_type_ == EndType::Polygon) OffsetPolygon(group, *path_in_it);
		else if (end_type_ == EndType::Joined) OffsetOpenJoined(group, *path_in_it);
		else OffsetOpenPath(group, *path_in_it);
	}
}

#ifdef USINGZ
void ClipperOffset::ZCB(const Point64& bot1, const Point64& top1,
	const Point64& bot2, const Point64& top2, Point64& ip)
{
	if (bot1.z && ((bot1.z == bot2.z) || (bot1.z == top2.z))) ip.z = bot1.z;
	else if (bot2.z && (bot2.z == top1.z)) ip.z = bot2.z;
	else if (top1.z && (top1.z == top2.z)) ip.z = top1.z;
	else if (zCallback64_) zCallback64_(bot1, top1, bot2, top2, ip);
}
#endif

size_t ClipperOffset::CalcSolutionCapacity()
{
	size_t result = 0;
	for (const Group& g : groups_)
		result += (g.end_type == EndType::Joined) ? g.paths_in.size() * 2 : g.paths_in.size();
	return result;
}

bool ClipperOffset::CheckReverseOrientation()
{
	// nb: this assumes there's consistency in orientation between groups
	bool is_reversed_orientation = false;
	for (const Group& g : groups_)
		if (g.end_type == EndType::Polygon)
		{
			is_reversed_orientation = g.is_reversed;
			break;
		}
	return is_reversed_orientation;
}

void ClipperOffset::ExecuteInternal(double delta)
{
	error_code_ = 0;
	if (groups_.size() == 0) return;
	solution->reserve(CalcSolutionCapacity());

	if (std::abs(delta) < 0.5) // ie: offset is insignificant
	{
		Paths64::size_type sol_size = 0;
		for (const Group& group : groups_) sol_size += group.paths_in.size();
		solution->reserve(sol_size);
		for (const Group& group : groups_)
			copy(group.paths_in.begin(), group.paths_in.end(), back_inserter(*solution));
	}
	else
	{

		temp_lim_ = (miter_limit_ <= 1) ?
			2.0 :
			2.0 / (miter_limit_ * miter_limit_);

		delta_ = delta;
		std::vector<Group>::iterator git;
		for (git = groups_.begin(); git != groups_.end(); ++git)
		{
			DoGroupOffset(*git);
			if (!error_code_) continue; // all OK
			solution->clear();
		}
	}

	if (!solution->size()) return;

	bool paths_reversed = CheckReverseOrientation();
	//clean up self-intersections ...
	Clipper64 c;
	c.PreserveCollinear(preserve_collinear_);
	//the solution should retain the orientation of the input
	c.ReverseSolution(reverse_solution_ != paths_reversed);
#ifdef USINGZ
	auto fp = std::bind(&ClipperOffset::ZCB, this, std::placeholders::_1,
		std::placeholders::_2, std::placeholders::_3,
		std::placeholders::_4, std::placeholders::_5);
	c.SetZCallback(fp);
#endif
	c.AddSubject(*solution);
	if (solution_tree)
	{
		if (paths_reversed)
			c.Execute(ClipType::Union, FillRule::Negative, *solution_tree);
		else
			c.Execute(ClipType::Union, FillRule::Positive, *solution_tree);
	}
	else
	{
		if (paths_reversed)
			c.Execute(ClipType::Union, FillRule::Negative, *solution);
		else
			c.Execute(ClipType::Union, FillRule::Positive, *solution);
	}
}

void ClipperOffset::Execute(double delta, Paths64& paths64)
{
	paths64.clear();
	solution = &paths64;
	solution_tree = nullptr;
	ExecuteInternal(delta);
}


void ClipperOffset::Execute(double delta, PolyTree64& polytree)
{
	polytree.Clear();
	solution_tree = &polytree;
	solution = new Paths64();
	ExecuteInternal(delta);
	delete solution;
	solution = nullptr;
}

void ClipperOffset::Execute(DeltaCallback64 delta_cb, Paths64& paths)
{
	deltaCallback64_ = delta_cb;
	Execute(1.0, paths);
}

} // namespace