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cgal/Packages/Planar_map/include/CGAL/Pm_segment_traits_2.h

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// ======================================================================
//
// Copyright (c) 1997 The CGAL Consortium
//
// This software and related documentation is part of an INTERNAL release
// of the Computational Geometry Algorithms Library (CGAL). It is not
// intended for general use.
//
// ----------------------------------------------------------------------
//
// release : $$
// release_date : $$
//
// file : include/CGAL/Pm_segment_traits_2.h
// package : Planar_map (5.87)
// maintainer : Eyal Flato <flato@math.tau.ac.il>
// source :
// revision :
// revision_date :
// author(s) : Iddo Hanniel <hanniel@math.tau.ac.il>
// Eyal Flato <flato@post.tau.ac.il>
// Oren Nechushtan <theoren@math.tau.ac.il>
// Eti Ezra <estere@post.tau.ac.il>
// Shai Hirsch <shaihi@post.tau.ac.il>
// Eugene Lipovetsky <eug@post.tau.ac.il>
// Efi Fogel <efif@post.tau.ac.il>
// Ron Wein <wein@post.tau.ac.il>
//
// coordinator : Tel-Aviv University (Dan Halperin <halperin@math.tau.ac.il>)
//
// Chapter :
// ======================================================================
#ifndef CGAL_PM_SEGMENT_TRAITS_2_H
#define CGAL_PM_SEGMENT_TRAITS_2_H
#include <CGAL/tags.h>
CGAL_BEGIN_NAMESPACE
template <class Kernel_>
class Pm_segment_traits_2 : public Kernel_
{
public:
typedef Kernel_ Kernel;
// Categories:
// #define HAS_LEFT_NOT
#if !defined(HAS_LEFT_NOT)
typedef Tag_true Has_left_category;
#else
typedef Tag_false Has_left_category;
#endif
// Traits objects
typedef typename Kernel::Point_2 Point_2;
typedef typename Kernel::Segment_2 X_curve_2;
// Backward compatability
typedef Point_2 Point;
typedef X_curve_2 X_curve;
protected:
// Functors:
typedef typename Kernel::Is_vertical_2 Is_vertical_2;
typedef typename Kernel::Construct_vertex_2 Construct_vertex_2;
typedef typename Kernel::Less_x_2 Less_x_2;
typedef typename Kernel::Equal_2 Equal_2;
public:
// Creation
Pm_segment_traits_2() {}
// Operations
// ----------
/*! compare_x() compares the x-coordinates of two given points
* \param p1 the first point
* \param p2 the second point
* \return LARGER if x(p1) > x(p2); SMALLER if x(p1) < x(p2); or else EQUAL
*
* \todo replace indirect use compare_x() with compare_x_2()
*/
Comparison_result compare_x(const Point_2 & p1, const Point_2 & p2) const
{ return compare_x_2_object()(p1, p2); }
/*! compare_xy() compares lexigoraphically the two points by x, then by y.
* \param p1 the first point
* \param p2 the second point
* \return LARGER if x(p1) > x(p2), or if x(p1) = x(p2) and y(p1) > y(p2);
* SMALLER if x(p1) < x(p2), or if x(p1) = x(p2) and y(p1) < y(p2);
* or else EQUAL
*/
Comparison_result compare_xy(const Point_2 & p1, const Point_2 & p2) const
{ return compare_xy_2_object()(p1, p2); }
/*! curve_is_vertical()
* \param cv the curve
* \return true iff the curve is vertical
*
* \todo replace indirect use curve_is_vertical() with is_vertical_2()
*/
bool curve_is_vertical(const X_curve_2 & cv) const
{ return is_vertical_2_object()(cv); }
/*! curve_is_in_x_range()
* \param cv the curve
* \param q the point
* \return true if q is in the x range of cv
*
* \todo Intorduce Is_in_x_range_2() or perhaps Is_in_x_closed_range_2()
* in kernel. Currently, this is implemented using existing traits (kernel)
* functions (curve_source(), curve_target()) that return the source and
* target points by value, which is not as efficient as possible.
*/
bool curve_is_in_x_range(const X_curve_2 & cv, const Point_2 & q) const
{
Construct_vertex_2 construct_vertex = construct_vertex_2_object();
const Point_2 & source = construct_vertex(cv, 0);
const Point_2 & target = construct_vertex(cv, 1);
Less_x_2 less_x = less_x_2_object();
return !((less_x(source, q) && less_x(target, q)) ||
(less_x(q, source) && less_x(q, target)));
}
/*! curve_compare_at_x() compares the y-coordinate of two given curves at
* the x-coordinate of a given point.
* \param cv1 the first curve
* \param cv2 the second curve
* \param q the point
* \return LARGER if cv1(x(q)) > cv2(x(q)); SMALLER if cv1(x(q)) < cv2(x(q));
* or else EQUAL.
* \pre The point q is in the x range of the two curves.
*
* \todo replace indirect use curve_compare_at_x() with compare_y_at_x_2()
*/
Comparison_result curve_compare_at_x(const X_curve_2 & cv1,
const X_curve_2 & cv2,
const Point_2 & q) const
{
CGAL_precondition(curve_is_in_x_range(cv1, q));
CGAL_precondition(curve_is_in_x_range(cv2, q));
return compare_y_at_x_2_object()(q, cv1, cv2);
}
#if !defined(HAS_LEFT_NOT)
/*! curve_compare_at_x_left() compares the y value of two curves in an
* epsilon environment to the left of the x value of the input point
* Preconditions: The point q is in the x range of the two curves, and both
* of them must be also be defined to its left. The two curves must also
* intersect at x(q).
*/
Comparison_result curve_compare_at_x_left(const X_curve_2 & cv1,
const X_curve_2 & cv2,
const Point_2 & q) const
{
// The two curves must not be vertical.
CGAL_precondition(! curve_is_vertical(cv1));
CGAL_precondition(! curve_is_vertical(cv2));
// The two curve must be defined at q and also to its left.
CGAL_precondition_code(
Construct_vertex_2 construct_vertex = construct_vertex_2_object();
Less_x_2 less_x = less_x_2_object();
const Point_2 & source1 = construct_vertex(cv1, 0);
const Point_2 & target1 = construct_vertex(cv1, 1);
const Point_2 & source2 = construct_vertex(cv2, 0);
const Point_2 & target2 = construct_vertex(cv2, 1);
);
CGAL_precondition (less_x(source1, q) || less_x(target1, q));
CGAL_precondition (!(less_x(source1, q) && less_x(target1, q)));
CGAL_precondition (less_x(source2, q) || less_x(target2, q));
CGAL_precondition (!(less_x(source2, q) && less_x(target2, q)));
// Since the curves are continuous, if they are not equal at q, the same
// result also applies to q's left.
CGAL_precondition (compare_y_at_x_2_object()(q, cv1, cv2) == EQUAL);
// <cv2> and <cv1> meet at a point with the same x-coordinate as q
// compare their derivatives.
return compare_slope_2_object()(cv2, cv1);
}
#else
/*! point_reflect_in_x_and_y() reflects the given point about the origin
*/
Point_2 point_reflect_in_x_and_y(const Point_2 & pt) const
{
Point_2 org = construct_point_2_object()(ORIGIN);
typename Kernel::Vector_2 v = construct_vector_2_object()(pt, org);
Point_2 reflected_pt(v);
return reflected_pt;
}
/*! curve_reflect_in_x_and_y reflects the given curve about the origin
*/
X_curve_2 curve_reflect_in_x_and_y(const X_curve_2 & cv) const
{
X_curve_2 reflected_cv(point_reflect_in_x_and_y ( cv.source()),
point_reflect_in_x_and_y ( cv.target()));
return reflected_cv;
}
#endif
/*! curve_compare_at_x_right() compares the y value of two curves in an
* epsilon environment to the right of the x value of the input point
* Preconditions: The point q is in the x range of the two curves, and both
* of them must be also be defined to its right. The two curves must also
* intersect at x(q).
*/
Comparison_result curve_compare_at_x_right(const X_curve_2 & cv1,
const X_curve_2 & cv2,
const Point_2 & q) const
{
// The two curves must not be vertical.
CGAL_precondition(! curve_is_vertical(cv1));
CGAL_precondition(! curve_is_vertical(cv2));
// The two curve must be defined at q and also to its right.
CGAL_precondition_code(
Construct_vertex_2 construct_vertex = construct_vertex_2_object();
Less_x_2 less_x = less_x_2_object();
const Point_2 & source1 = construct_vertex(cv1, 0);
const Point_2 & target1 = construct_vertex(cv1, 1);
const Point_2 & source2 = construct_vertex(cv2, 0);
const Point_2 & target2 = construct_vertex(cv2, 1);
);
CGAL_precondition (less_x(q, source1) || less_x(q, target1));
CGAL_precondition (!(less_x(q, source1) && less_x(q, target1)));
CGAL_precondition (less_x(q, source2) || less_x(q, target2));
CGAL_precondition (!(less_x(q, source2) && less_x(q, target2)));
// Since the curves are continuous, if they are not equal at q, the same
// result also applies to q's left.
CGAL_precondition (curve_compare_at_x(cv1, cv2, q) == EQUAL);
// <cv1> and <cv2> meet at a point with the same x-coordinate as q
// compare their derivatives
return compare_slope_2_object()(cv1, cv2);
}
/*! Return the curve-point status of the input objects.
* \pre p must be in the x-range of cv.
*/
Comparison_result curve_get_point_status (const X_curve_2 & cv,
const Point_2 & p) const
{
CGAL_precondition(curve_is_in_x_range(cv, p));
Comparison_result res = compare_y_at_x_2_object()(p, cv);
if (res == SMALLER)
return (LARGER);
else if (res == LARGER)
return (SMALLER);
return (EQUAL);
}
/*! \todo replace indirect use curve_is_same() with equal_2()
*/
bool curve_is_same(const X_curve_2 & cv1,const X_curve_2 & cv2) const
{
Equal_2 equal = equal_2_object();
const X_curve_2 & ocv1 = construct_opposite_segment_2_object()(cv1);
return equal(cv1, cv2) || equal(ocv1, cv2);
}
/*! \todo replace indirect use point_is_same() with equal_2()
*/
bool point_is_same(const Point_2 & p1, const Point_2 & p2) const
{ return equal_2_object()(p1, p2); }
/*! \todo replace indirect use curve_source() with construct_vertex_2()
*/
Point_2 curve_source(const X_curve_2 & cv) const
{ return construct_vertex_2_object()(cv, 0); }
/*! \todo replace indirect use curve_target() with construct_vertex_2()
*/
Point_2 curve_target(const X_curve_2 & cv) const
{ return construct_vertex_2_object()(cv, 1); }
};
CGAL_END_NAMESPACE
#endif
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