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

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// Copyright (c) 1997 Tel-Aviv University (Israel).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $Source$
// $Revision$ $Date$
// $Name$
//
// 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>
#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_monotone_curve_2;
// Backward compatability
typedef Point_2 Point;
typedef X_monotone_curve_2 X_curve;
protected:
// Functors:
typedef typename Kernel::Compare_x_2 Compare_x_2;
typedef typename Kernel::Compare_xy_2 Compare_xy_2;
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
*/
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
*/
bool curve_is_vertical(const X_monotone_curve_2 & cv) const
{ return is_vertical_2_object()(cv); }
/*! point_in_x_range()
* \param cv the curve
* \param q the point
* \return true if q is in the x range of cv
*/
bool point_in_x_range(const X_monotone_curve_2 & cv, const Point_2 & q) const
{
#if 1
Compare_x_2 compare_x = compare_x_2_object();
Construct_vertex_2 construct_vertex = construct_vertex_2_object();
Comparison_result res1 = compare_x(construct_vertex(cv, 0), q);
Comparison_result res2 = compare_x(construct_vertex(cv, 1), q);
// We check if x(p) equals the x value of one of the end-points.
// If not, we check whether one end-point is to p's left and the other is
// to its right.
return ((res1 == EQUAL) || (res2 == EQUAL) || (res1 != res2));
#else
// \todo use this code instead, after the calls it uses are supported
// in the LEDA kernel.
Compare_x_2 compare_x = compare_x_2_object();
Comparison_result res1 = compare_x(cv, 0, q);
Comparison_result res2 = compare_x(cv, 1, q);
// We check if x(p) equals the x value of one of the end-points.
// If not, we check whether one end-point is to p's left and the other is
// to its right.
return ((res1 == EQUAL) || (res2 == EQUAL) || (res1 != res2));
#endif
}
/*! curves_compare_y_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.
*/
Comparison_result curves_compare_y_at_x(const X_monotone_curve_2 & cv1,
const X_monotone_curve_2 & cv2,
const Point_2 & q) const
{
CGAL_precondition(point_in_x_range(cv1, q));
CGAL_precondition(point_in_x_range(cv2, q));
return compare_y_at_x_2_object()(q, cv1, cv2);
}
#if !defined(HAS_LEFT_NOT)
/*! curves_compare_y_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 curves_compare_y_at_x_left(const X_monotone_curve_2 & cv1,
const X_monotone_curve_2 & cv2,
const Point_2 & q) const
{
// 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();
Compare_xy_2 cmp_xy = compare_xy_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);
const Is_vertical_2 is_vertical = is_vertical_2_object();
);
CGAL_precondition((cmp_xy(source1, q) == SMALLER) ||
(cmp_xy(target1, q) == SMALLER));
CGAL_precondition((cmp_xy(source1, q) != SMALLER) ||
(cmp_xy(target1, q) != SMALLER));
CGAL_precondition((cmp_xy(source2, q) == SMALLER) ||
(cmp_xy(target2, q) == SMALLER));
CGAL_precondition((cmp_xy(source2, q) != SMALLER) ||
(cmp_xy(target2, q) != SMALLER));
// Since the curves are continuous, if they are not equal at q, the same
// result also applies to q's left.
CGAL_precondition((is_vertical(cv1) && has_on_2_object()(cv1, q)) ||
(is_vertical(cv2) && has_on_2_object()(cv2, q)) ||
(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_monotone_curve_2
curve_reflect_in_x_and_y(const X_monotone_curve_2 & cv) const
{
X_monotone_curve_2 reflected_cv(point_reflect_in_x_and_y(cv.source()),
point_reflect_in_x_and_y(cv.target()));
return reflected_cv;
}
#endif
/*! curves_compare_y_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 curves_compare_y_at_x_right(const X_monotone_curve_2 & cv1,
const X_monotone_curve_2 & cv2,
const Point_2 & q) const
{
// 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();
Compare_xy_2 cmp_xy = compare_xy_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((cmp_xy(q, source1) == SMALLER)||
(cmp_xy(q, target1) == SMALLER));
CGAL_precondition((cmp_xy(q, source1) != SMALLER) |
(cmp_xy(q, target1) != SMALLER));
CGAL_precondition((cmp_xy(q, source2) == SMALLER) ||
(cmp_xy(q, target2) == SMALLER));
CGAL_precondition((cmp_xy(q, source2) != SMALLER) ||
(cmp_xy(q, target2) != SMALLER));
// Since the curves are continuous, if they are not equal at q, the same
// result also applies to q's left.
CGAL_precondition((is_vertical_2_object()(cv1) &&
has_on_2_object()(cv1, q)) ||
(is_vertical_2_object()(cv2) &&
has_on_2_object()(cv2, q)) ||
(compare_y_at_x_2_object()(q, cv1, cv2) == 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 location of the given point with respect to the input curve.
* \param cv The curve.
* \param p The point.
* \pre p is in the x-range of cv.
* \return SMALLER if y(p) < cv(x(p)), that is the point is below the curve;
* LARGER if y(p) > cv(x(p)), that is the point is above the curve;
* or else (if p is on the curve) EQUAL.
*/
Comparison_result curve_compare_y_at_x (const Point_2 & p,
const X_monotone_curve_2 & cv) const
{
CGAL_precondition(point_in_x_range(cv, p));
return compare_y_at_x_2_object()(p, cv);
}
/*! Check if the two curves are the same (have the same graph).
* \param cv1 The first curve.
* \param cv2 The second curve.
* \return (true) if the two curves are the same.
*/
bool curve_equal(const X_monotone_curve_2 & cv1,
const X_monotone_curve_2 & cv2) const
{
Equal_2 equal = equal_2_object();
const X_monotone_curve_2 & ocv1 =
construct_opposite_segment_2_object()(cv1);
return equal(cv1, cv2) || equal(ocv1, cv2);
}
/*! Check if the two points are the same.
* \param p1 The first point.
* \param p2 The second point.
* \return (true) if p1 == p2.
*/
bool point_equal(const Point_2 & p1, const Point_2 & p2) const
{ return equal_2_object()(p1, p2); }
/*! Get the curve source.
* \param cv The curve.
* \return The source point.
*/
Point_2 curve_source(const X_monotone_curve_2 & cv) const
{ return construct_vertex_2_object()(cv, 0); }
/*! Get the curve target.
* \param cv The curve.
* \return The target point.
*/
Point_2 curve_target(const X_monotone_curve_2 & cv) const
{ return construct_vertex_2_object()(cv, 1); }
};
CGAL_END_NAMESPACE
#endif
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