/*******************************************************************************
+
+  LEDA 7.2.3  
+
+
+  r_circle_gen_polygon.h
+
+
+  Copyright (c) 1995-2026
+  by Algorithmic Solutions Software GmbH
+  All rights reserved.
+ 
*******************************************************************************/



#ifndef LEDA_R_CIRCLE_GEN_POLYGON_H
#define LEDA_R_CIRCLE_GEN_POLYGON_H

#if !defined(LEDA_ROOT_INCL_ID)
#define LEDA_ROOT_INCL_ID 723110
#include <LEDA/internal/PREAMBLE.h>
#endif

#include <LEDA/geo/r_circle_polygon.h>

LEDA_BEGIN_NAMESPACE

//------------------------------------------------------------------------------
// r_circle_gen_polygon:   generalized polygon with r_circle_segment edges
//------------------------------------------------------------------------------

/// r_circle_gen_polygon /////////////////////////////////////////////////////////////////////

class r_circle_gen_polygon_rep : public handle_rep {
public:
	enum KIND { EMPTY       = r_circle_polygon::EMPTY, 
		        FULL        = r_circle_polygon::FULL,
				NON_TRIVIAL = r_circle_polygon::NON_TRIVIAL };

public:
	r_circle_gen_polygon_rep(KIND k = EMPTY) : Kind(k) {}

	r_circle_gen_polygon_rep(const r_circle_polygon& p)
	{
		switch (p.kind()) {
		case r_circle_polygon::EMPTY: Kind = EMPTY; break;
		case r_circle_polygon::FULL:  Kind = FULL;  break;
		default: Kind = NON_TRIVIAL; BoundaryChains.append(p); break;
		}
	}

	r_circle_gen_polygon_rep(const list<r_circle_polygon>& chains) : BoundaryChains(chains)
	{ Kind = chains.empty() ? EMPTY : NON_TRIVIAL; }

	virtual ~r_circle_gen_polygon_rep() {}

private:
	KIND                   Kind;
	list<r_circle_polygon> BoundaryChains;

	friend class __exportC r_circle_gen_polygon;
};

class __exportC rat_gen_polygon;
class __exportC gen_polygon;

/*{\Manpage {r_circle_gen_polygon} {} {Generalized polygons with circular edges} {P}}*/

class __exportC r_circle_gen_polygon : public HANDLE_BASE(r_circle_gen_polygon_rep) {
/*{\Mdefinition
The data type |r_circle_polygon| is not closed under boolean operations, 
e.g., the set difference of a polygon $P$ and a polygon $Q$ nested in $P$ 
is a region that contains a ``hole''. Therefore we provide a generalization
called |\Mtype| which is closed under (regularized) boolean operations (see
below).

A formal definition follows:
An instance |\Mvar| of the data type |\Mtype| is a regular 
polygonal region in the plane. A regular region is an open set that is 
equal to the interior of its closure. A region is polygonal if its boundary
consists of a finite number of |r_circle_segments|.

The boundary of an |\Mtype| consists of zero or more weakly 
simple closed polygonal chains. Each such chain is represented by an 
object of type |r_circle_ploygon|.
There are two regions whose boundary is empty, namely the \emph{empty region}
and the \emph{full region}. The full region encompasses the entire plane. 
We call a region \emph{trivial} if its boundary is empty.
The boundary cycles $P_1$, $P_2$, \ldots, $P_k$ of an |\Mtype| are ordered
such that no $P_i$ is nested in a $P_j$ with $i < j$. 
}*/

public:
	typedef r_circle_gen_polygon_rep rep;
	typedef HANDLE_BASE(rep)         base;
	typedef r_circle_gen_polygon     gp_type;

private:
	rep* ptr() const { return (rep*) PTR; }

public:
/*{\Mtypes}*/

	typedef real coord_type;
	/*{\Mtypemember the coordinate type (|real|).}*/

	typedef r_circle_point point_type;
	/*{\Mtypemember the point type (|r_circle_point|).}*/

	typedef r_circle_segment segment_type;
	/*{\Mtypemember the segment type (|r_circle_segment|).}*/

	typedef r_circle_polygon polygon_type;
	/*{\Mtypemember the polygon type (|r_circle_polygon|).}*/


	enum KIND { EMPTY       = r_circle_polygon::EMPTY, 
		        FULL        = r_circle_polygon::FULL,
				NON_TRIVIAL = r_circle_polygon::NON_TRIVIAL };
	/*{\Menum describes the kind of the polygon: the empty set, the full plane 
	          or a non-trivial polygon.}*/

	enum CHECK_TYPE { NO_CHECK          = r_circle_polygon::NO_CHECK, 
			  SIMPLE            = r_circle_polygon::SIMPLE, 
			  WEAKLY_SIMPLE     = r_circle_polygon::WEAKLY_SIMPLE, 
			  NOT_WEAKLY_SIMPLE = r_circle_polygon::NOT_WEAKLY_SIMPLE };
	/*{\Menum used to specify which checks should be applied and also describes
	          the outcome of a simplicity check.}*/

	enum RESPECT_TYPE { DISREGARD_ORIENTATION = r_circle_polygon::DISREGARD_ORIENTATION, 
						RESPECT_ORIENTATION   = r_circle_polygon::RESPECT_ORIENTATION };
	/*{\Menum used in contructors to specify whether to force a positive
	          orientation for the constructed object (|DISREGARD_ORIENTATION|)
			  or to keep the orientation of the input (|RESPECT_ORIENTATION|).}*/

	enum BOOL_OP { UNITE, INTERSECT, DIFF, SYMDIFF };

public:
/*{\Mcreation}*/

	r_circle_gen_polygon() { PTR = new rep; }
	/*{\Mcreate creates an empty polygon |\Mvar|.}*/

	r_circle_gen_polygon(KIND k);
	/*{\Mcreate creates a polygon |\Mvar| of kind |k|, where |k| is either 
	            |EMPTY| or |FULL|.}*/

	r_circle_gen_polygon(const list<r_circle_segment>& seg_chain, 
			     CHECK_TYPE check = WEAKLY_SIMPLE, 
                             RESPECT_TYPE respect_orient = RESPECT_ORIENTATION)
	{ PTR = new rep(r_circle_polygon(seg_chain, r_circle_polygon::CHECK_TYPE(check), r_circle_polygon::RESPECT_TYPE(respect_orient))); }
	/*{\Mcreate creates a polygon |\Mvar| from a single closed chain of 
	            segments.}*/

	r_circle_gen_polygon(const r_circle_polygon& Q,
						 CHECK_TYPE check = NO_CHECK, RESPECT_TYPE respect_orient = RESPECT_ORIENTATION);
	/*{\Mcreate converts an |r_circle_polygon| $Q$ to an |\Mtype| |\Mvar|.}*/

	r_circle_gen_polygon(const list<rat_point>& L,
						 CHECK_TYPE check = NO_CHECK, RESPECT_TYPE respect_orient = RESPECT_ORIENTATION)
	{ PTR = new rep(r_circle_polygon(L, r_circle_polygon::CHECK_TYPE(check), r_circle_polygon::RESPECT_TYPE(respect_orient))); }
	/*{\Mcreate creates a polygon |\Mvar| with straight line edges from a 
	            list |L| of vertices.}*/

	r_circle_gen_polygon(const list<r_circle_polygon>& polys, 
						 CHECK_TYPE check = NO_CHECK, RESPECT_TYPE respect_orient = RESPECT_ORIENTATION)
	{ init(polys, check, respect_orient); }
	/*{\Mcreate introduces a variable |\Mvar| of type |\Mname|.
	            |\Mvar| is initialized to the polygon with boundary 
				representation |polys|.\\
	            \precond |polys| must be a boundary representation.}*/

	r_circle_gen_polygon(const list<r_circle_gen_polygon>& gen_polys);
	/*{\Mcreate creates a polygon |\Mvar| as the union of all the polygons in 
	            |gen_polys|.\\
	            \precond Every polygon in |gen_polys| must be weakly simple.}*/

	r_circle_gen_polygon(const rat_gen_polygon& Q,
						 CHECK_TYPE check = NO_CHECK, RESPECT_TYPE respect_orient = RESPECT_ORIENTATION);
	/*{\Mcreate converts a |rat_gen_polygon| $Q$ to an |\Mtype| |\Mvar|.}*/

	r_circle_gen_polygon(const gen_polygon& Q, 
						 CHECK_TYPE check = NO_CHECK, RESPECT_TYPE respect_orient = RESPECT_ORIENTATION, 
						 int prec = rat_point::default_precision);
	/*{\Mcreate converts the (floating point) |gen_polygon| $Q$ to an |\Mtype|.
	            |\Mvar| is initialized to a rational approximation of $Q$ of 
				coordinates with denominator at most |prec|. 
				If |prec| is zero, the implementation chooses |prec| large 
				enough such that there is no loss of precision in the 
				conversion.}*/

	r_circle_gen_polygon(const rat_circle& circ, RESPECT_TYPE respect_orient = RESPECT_ORIENTATION)
	{ PTR = new rep(r_circle_polygon(circ, r_circle_polygon::RESPECT_TYPE(respect_orient))); }
	/*{\Mcreate creates a polygon |\Mvar| whose boundary is the 
	            circle |circ|.}*/

	r_circle_gen_polygon(const r_circle_gen_polygon& Q) : base(Q) {}

	const r_circle_gen_polygon& operator=(const r_circle_gen_polygon& Q)
	{ base::operator=(Q); return *this; }

/*{\Moperations}*/

	KIND kind() const { return KIND(ptr()->Kind); }
	/*{\Mop     returns the kind of |\Mvar|.}*/

	/*{\Moptions nextwarning=no}*/
	bool is_trivial() const { return kind() != NON_TRIVIAL; }
	bool trivial() const { return is_trivial(); } // for compatibility with GEN_POLYGON
	/*{\Mop     returns true iff |\Mvar| is trivial.}*/

	/*{\Moptions nextwarning=no}*/
	bool is_empty() const { return kind() == EMPTY; }
	bool empty() const { return is_empty(); } // for compatibility with GEN_POLYGON
	/*{\Mop     returns true iff |\Mvar| is empty.}*/

	/*{\Moptions nextwarning=no}*/
	bool is_full() const { return kind() == FULL; }
	bool full() const { return is_full(); } // for compatibility with GEN_POLYGON
	/*{\Mop     returns true iff |\Mvar| is full.}*/

	void normalize();
	/*{\Mop     simplifies the representation by calling
	            |c.normalize()| for every polygonal chain |c| of |\Mvar|.}*/

	bool verify(bool report_errors = true) const;

	bool is_simple() const
	{ return r_circle_polygon::check_chains_for_simplicity(polygons()) 
	         == r_circle_polygon::SIMPLE; }
	/*{\Mop   tests whether |\Mvar| is simple or not.}*/

	bool is_weakly_simple() const
	{ return r_circle_polygon::check_chains_for_simplicity(polygons()) 
	         != r_circle_polygon::NOT_WEAKLY_SIMPLE; }
	/*{\Mop   tests whether |\Mvar| is weakly simple or not.}*/

	bool is_weakly_simple(list<r_circle_point>& crossings) const
	{ return r_circle_polygon::check_chains_for_simplicity(polygons(), &crossings) 
	         != r_circle_polygon::NOT_WEAKLY_SIMPLE; }
	/*{\Mop   as above, returns all proper points of intersection in 
	          |crossings|. }*/

	static bool check_representation(const list<r_circle_polygon>& polys, 
		                             CHECK_TYPE check = WEAKLY_SIMPLE);
	/*{\Mstatic checks whether |polys| is a boundary representation.
	            Currently the nesting order is not checked, 
				we check only for (weak) simplicity.}*/

	bool check_representation() const
	{ return check_representation(polygons()); }
	/*{\Mop   checks the representation of |\Mvar| (see above).}*/

	bool is_convex() const;
	/*{\Mop     returns true iff |\Mvar| is convex.}*/

	int size() const;
	/*{\Mop     returns the size of |\Mvar|, i.e.~the number of segments in 
	            its boundary representation.}*/

	const list<r_circle_polygon>& polygons() const { return ptr()->BoundaryChains; }
	/*{\Mop     returns the boundary representation of |\Mvar|.}*/

	/*{\Moptions nextwarning=no}*/
	list<r_circle_segment> segments() const;
	list<r_circle_segment> edges() const { return segments(); }
	/*{\Mop     returns a chain of segments that bound |\Mvar|. 
	            The orientation of the chain corresponds to the orientation 
				of |\Mvar|.}*/

	list<r_circle_point> vertices() const;
	/*{\Mop     returns the vertices of |\Mvar|.}*/

	list<r_circle_point> intersection(const r_circle_segment& s) const;
	/*{\Mopl    returns the list of all proper intersections between $s$ and the
	            boundary of |\Mvar|.}*/

	list<r_circle_point> intersection(const rat_line& l) const;
	/*{\Mopl    returns the list of all proper intersections between $l$ and the
	            boundary of |\Mvar|.}*/

	r_circle_gen_polygon translate(rational dx, rational dy) const;
	/*{\Mopl    returns |\Mvar| translated by vector $(dx,dy)$.}*/

	r_circle_gen_polygon translate(const rat_vector& v) const { return translate(v[0], v[1]); }
	/*{\Mop     returns |\Mvar| translated by vector $v$.}*/

	r_circle_gen_polygon operator+(const rat_vector& v) const { return translate(v); }
	/*{\Mbinop  returns |\Mvar| translated by vector $v$.}*/

	r_circle_gen_polygon operator-(const rat_vector& v) const { return translate(-v); }
	/*{\Mbinop  returns |\Mvar| translated by vector $-v$.}*/

	r_circle_gen_polygon rotate90(const rat_point& q, int i=1) const;
	/*{\Mopl    returns |\Mvar| rotated about $q$ by an angle of $i\times 90$ 
				degrees. If $i > 0$ the rotation is counter-clockwise otherwise
				it is clockwise. }*/

	r_circle_gen_polygon reflect(const rat_point& p, const rat_point& q) const;
	/*{\Mop     returns |\Mvar| reflected  across the straight line passing
				through $p$ and $q$.}*/

	r_circle_gen_polygon reflect(const rat_point& p) const;
	/*{\Mop     returns |\Mvar| reflected  across point $p$.}*/


	real sqr_dist(const real_point& p) const;
	/*{\Mop computes the squared Euclidean distance between the boundary of 
	        |\Mvar| and $p$. (If |\Mvar| is zero, the result is zero.)}*/

	real dist(const real_point& p) const { return sqrt(sqr_dist(p)); }
	/*{\Mop computes the Euclidean distance between the boundary of 
	        |\Mvar| and $p$. (If |\Mvar| is zero, the result is zero.)}*/


	r_circle_gen_polygon make_weakly_simple(bool del_bridges) const
	{ return is_trivial() ? *this : make_weakly_simple(segments(), del_bridges); }

	r_circle_gen_polygon make_weakly_simple() const
	{ return make_weakly_simple(true); }
	/*{\Mopl creates a weakly simple generalized polygon |Q| from a possibly
		     non-simple polygon |\Mvar| such that |Q| and |\Mvar| have the same
			 inner points. (This function is experimental.)}*/

	static r_circle_gen_polygon make_weakly_simple(const r_circle_polygon& Q, bool del_bridges)
	{ return Q.is_trivial() ? r_circle_gen_polygon(Q) : make_weakly_simple(Q.segments(), del_bridges); }

	static r_circle_gen_polygon make_weakly_simple(const r_circle_polygon& Q)
	{ return make_weakly_simple(Q, true); }
	/*{\Mstatic same as above, but the input is a polygon |Q|. 
	            (This function is experimental.)}*/

	static r_circle_gen_polygon convert_bridge_representation(const r_circle_polygon& p, int input_tolerance = 3);
	// the higher the tolerance the less accurate the input data has to be but the slower ...

	r_circle_gen_polygon complement() const;
	/*{\Mopl    returns the complement of |\Mvar|.}*/

	r_circle_gen_polygon contour() const;
	/*{\Mopl    returns the contour of |\Mvar|, i.e. all holes are removed from |\Mvar|.}*/

	r_circle_gen_polygon eliminate_cocircular_vertices() const;
	/*{\Mopl    returns a copy of |\Mvar| without cocircular vertices.}*/

	r_circle_gen_polygon round(int prec = 0) const;
	/*{\Mop returns a rounded representation of |\Mvar|. (experimental)}*/


	bool is_r_circle_polygon() const { return polygons().size() <= 1; }
	/*{\Mopl    checks if the boundary of |\Mvar| consists of at most one chain.}*/

	r_circle_polygon to_r_circle_polygon() const;
	/*{\Mopl    converts |\Mvar| to an |r_circle_polygon|.\\ 
	            \precond |is_r_circle_polygon| is true.}*/


	bool is_rat_gen_polygon() const;
	/*{\Mopl    returns whether |\Mvar| can be converted to a |rat_polygon|.}*/

	rat_gen_polygon to_rat_gen_polygon() const;
	/*{\Mopl    converts |\Mvar| to a |rat_gen_polygon|.\\ 
	            \precond |is_rat_gen_polygon| is true.}*/

	rat_gen_polygon approximate_by_rat_gen_polygon(double dist) const;
	/*{\Mopl    approximates |\Mvar| by a |rat_gen_polygon|. The maxmum distance
	            between a point on |\Mvar| and the approximation is bounded by
				|dist|.}*/

	gen_polygon to_float() const;
	/*{\Mopl    computes a floating point approximation of |\Mvar| with 
	            straight line segments.\\ 
	            \precond |is_rat_gen_polygon| is true.}*/

	bool is_rat_circle() const;
	/*{\Mopl    returns whether |\Mvar| can be converted to a |rat_circle|.}*/

	rat_circle to_rat_circle() const;
	/*{\Mopl    converts |\Mvar| to a |rat_circle|.\\ 
	            \precond |is_rat_circle| is true.}*/

	void bounding_box(real& xmin, real& ymin, real& xmax, real& ymax) const;
	/*{\Mop computes a tight bounding box for |\Mvar|.}*/

	void bounding_box(double& xmin, double& ymin, double& xmax, double& ymax) const;
	/*{\Mop computes a bounding box for |\Mvar|, but not necessarily a tight one.}*/

        static CHECK_TYPE input_check_type;

	static void write(ostream& out, const r_circle_gen_polygon& p);
	static void read(istream& in, r_circle_gen_polygon& p, 
		             CHECK_TYPE check = WEAKLY_SIMPLE, 
                             RESPECT_TYPE respect_orient = RESPECT_ORIENTATION);
/*{\Mtext 
\medskip
{\bf All functions below assume that |\Mvar| is weakly simple.}
\medskip
}*/

	int orientation() const
	{ return is_trivial() ? 0 : polygons().head().orientation(); }
	/*{\Mop     returns the orientation of |\Mvar|. }*/

	int         side_of(const r_circle_point& p) const;
	/*{\Mop     returns $+1$ if $p$ lies to the left of |\Mvar|, $0$ if 
				$p$ lies on |\Mvar|, and $-1$ if $p$ lies to the 
				right of |\Mvar|.}*/ 

	region_kind region_of(const r_circle_point& p) const;
	/*{\Mop     returns BOUNDED\_REGION if $p$ lies in the 
				bounded region of |\Mvar|, returns ON\_REGION if $p$ lies on 
				|\Mvar|, and returns UNBOUNDED\_REGION if $p$ lies in the 
				unbounded region. The bounded region of the full polygon is the entire plane. }*/

	bool        inside(const r_circle_point& p) const 
	            { return side_of(p) == 1; }
	/*{\Mop     returns true if $p$ lies to the left of |\Mvar|, i.e.,
				|side_of(p) == +1|. }*/

	bool        on_boundary(const r_circle_point& p) const  
				{ return side_of(p) == 0; }
	/*{\Mop     returns true if $p$ lies on |\Mvar|, i.e., 
				|side_of(p) == 0|. }*/

	bool        outside(const r_circle_point& p) const 
				{ return side_of(p) == -1; }
	/*{\Mop     returns true if $p$ lies to the right of |\Mvar|, i.e., 
				|side_of(p) == -1|.}*/

	bool        contains(const r_circle_point& p) const
				{ return !outside(p); }
	/*{\Mop     returns true if $p$ lies to the left of or on |\Mvar|.}*/


	double approximate_area() const;
	/*{\Mop     approximates the (oriented) area of the bounded region of 
	            |\Mvar|.\\
				\precond |\Mvar.kind()| is not full.}*/

/*{\Mtext \newcommand{\regp}{\mathop {\rm reg}} 
All boolean operations are regularized, i.e., the result 
$R$ of the standard boolean operation is replaced by the interior 
of the closure of $R$. We use $\regp X$ to denote the regularization 
of a set $X$.
}*/

	/*{\Moptions nextwarning=no}*/
	r_circle_gen_polygon unite(const r_circle_gen_polygon& Q) const
	{ return bool_operation(UNITE, *this, Q); }
	/*{\Mopl    returns $\regp (P \cup Q)$. }*/

	/*{\Moptions nextwarning=no}*/
	r_circle_gen_polygon intersection(const r_circle_gen_polygon& Q) const
	{ return bool_operation(INTERSECT, *this, Q); }
	/*{\Mopl    returns $\regp(P \cap Q)$.}*/

	/*{\Moptions nextwarning=no}*/
	r_circle_gen_polygon diff(const r_circle_gen_polygon& Q) const
	{ return bool_operation(DIFF, *this, Q); }
	/*{\Mopl    returns $\regp(P \setminus Q)$.}*/

	/*{\Moptions nextwarning=no}*/
	r_circle_gen_polygon sym_diff(const r_circle_gen_polygon& Q) const
	{ return bool_operation(SYMDIFF, *this, Q); }
	/*{\Mopl    returns $\regp( (P\cup Q) - (P\cap Q))$.}*/

/*{\Mtext 
For optimization purposes we provide a union operation of arbitrary arity. 
It computes the union of a set of polygons much faster than with binary operations.
}*/

	static r_circle_gen_polygon unite(const list<r_circle_gen_polygon>& L)
	{ return unite_parallel(L); }
	/*{\Mstatic returns the (regularized) union of all polygons in $L$.}*/

	static r_circle_gen_polygon unite_with_bool_ops(const list<r_circle_gen_polygon>& L);
	static r_circle_gen_polygon unite_parallel(const list<r_circle_gen_polygon>& L, int step_size = 128);

/*{\Mtext \newcommand{\appr}{\mathop {\rm appr}}
We offer fast versions of the boolean operations which compute an approximate 
result.
These operations work as follows: every curved segment is approximated by 
straight line segments, then the respective boolean operation is performed on 
the straight polygons. Finally, we identify those straight segments in the 
result that originate from a curved segment and replace them by curved segments 
again. (We denote the approximate computation of an operation |op| scheme by 
$\appr(|op|)$. )
Every operation below takes a parameter |dist| that controls the accuracy of 
the approximation: |dist| is an upper bound on the distance of any point on 
an original polygon $P$ to the approximated polygon $P'$.
}*/

	/*{\Moptions nextwarning=no}*/
	r_circle_gen_polygon unite_approximate(const r_circle_gen_polygon& Q, double dist = 1e-2) const;
	/*{\Mopl    returns $\appr (P \cup Q)$. }*/

	/*{\Moptions nextwarning=no}*/
	r_circle_gen_polygon intersection_approximate(const r_circle_gen_polygon& Q, double dist = 1e-2) const;
	/*{\Mopl    returns $\appr(P \cap Q)$.}*/

	/*{\Moptions nextwarning=no}*/
	r_circle_gen_polygon diff_approximate(const r_circle_gen_polygon& Q, double dist = 1e-2) const;
	/*{\Mopl    returns $\appr(P \setminus Q)$.}*/

	/*{\Moptions nextwarning=no}*/
	r_circle_gen_polygon sym_diff_approximate(const r_circle_gen_polygon& Q, double dist = 1e-2) const;
	/*{\Mopl    returns $\appr( (P\cup Q) - (P\cap Q))$.}*/

	static r_circle_gen_polygon unite_approximate(const list<r_circle_gen_polygon>& L, double dist = 1e-2)
	{ return unite_approximate(L, dist, 128); }
	/*{\Mstatic returns the (approximated) union of all polygons in $L$.}*/

	static r_circle_gen_polygon unite_approximate(const list<r_circle_gen_polygon>& L, double dist, int step_size);


r_circle_gen_polygon buffer(double d) const;
/*{\Mopl adds an exterior buffer zone to |\Mvar|($d > 0$),
         or removes an interior buffer zone from |\Mvar| ($d < 0$).
         More precisely, for $d \geq 0$ define the buffer tube $T$ as
         the set of all points in the complement of |\Mvar| whose distance 
         to |\Mvar| is at most $d$. Then the function returns |\Mvar| $\cup T$.
         For $d < 0$ let $T$ denote the set of all points in |\Mvar| whose
         distance to the complement is less than $\Labs{d}$. Then the result
         is |\Mvar| $\setminus T$. }*/



	bool operator==(const r_circle_gen_polygon& Q) const;
	bool operator!=(const r_circle_gen_polygon& Q) const { return ! operator==(Q); }

private:
	void init(const list<r_circle_polygon>& polys, CHECK_TYPE check, RESPECT_TYPE respect_orient);

private: // helpers for boolean operations
	static gp_type bool_operation(BOOL_OP op, const gp_type& gp1, const gp_type& gp2);
	static gp_type bool_op_trivial_case(BOOL_OP op, const gp_type& gp1, const gp_type& gp2);
	static void    bool_op_construct_map(const gp_type& gp1, const gp_type& gp2, GRAPH<r_circle_point, r_circle_segment>& G, edge_array<unsigned>& label);
	static void    bool_op_mark_relevant_edges(BOOL_OP op, const GRAPH<r_circle_point, r_circle_segment>& G, const edge_array<unsigned>& label, edge_array<bool>& relevant);
	static bool    bool_op_simplify_graph(GRAPH<r_circle_point, r_circle_segment>& G, const edge_array<bool>& relevant);
	static gp_type bool_op_extract_result(GRAPH<r_circle_point, r_circle_segment>& G, const edge_array<bool>& relevant, bool non_empty);

	static r_circle_gen_polygon unite_parallel_step(const list<r_circle_gen_polygon>& L);

	static rat_gen_polygon convert_curved_gp_to_straight_gp
	       (const r_circle_gen_polygon& curved_gp, double dist, list<r_circle_segment>& all_orig_segs, map<rat_segment, GenPtr>& orig_seg);
	static r_circle_gen_polygon convert_straight_gp_to_curved_gp
	       (const rat_gen_polygon& straight_gp, map<rat_segment, GenPtr>& orig_seg);

	static r_circle_gen_polygon make_weakly_simple(const list<r_circle_segment>& chains, bool del_bridges);
	static r_circle_gen_polygon assemble(const list<r_circle_polygon>& pos_parts, const list<r_circle_polygon>& neg_parts);
};

__exportF ostream& operator<<(ostream& out, const r_circle_gen_polygon& gp);
__exportF istream& operator>>(istream& in,  r_circle_gen_polygon& gp);

/*{\Mtext
\bigskip
{\bf Iterations Macros}

{\bf forall\_polygons}($p,P$)       
$\{$ ``the boundary polygons of $P$ are successively assigned to 
|r_circle_polygon| $p$'' $\}$ 
}*/

#if !defined(forall_polygons)
#define forall_polygons(v,P)  forall(v,(P).polygons())
#endif


#if LEDA_ROOT_INCL_ID == 723110
#undef LEDA_ROOT_INCL_ID
#include <LEDA/internal/POSTAMBLE.h>
#endif


LEDA_END_NAMESPACE

#endif
