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Added support for boundary conditions

This commit is contained in:
Efi Fogel 2013-07-21 15:49:56 +03:00
parent 58b8ecd090
commit c935bfb236
1 changed files with 437 additions and 19 deletions
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456
Arrangement_on_surface_2/include/CGAL/Arr_polyline_traits_2.h
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@ -39,9 +39,10 @@
#include <CGAL/basic.h>
#include <CGAL/tags.h>
#include <CGAL/Arr_tags.h>
#include <CGAL/Arr_segment_traits_2.h>
#include <CGAL/Arr_geometry_traits/Polyline_2.h>
#include <CGAL/Arr_tags.h>
#include <CGAL/Arr_enums.h>
namespace CGAL {
@ -55,16 +56,16 @@ namespace CGAL {
typedef Tag_true Has_merge_category;
typedef Tag_false Has_do_intersect_category;
typedef Arr_oblivious_side_tag Left_side_category;
typedef Arr_oblivious_side_tag Bottom_side_category;
typedef Arr_oblivious_side_tag Top_side_category;
typedef Arr_oblivious_side_tag Right_side_category;
typedef typename Segment_traits_2::Left_side_category Left_side_category;
typedef typename Segment_traits_2::Bottom_side_category Bottom_side_category;
typedef typename Segment_traits_2::Top_side_category Top_side_category;
typedef typename Segment_traits_2::Right_side_category Right_side_category;
private:
typedef Arr_polyline_traits_2<Segment_traits_2> Self;
// Data members:
const Segment_traits_2* m_seg_traits; // The base segment-traits class.
const Segment_traits_2* m_seg_traits; // The base segment-traits class.
bool m_own_traits;
private:
@ -283,8 +284,7 @@ namespace CGAL {
const X_monotone_curve_2& cv) const
{
// Get the index of the segment in cv containing p.
unsigned int i = // What is a smart way to call _locate()?
m_poly_traits.locate(cv, p);
unsigned int i = m_poly_traits.locate(cv, p);
CGAL_precondition(i != INVALID_INDEX);
// Compare the segment cv[i] and p.
@ -326,8 +326,8 @@ namespace CGAL {
{
// Get the indices of the segments in cv1 and cv2 containing p and
// defined to its left.
unsigned int i1=m_poly_traits.locate_side(cv1, p, false);
unsigned int i2=m_poly_traits.locate_side(cv2, p, false);
unsigned int i1 = m_poly_traits.locate_side(cv1, p, false);
unsigned int i2 = m_poly_traits.locate_side(cv2, p, false);
CGAL_precondition(i1 != INVALID_INDEX);
CGAL_precondition(i2 != INVALID_INDEX);
@ -1172,10 +1172,139 @@ namespace CGAL {
class Intersect_2 {
protected:
typedef typename Arr_are_all_sides_oblivious_tag<
Left_side_category, Bottom_side_category,
Top_side_category, Right_side_category >::result
Are_all_sides_oblivious_tag;
typedef Arr_polyline_traits_2<Segment_traits_2> Geometry_traits_2;
/*! The polyline traits (in case it has state) */
const Geometry_traits_2& m_poly_traits;
Comparison_result compare_xy_max_impl(const X_monotone_segment_2& s1,
const X_monotone_segment_2& s2,
Arr_all_sides_oblivious_tag) const
{
const Segment_traits_2* seg_traits = m_poly_traits.segment_traits_2();
typename Segment_traits_2::Construct_max_vertex_2 max_vertex =
seg_traits->construct_max_vertex_2_object();
typename Segment_traits_2::Compare_xy_2 compare_xy =
seg_traits->compare_xy_2_object();
return compare_xy(max_vertex(s1), max_vertex(s2));
}
Comparison_result compare_xy_max_impl(const X_monotone_segment_2& s1,
const X_monotone_segment_2& s2,
Arr_not_all_sides_oblivious_tag)
const
{
const Segment_traits_2* seg_traits = m_poly_traits.segment_traits_2();
typename Segment_traits_2::Parameter_space_in_x_2 ps_x =
seg_traits->parameter_space_in_x_2_object();
typename Segment_traits_2::Parameter_space_in_y_2 ps_y =
seg_traits->parameter_space_in_y_2_object();
const Arr_parameter_space ps_x1 = ps_x(s1, ARR_MAX_END);
const Arr_parameter_space ps_y1 = ps_y(s1, ARR_MAX_END);
const Arr_parameter_space ps_x2 = ps_x(s2, ARR_MAX_END);
const Arr_parameter_space ps_y2 = ps_y(s2, ARR_MAX_END);
CGAL_assertion(ps_x1 != ARR_LEFT_BOUNDARY);
CGAL_assertion(ps_x2 != ARR_LEFT_BOUNDARY);
if (ps_x1 == ARR_INTERIOR) {
if (ps_x2 == ARR_INTERIOR) {
// EFEF: This is for the Sphere only
if (ps_y1 == ARR_INTERIOR) {
typename Segment_traits_2::Construct_max_vertex_2 max_vertex =
seg_traits->construct_max_vertex_2_object();
const Point_2& p1 = max_vertex(s1);
if (ps_y2 == ARR_INTERIOR)
return seg_traits->compare_xy_2_object()(p1, max_vertex(s2));
// ps_y1 == ARR_INTERIOR
// ps_y2 != ARR_INTERIOR
return
seg_traits->compare_x_on_boundary_2_object()(p1, s2,
ARR_MAX_END);
}
// ps_y1 != ARR_INTERIOR
if (ps_y2 == ARR_INTERIOR) {
typename Segment_traits_2::Construct_max_vertex_2 max_vertex =
seg_traits->construct_max_vertex_2_object();
const Point_2& p2 = max_vertex(s2);
typename Segment_traits_2::Compare_x_on_boundary_2 compare =
seg_traits->compare_x_on_boundary_2_object();
return opposite(compare(p2, s1, ARR_MAX_END));
}
// ps_y1 != ARR_INTERIOR
// ps_y2 != ARR_INTERIOR
return
seg_traits->compare_x_on_boundary_2_object()(s1, ARR_MAX_END,
s2, ARR_MAX_END);
}
return SMALLER;
}
// x1 right
if (ps_x2 == ARR_INTERIOR) return LARGER;
typename Segment_traits_2::Construct_max_vertex_2 max_vertex =
seg_traits->construct_max_vertex_2_object();
return seg_traits->compare_y_on_boundary_2_object()(max_vertex(s1),
max_vertex(s2));
}
Comparison_result compare_y_at_x_max_impl(const X_monotone_segment_2& s1,
const X_monotone_segment_2& s2,
Arr_all_sides_oblivious_tag)
const
{
const Segment_traits_2* seg_traits = m_poly_traits.segment_traits_2();
typename Segment_traits_2::Construct_max_vertex_2 max_vertex =
seg_traits->construct_max_vertex_2_object();
typename Segment_traits_2::Compare_y_at_x_2 compare =
seg_traits->compare_y_at_x_2_object();
return compare(max_vertex(s1), s2);
}
Comparison_result compare_y_at_x_max_impl(const X_monotone_segment_2& s1,
const X_monotone_segment_2& s2,
Arr_not_all_sides_oblivious_tag)
const
{
const Segment_traits_2* seg_traits = m_poly_traits.segment_traits_2();
typename Segment_traits_2::Parameter_space_in_x_2 ps_x =
seg_traits->parameter_space_in_x_2_object();
typename Segment_traits_2::Parameter_space_in_y_2 ps_y =
seg_traits->parameter_space_in_y_2_object();
typename Segment_traits_2::Construct_max_vertex_2 max_vertex =
seg_traits->construct_max_vertex_2_object();
typename Segment_traits_2::Construct_min_vertex_2 min_vertex =
seg_traits->construct_min_vertex_2_object();
const Arr_parameter_space ps_x1 = ps_x(s1, ARR_MAX_END);
const Arr_parameter_space ps_y1 = ps_y(s1, ARR_MAX_END);
CGAL_assertion(ps_x1 != ARR_LEFT_BOUNDARY);
if (ps_x1 == ARR_INTERIOR) {
if (ps_y1 == ARR_TOP_BOUNDARY) {
typename Segment_traits_2::Equal_2 equal =
seg_traits->equal_2_object();
if (equal(max_vertex(s1), max_vertex(s2))) return EQUAL;
if (equal(max_vertex(s1), min_vertex(s2))) return EQUAL;
return LARGER;
}
if (ps_y1 == ARR_BOTTOM_BOUNDARY) {
typename Segment_traits_2::Equal_2 equal =
seg_traits->equal_2_object();
if (equal(max_vertex(s1), max_vertex(s2))) return EQUAL;
if (equal(max_vertex(s1), min_vertex(s2))) return EQUAL;
return SMALLER;
}
// ps_y1 == ARR_INTERIOR
return seg_traits->compare_y_at_x_2_object()(max_vertex(s1), s2);
}
// ps_x1 == ARR_RIGHT_BOUNDARY
return seg_traits->compare_y_on_boundary_2_object()(max_vertex(s1),
max_vertex(s2));
}
public:
/*! Constructor. */
Intersect_2(const Geometry_traits_2& traits) : m_poly_traits(traits) {}
@ -1191,7 +1320,7 @@ namespace CGAL {
* \param oi The output iterator.
* \return The past-the-end iterator.
*/
template<class OutputIterator>
template <typename OutputIterator>
OutputIterator operator()(const X_monotone_curve_2& cv1,
const X_monotone_curve_2& cv2,
OutputIterator oi) const
@ -1238,7 +1367,7 @@ namespace CGAL {
((dir1 == LARGER) && (i1 == 0))){
// cv1's right endpoint equals cv2's left endpoint
// Thus we can return this single(!) intersection point
std::pair<Point_2,Multiplicity> p(max_vertex(cv1[i1]), 0);
std::pair<Point_2, Multiplicity> p(max_vertex(cv1[i1]), 0);
*oi++ = make_object(p);
return oi;
}
@ -1258,7 +1387,7 @@ namespace CGAL {
((dir2 == LARGER) && (i2 == 0))){
// cv2's right endpoint equals cv1's left endpoint
// Thus we can return this single(!) intersection point
std::pair<Point_2,Multiplicity> p(max_vertex(cv2[i2]), 0);
std::pair<Point_2, Multiplicity> p(max_vertex(cv2[i2]), 0);
*oi++ = make_object(p);
return oi;
}
@ -1292,15 +1421,20 @@ namespace CGAL {
((dir1!=SMALLER) && (dir2 != SMALLER) && (i1 >= 0) &&(i2 >= 0)&&
(i1 != INVALID_INDEX) && (i2 != INVALID_INDEX)))
{
right_res = compare_xy(max_vertex(cv1[i1]), max_vertex(cv2[i2]));
right_res = compare_xy_max_impl(cv1[i1], cv2[i2],
Are_all_sides_oblivious_tag());
right_coincides = (right_res == EQUAL);
if (right_res == SMALLER)
right_coincides = (compare_y_at_x(max_vertex(cv1[i1]),
cv2[i2]) == EQUAL);
right_coincides =
(compare_y_at_x_max_impl(cv1[i1], cv2[i2],
Are_all_sides_oblivious_tag()) ==
EQUAL);
else if (right_res == LARGER)
right_coincides = (compare_y_at_x(max_vertex(cv2[i2]),
cv1[i1]) == EQUAL);
right_coincides =
(compare_y_at_x_max_impl(cv2[i2], cv1[i1],
Are_all_sides_oblivious_tag()) ==
EQUAL);
right_overlap = false;
@ -1934,6 +2068,291 @@ namespace CGAL {
{ return Construct_x_monotone_curve_2(*this); }
//@}
/*! A function object that obtains the parameter space of a geometric
* entity along the x-axis
*/
class Parameter_space_in_x_2 {
protected:
typedef Arr_polyline_traits_2<Segment_traits_2> Geometry_traits_2;
/*! The polyline traits (in case it has state) */
const Geometry_traits_2& m_poly_traits;
public:
/*! Constructor. */
Parameter_space_in_x_2(const Geometry_traits_2& traits) :
m_poly_traits(traits)
{}
/*! Obtains the parameter space at the end of an arc along the x-axis .
* Note that if the arc end coincides with a pole, then unless the arc
* coincides with the identification arc, the arc end is considered to
* be approaching the boundary, but not on the boundary.
* If the arc coincides with the identification arc, it is assumed to
* be smaller than any other object.
* \param xcv the arc
* \param ce the arc end indicator:
* ARR_MIN_END - the minimal end of xc or
* ARR_MAX_END - the maximal end of xc
* \return the parameter space at the ce end of the arc xcv.
* ARR_LEFT_BOUNDARY - the arc approaches the identification arc from
* the right at the arc left end.
* ARR_INTERIOR - the arc does not approache the identification arc.
* ARR_RIGHT_BOUNDARY - the arc approaches the identification arc from
* the left at the arc right end.
* \pre xcv does not coincide with the vertical identification arc.
*/
Arr_parameter_space operator()(const X_monotone_curve_2& xcv,
Arr_curve_end ce) const
{
const Segment_traits_2* seg_traits = m_poly_traits.segment_traits_2();
Comparison_result direction =
seg_traits->compare_endpoints_xy_2_object()(xcv[0]);
const X_monotone_segment_2& xs =
(((direction == SMALLER) && (ce == ARR_MAX_END)) ||
((direction == LARGER) && (ce == ARR_MIN_END))) ?
xcv[0] : xcv[xcv.number_of_segments()-1];
return seg_traits->parameter_space_in_x_2_object()(xs, ce);
}
/*! Obtains the parameter space at a point along the x-axis.
* \param p the point.
* \return the parameter space at p.
* \pre p does not lie on the vertical identification curve.
*/
Arr_parameter_space operator()(const Point_2 p) const
{
const Segment_traits_2* seg_traits = m_poly_traits.segment_traits_2();
return seg_traits->parameter_space_in_x_2_object()(p);
}
};
/*! Obtain a Parameter_space_in_x_2 function object */
Parameter_space_in_x_2 parameter_space_in_x_2_object() const
{ return Parameter_space_in_x_2(*this); }
/*! A function object that obtains the parameter space of a geometric
* entity along the y-axis
*/
class Parameter_space_in_y_2 {
protected:
typedef Arr_polyline_traits_2<Segment_traits_2> Geometry_traits_2;
/*! The polyline traits (in case it has state) */
const Geometry_traits_2& m_poly_traits;
public:
/*! Constructor. */
Parameter_space_in_y_2(const Geometry_traits_2& traits) :
m_poly_traits(traits)
{}
/*! Obtains the parameter space at the end of an arc along the y-axis .
* Note that if the arc end coincides with a pole, then unless the arc
* coincides with the identification arc, the arc end is considered to
* be approaching the boundary, but not on the boundary.
* If the arc coincides with the identification arc, it is assumed to
* be smaller than any other object.
* \param xcv the arc
* \param ce the arc end indicator:
* ARR_MIN_END - the minimal end of xc or
* ARR_MAX_END - the maximal end of xc
* \return the parameter space at the ce end of the arc xcv.
* ARR_BOTTOM_BOUNDARY - the arc approaches the south pole at the arc
* left end.
* ARR_INTERIOR - the arc does not approache a contraction point.
* ARR_TOP_BOUNDARY - the arc approaches the north pole at the arc
* right end.
* There are no horizontal identification arcs!
*/
Arr_parameter_space operator()(const X_monotone_curve_2& xcv,
Arr_curve_end ce) const
{
const Segment_traits_2* seg_traits = m_poly_traits.segment_traits_2();
Comparison_result direction =
seg_traits->compare_endpoints_xy_2_object()(xcv[0]);
const X_monotone_segment_2& xs =
(((direction == SMALLER) && (ce == ARR_MAX_END)) ||
((direction == LARGER) && (ce == ARR_MIN_END))) ?
xcv[0] : xcv[xcv.number_of_segments()-1];
return seg_traits->parameter_space_in_y_2_object()(xs, ce);
}
/*! Obtains the parameter space at a point along the y-axis.
* \param p the point.
* \return the parameter space at p.
* \pre p does not lie on the horizontal identification curve.
* There are no horizontal identification arcs!
*/
Arr_parameter_space operator()(const Point_2 p) const
{
const Segment_traits_2* seg_traits = m_poly_traits.segment_traits_2();
return seg_traits->parameter_space_in_y_2_object()(p);
}
};
/*! Obtain a Parameter_space_in_y_2 function object */
Parameter_space_in_y_2 parameter_space_in_y_2_object() const
{ return Parameter_space_in_y_2(*this); }
/*! A functor that compares the x-coordinate of arc ends and points on the
* boundary of the parameter space.
*/
class Compare_x_on_boundary_2 {
protected:
typedef Arr_polyline_traits_2<Segment_traits_2> Geometry_traits_2;
/*! The polyline traits (in case it has state) */
const Geometry_traits_2& m_poly_traits;
public:
/*! Constructor. */
Compare_x_on_boundary_2(const Geometry_traits_2& traits) :
m_poly_traits(traits)
{}
/*! Compare the x-limit of a point with the x-coordinate of an
* x-curve end on the boundary.
* \param point the point.
* \param xcv the x-curve, the endpoint of which is compared.
* \param ce the x-curve-end indicator -
* ARR_MIN_END - the minimal end of xc or
* ARR_MAX_END - the maximal end of xc.
* \return the comparison result:
* SMALLER - x(p) < x(xc, ce);
* EQUAL - x(p) = x(xc, ce);
* LARGER - x(p) > x(xc, ce).
* \pre p lies in the interior of the parameter space.
* \pre the ce end of the x-curve xcv lies on the top boundary.
* \pre xcv does not coincide with the vertical identification curve.
*/
Comparison_result operator()(const Point_2& point,
const X_monotone_curve_2& xcv,
Arr_curve_end ce) const
{
const Segment_traits_2* seg_traits =
m_poly_traits.segment_traits_2();
Comparison_result direction =
seg_traits->compare_endpoints_xy_2_object()(xcv[0]);
const X_monotone_segment_2& xs =
(((direction == SMALLER) && (ce == ARR_MAX_END)) ||
((direction == LARGER) && (ce == ARR_MIN_END))) ?
xcv[0] : xcv[xcv.number_of_segments()-1];
return seg_traits->compare_x_on_boundary_2_object()(point, xs, ce);
}
/*! Compare the x-coordinates of 2 arc ends near the boundary of the
* parameter space.
* \param xcv1 the first arc.
* \param ce1 the first arc end indicator -
* ARR_MIN_END - the minimal end of xcv1 or
* ARR_MAX_END - the maximal end of xcv1.
* \param xcv2 the second arc.
* \param ce2 the second arc end indicator -
* ARR_MIN_END - the minimal end of xcv2 or
* ARR_MAX_END - the maximal end of xcv2.
* \return the second comparison result:
* SMALLER - x(xcv1, ce1) < x(xcv2, ce2);
* EQUAL - x(xcv1, ce1) = x(xcv2, ce2);
* LARGER - x(xcv1, ce1) > x(xcv2, ce2).
* \pre the ce1 end of the arc xcv1 lies on a pole (implying ce1 is
* vertical).
* \pre the ce2 end of the arc xcv2 lies on a pole (implying ce2 is
* vertical).
* \pre xcv1 does not coincide with the vertical identification curve.
* \pre xcv2 does not coincide with the vertical identification curve.
*/
Comparison_result operator()(const X_monotone_curve_2& xcv1,
Arr_curve_end ce1,
const X_monotone_curve_2& xcv2,
Arr_curve_end ce2) const
{
const Segment_traits_2* seg_traits =
m_poly_traits.segment_traits_2();
Comparison_result direction1 =
seg_traits->compare_endpoints_xy_2_object()(xcv1[0]);
const X_monotone_segment_2& xs1 =
(((direction1 == SMALLER) && (ce1 == ARR_MAX_END)) ||
((direction1 == LARGER) && (ce1 == ARR_MIN_END))) ?
xcv1[0] : xcv1[xcv1.number_of_segments()-1];
Comparison_result direction2 =
seg_traits->compare_endpoints_xy_2_object()(xcv2[0]);
const X_monotone_segment_2& xs2 =
(((direction2 == SMALLER) && (ce2 == ARR_MAX_END)) ||
((direction2 == LARGER) && (ce2 == ARR_MIN_END))) ?
xcv2[0] : xcv2[xcv2.number_of_segments()-1];
return seg_traits->compare_x_on_boundary_2_object()(xs1, ce1, xs2, ce2);
}
};
/*! Obtain a Compare_x_on_boundary_2 function object. */
Compare_x_on_boundary_2 compare_x_on_boundary_2_object() const
{ return Compare_x_on_boundary_2(*this); }
/*! A functor that compares the y-coordinate of two given points
* that lie on the vertical identification arc.
*/
class Compare_y_on_boundary_2 {
protected:
typedef Arr_polyline_traits_2<Segment_traits_2> Geometry_traits_2;
/*! The polyline traits (in case it has state) */
const Geometry_traits_2& m_poly_traits;
public:
/*! Constructor. */
Compare_y_on_boundary_2(const Geometry_traits_2& traits) :
m_poly_traits(traits)
{}
/*! Compare the y-coordinate of two given points that lie on the vertical
* identification curve.
* \param p1 the first point.
* \param p2 the second point.
* \return SMALLER - p1 is lexicographically smaller than p2;
* EQUAL - p1 and p2 coincides;
* LARGER - p1 is lexicographically larger than p2;
* \pre p1 lies on the vertical identification arc.
* \pre p2 lies on the vertical identification arc.
*/
Comparison_result operator()(const Point_2& p1, const Point_2& p2) const
{
// EFEF: not implemented yet
CGAL_error();
return EQUAL;
}
};
/*! Obtain a Compare_y_on_boundary_2 function object */
Compare_y_on_boundary_2 compare_y_on_boundary_2_object() const
{ return Compare_y_on_boundary_2(*this); }
/*! A functor that compares the y-coordinates of arc ends near the
* boundary of the parameter space.
*/
class Compare_y_near_boundary_2 {
public:
/*! Compare the y-coordinates of 2 curves at their ends near the boundary
* of the parameter space.
* \param xcv1 the first arc.
* \param xcv2 the second arc.
* \param ce the arc end indicator.
* \return the second comparison result.
* \pre the ce ends of the arcs xcv1 and xcv2 lie either on the left
* boundary or on the right boundary of the parameter space (implying
* that they cannot be vertical).
* There is no horizontal identification curve!
*/
Comparison_result operator()(const X_monotone_curve_2& xcv1,
const X_monotone_curve_2& xcv2,
Arr_curve_end ce) const
{
// EFEF: not implemented yet
CGAL_error();
return EQUAL;
}
};
/*! Obtain a Compare_y_near_boundary_2 function object */
Compare_y_near_boundary_2 compare_y_near_boundary_2_object() const
{ return Compare_y_near_boundary_2(); }
private:
/*
* Roadmap: locate() should return an iterator to the located segment
@ -2158,7 +2577,6 @@ namespace CGAL {
}
};
} //namespace CGAL
#endif