495 lines
14 KiB
C
495 lines
14 KiB
C
|
// Copyright (c) 2005 Tel-Aviv University (Israel).
|
||
|
|
// All rights reserved.
|
||
|
|
//
|
||
|
|
// This file is part of CGAL (www.cgal.org).
|
||
|
|
// You can redistribute it and/or modify it under the terms of the GNU
|
||
|
|
// General Public License as published by the Free Software Foundation,
|
||
|
|
// either version 3 of the License, or (at your option) any later version.
|
||
|
|
//
|
||
|
|
// 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.
|
||
|
|
//
|
||
|
|
// $URL$
|
||
|
|
// $Id$
|
||
|
|
// SPDX-License-Identifier: GPL-3.0+
|
||
|
|
//
|
||
|
|
// Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
|
||
|
|
|
||
|
|
#ifndef CGAL_ENV_PLANE_TRAITS_3_H
|
||
|
|
#define CGAL_ENV_PLANE_TRAITS_3_H
|
||
|
|
|
||
|
|
#include <CGAL/license/Envelope_3.h>
|
||
|
|
|
||
|
|
|
||
|
|
#include <CGAL/basic.h>
|
||
|
|
#include <CGAL/tags.h>
|
||
|
|
#include <CGAL/representation_tags.h>
|
||
|
|
#include <CGAL/enum.h>
|
||
|
|
#include <CGAL/Arr_tags.h>
|
||
|
|
#include <CGAL/Arr_linear_traits_2.h>
|
||
|
|
#include <CGAL/number_utils.h>
|
||
|
|
#include <CGAL/Envelope_3/Envelope_base.h>
|
||
|
|
#include <CGAL/Envelope_3/Env_plane_traits_3_functions.h>
|
||
|
|
|
||
|
|
namespace CGAL {
|
||
|
|
|
||
|
|
template <class Kernel_>
|
||
|
|
class Env_plane_traits_3 : public Arr_linear_traits_2<Kernel_>
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
typedef Kernel_ Kernel;
|
||
|
|
typedef typename Kernel::FT FT;
|
||
|
|
typedef Arr_linear_traits_2<Kernel> Base;
|
||
|
|
typedef Env_plane_traits_3<Kernel> Self;
|
||
|
|
|
||
|
|
typedef typename Base::Multiplicity Multiplicity;
|
||
|
|
typedef typename Base::Point_2 Point_2;
|
||
|
|
typedef typename Base::Curve_2 Curve_2;
|
||
|
|
typedef typename Base::X_monotone_curve_2 X_monotone_curve_2;
|
||
|
|
typedef typename Kernel::Plane_3 Plane_3;
|
||
|
|
typedef typename Kernel::Vector_2 Vector_2;
|
||
|
|
typedef typename Kernel::Vector_3 Vector_3;
|
||
|
|
typedef typename Kernel::Segment_2 Segment_2;
|
||
|
|
typedef typename Kernel::Ray_2 Ray_2;
|
||
|
|
typedef typename Kernel::Line_2 Line_2;
|
||
|
|
typedef typename Kernel::Line_3 Line_3;
|
||
|
|
typedef typename Kernel::Object_3 Object_3;
|
||
|
|
typedef std::pair<Curve_2, Multiplicity> Intersection_curve;
|
||
|
|
|
||
|
|
typedef typename Base::Left_side_category Left_side_category;
|
||
|
|
typedef typename Base::Bottom_side_category Bottom_side_category;
|
||
|
|
typedef typename Base::Top_side_category Top_side_category;
|
||
|
|
typedef typename Base::Right_side_category Right_side_category;
|
||
|
|
|
||
|
|
class Is_vertical_3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
bool operator()(const Plane_3& h) const
|
||
|
|
{
|
||
|
|
return CGAL::is_zero(h.c());
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
Is_vertical_3 is_vertical_3_object() const
|
||
|
|
{
|
||
|
|
return Is_vertical_3();
|
||
|
|
}
|
||
|
|
|
||
|
|
class _Env_plane
|
||
|
|
{
|
||
|
|
protected:
|
||
|
|
Plane_3 m_plane;
|
||
|
|
Line_2 m_line;
|
||
|
|
bool m_is_all_plane; // true -> all plane, false -> halfplane
|
||
|
|
bool m_is_vert;
|
||
|
|
|
||
|
|
public:
|
||
|
|
_Env_plane()
|
||
|
|
{}
|
||
|
|
|
||
|
|
_Env_plane(const Plane_3& h) : m_plane(h),
|
||
|
|
m_is_all_plane(true)
|
||
|
|
{
|
||
|
|
Self s;
|
||
|
|
m_is_vert = s.is_vertical_3_object()(h);
|
||
|
|
}
|
||
|
|
|
||
|
|
_Env_plane(const Plane_3& h, const Line_2& l) : m_plane(h),
|
||
|
|
m_line(l),
|
||
|
|
m_is_all_plane(false),
|
||
|
|
m_is_vert(false)
|
||
|
|
{
|
||
|
|
CGAL_precondition_code(Self s);
|
||
|
|
CGAL_precondition(!s.is_vertical_3_object()(h));
|
||
|
|
}
|
||
|
|
|
||
|
|
bool is_vertical() const
|
||
|
|
{
|
||
|
|
return m_is_vert;
|
||
|
|
}
|
||
|
|
|
||
|
|
const Plane_3& plane() const
|
||
|
|
{
|
||
|
|
return m_plane;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
operator Plane_3 () const
|
||
|
|
{
|
||
|
|
return (m_plane);
|
||
|
|
}
|
||
|
|
|
||
|
|
const Line_2& line() const
|
||
|
|
{
|
||
|
|
CGAL_assertion(!m_is_all_plane);
|
||
|
|
return m_line;
|
||
|
|
}
|
||
|
|
|
||
|
|
bool is_all_plane() const
|
||
|
|
{
|
||
|
|
return m_is_all_plane;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
typedef _Env_plane Xy_monotone_surface_3;
|
||
|
|
typedef _Env_plane Surface_3;
|
||
|
|
|
||
|
|
class Make_xy_monotone_3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
|
||
|
|
template <class OutputIterator>
|
||
|
|
OutputIterator operator()(const Surface_3& s,
|
||
|
|
bool /* is_lower */,
|
||
|
|
OutputIterator o) const
|
||
|
|
{
|
||
|
|
*o++ = s;
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
Make_xy_monotone_3 make_xy_monotone_3_object() const
|
||
|
|
{
|
||
|
|
return Make_xy_monotone_3();
|
||
|
|
}
|
||
|
|
|
||
|
|
class Compare_z_at_xy_3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
|
||
|
|
Comparison_result operator()(const Point_2& p,
|
||
|
|
const Xy_monotone_surface_3& h1,
|
||
|
|
const Xy_monotone_surface_3& h2) const
|
||
|
|
{
|
||
|
|
const Plane_3& plane1 = h1.plane();
|
||
|
|
const Plane_3& plane2 = h2.plane();
|
||
|
|
Sign sign_of_c1c2 = CGAL::sign(plane1.c() * plane2.c());
|
||
|
|
Sign sign_of_expr =
|
||
|
|
CGAL::sign ((p.x()*plane1.a() + p.y()*plane1.b() +
|
||
|
|
plane1.d())*plane2.c() -
|
||
|
|
(p.x()*plane2.a() + p.y()*plane2.b() +
|
||
|
|
plane2.d())*plane1.c());
|
||
|
|
int i = -1 * static_cast<int>(sign_of_c1c2) *
|
||
|
|
static_cast<int>(sign_of_expr);
|
||
|
|
return static_cast<Comparison_result>(i);
|
||
|
|
}
|
||
|
|
|
||
|
|
Comparison_result operator()(const X_monotone_curve_2& cv,
|
||
|
|
const Xy_monotone_surface_3& h1,
|
||
|
|
const Xy_monotone_surface_3& h2) const
|
||
|
|
{
|
||
|
|
Kernel k;
|
||
|
|
Point_2 p;
|
||
|
|
if(cv.is_segment())
|
||
|
|
p = k.construct_midpoint_2_object()(cv.left(), cv.right());
|
||
|
|
else
|
||
|
|
if(cv.is_ray())
|
||
|
|
p = k.construct_point_on_2_object()(cv.ray(), 1);
|
||
|
|
else
|
||
|
|
{
|
||
|
|
CGAL_assertion(cv.is_line());
|
||
|
|
p = k.construct_point_on_2_object()(cv.line(), 1);
|
||
|
|
}
|
||
|
|
|
||
|
|
return this->operator()(p, h1, h2);
|
||
|
|
}
|
||
|
|
|
||
|
|
Comparison_result operator()(const Xy_monotone_surface_3& h1,
|
||
|
|
const Xy_monotone_surface_3& h2) const
|
||
|
|
{
|
||
|
|
CGAL_assertion(h1.is_all_plane() && h2.is_all_plane());
|
||
|
|
|
||
|
|
const Plane_3& p1 = h1.plane();
|
||
|
|
const Plane_3& p2 = h2.plane();
|
||
|
|
const FT& res = p2.d()*p1.c() - p1.d()*p2.c();
|
||
|
|
int i = static_cast<int>(CGAL::sign(p1.c()*p2.c())) *
|
||
|
|
static_cast<int>(CGAL::sign (res));
|
||
|
|
return static_cast<Comparison_result>(i);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
Compare_z_at_xy_3 compare_z_at_xy_3_object() const
|
||
|
|
{
|
||
|
|
return Compare_z_at_xy_3();
|
||
|
|
}
|
||
|
|
|
||
|
|
class Compare_z_at_xy_above_3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
Comparison_result operator()(const X_monotone_curve_2& cv,
|
||
|
|
const Xy_monotone_surface_3& h1,
|
||
|
|
const Xy_monotone_surface_3& h2) const
|
||
|
|
{
|
||
|
|
const Plane_3& plane1 = h1.plane();
|
||
|
|
const Plane_3& plane2 = h2.plane();
|
||
|
|
|
||
|
|
const FT& a1 = plane1.a(),
|
||
|
|
b1 = plane1.b(),
|
||
|
|
c1 = plane1.c();
|
||
|
|
|
||
|
|
const FT& a2 = plane2.a(),
|
||
|
|
b2 = plane2.b(),
|
||
|
|
c2 = plane2.c();
|
||
|
|
|
||
|
|
// our line is a3*x + b3*y + c3 = 0
|
||
|
|
// it is assumed that the planes intersect over this line
|
||
|
|
const Line_2& line = cv.supp_line();
|
||
|
|
const FT& a3 = line.a(),
|
||
|
|
b3 = line.b(),
|
||
|
|
c3 = line.c();
|
||
|
|
|
||
|
|
// if the line was parallel to the y-axis (i.e x = const),
|
||
|
|
// then it was enough to compare dz/dx of both planes
|
||
|
|
// for general line, we change coordinates to (v, w), preserving
|
||
|
|
// orientation, so the line is the w-axis in the new coordinates
|
||
|
|
// (i.e v = const).
|
||
|
|
//
|
||
|
|
// ( v ) = A ( x ) where A = ( a3 b3 )
|
||
|
|
// w y -b3 a3
|
||
|
|
//
|
||
|
|
// so v = a3*x + b3*y
|
||
|
|
// w = -b3*x + a3*y
|
||
|
|
// preserving orientation since detA = a3^2 +b3^2 > 0
|
||
|
|
//
|
||
|
|
// We compute the planes equations in the new coordinates
|
||
|
|
// and compare dz/dv
|
||
|
|
//
|
||
|
|
// ( x ) = A^(-1) ( v ) where A^(-1) = ( a3 -b3 ) * detA^(-1)
|
||
|
|
// y w b3 a3
|
||
|
|
// so x = (a3*v - b3*w)*(1/detA)
|
||
|
|
// y = (b3*v + a3*w)*(1/detA)
|
||
|
|
// plane1 ==> (a1a3 + b1b3)v + (b1a3 - a1b3)w + (c1z + d1)*detA = 0
|
||
|
|
// plane2 ==> (a2a3 + b2b3)v + (b2a3 - a2b3)w + (c2z + d2)*detA = 0
|
||
|
|
//
|
||
|
|
// dz/dv(1) = (-a1a3 - b1b3) / c1*detA
|
||
|
|
// dz/dv(2) = (-a2a3 - b2b3) / c2*detA
|
||
|
|
// since detA>0 we can omit it.
|
||
|
|
//
|
||
|
|
Sign s1 = CGAL_NTS sign((a2*a3+b2*b3)/c2-(a1*a3+b1*b3)/c1);
|
||
|
|
|
||
|
|
// We only need to make sure that w is in the correct direction
|
||
|
|
// (going from down to up)
|
||
|
|
// the original segment endpoints p1=(x1,y1) and p2=(x2,y2)
|
||
|
|
// are transformed to (v1,w1) and (v2,w2), so we need that w2 > w1
|
||
|
|
// (otherwise the result should be multiplied by -1)
|
||
|
|
|
||
|
|
Kernel k;
|
||
|
|
Point_2 p1 (k.construct_point_on_2_object()(line, 0));
|
||
|
|
Point_2 p2 (k.construct_point_on_2_object()(line, 1));
|
||
|
|
|
||
|
|
if(k.compare_xy_2_object()(p1, p2) == LARGER)
|
||
|
|
std::swap(p1, p2);
|
||
|
|
|
||
|
|
CGAL_assertion(k.compare_xy_2_object()(p1, p2) == SMALLER);
|
||
|
|
|
||
|
|
const FT& x1 = p1.x(),
|
||
|
|
y1 = p1.y(),
|
||
|
|
x2 = p2.x(),
|
||
|
|
y2 = p2.y();
|
||
|
|
|
||
|
|
Sign s2 = CGAL_NTS sign(-b3*x1+a3*y1-(-b3*x2+a3*y2));
|
||
|
|
return s1 * s2;
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
Compare_z_at_xy_above_3 compare_z_at_xy_above_3_object() const
|
||
|
|
{
|
||
|
|
return Compare_z_at_xy_above_3();
|
||
|
|
}
|
||
|
|
|
||
|
|
class Compare_z_at_xy_below_3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
Comparison_result operator()(const X_monotone_curve_2& cv,
|
||
|
|
const Xy_monotone_surface_3& h1,
|
||
|
|
const Xy_monotone_surface_3& h2) const
|
||
|
|
{
|
||
|
|
Compare_z_at_xy_above_3 cmp_above;
|
||
|
|
return CGAL::opposite(cmp_above(cv, h1, h2));
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
Compare_z_at_xy_below_3 compare_z_at_xy_below_3_object() const
|
||
|
|
{
|
||
|
|
return Compare_z_at_xy_below_3();
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
class Construct_projected_boundary_2
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
|
||
|
|
template <class OutputIterator>
|
||
|
|
OutputIterator operator()(const Xy_monotone_surface_3& s,
|
||
|
|
OutputIterator o) const
|
||
|
|
{
|
||
|
|
if(s.is_all_plane())
|
||
|
|
{
|
||
|
|
if(!s.is_vertical())
|
||
|
|
return o;
|
||
|
|
|
||
|
|
const Plane_3& h = s.plane();
|
||
|
|
Line_2 proj_line(h.a(), h.b(), h.d());
|
||
|
|
*o++ = make_object(std::make_pair(X_monotone_curve_2(proj_line),
|
||
|
|
ON_ORIENTED_BOUNDARY));
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
|
||
|
|
// s is half-plane
|
||
|
|
Kernel k;
|
||
|
|
const Point_2& p1 = k.construct_point_on_2_object()(s.line(), 0);
|
||
|
|
const Point_2& p2 = k.construct_point_on_2_object()(s.line(), 1);
|
||
|
|
Comparison_result res = k.compare_xy_2_object()(p1, p2);
|
||
|
|
|
||
|
|
Oriented_side side =
|
||
|
|
(res == SMALLER) ? ON_POSITIVE_SIDE : ON_NEGATIVE_SIDE;
|
||
|
|
*o++ = make_object(std::make_pair(X_monotone_curve_2(s.line()), side));
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
Construct_projected_boundary_2
|
||
|
|
construct_projected_boundary_2_object() const
|
||
|
|
{
|
||
|
|
return Construct_projected_boundary_2();
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
class Construct_projected_intersections_2
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
|
||
|
|
template <class OutputIterator>
|
||
|
|
OutputIterator operator()(const Xy_monotone_surface_3& s1,
|
||
|
|
const Xy_monotone_surface_3& s2,
|
||
|
|
OutputIterator o) const
|
||
|
|
{
|
||
|
|
Kernel k;
|
||
|
|
|
||
|
|
const Plane_3& h1 = s1.plane();
|
||
|
|
const Plane_3& h2 = s2.plane();
|
||
|
|
|
||
|
|
if(s1.is_vertical() && s2.is_vertical())
|
||
|
|
{
|
||
|
|
Line_2 l1(h1.a(), h1.b(), h1.d());
|
||
|
|
Line_2 l2(h2.a(), h2.b(), h2.d());
|
||
|
|
Object obj = k.intersect_2_object()(l1, l2);
|
||
|
|
|
||
|
|
Point_2 p;
|
||
|
|
if(assign(p, obj))
|
||
|
|
*o++ = make_object(p);
|
||
|
|
|
||
|
|
// otherwise, the vertical planes are parallel or overlap, so we return
|
||
|
|
// nothing.
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
|
||
|
|
if(s1.is_all_plane() && s2.is_all_plane())
|
||
|
|
{
|
||
|
|
Object obj = k.intersect_3_object()(h1, h2);
|
||
|
|
Line_3 l;
|
||
|
|
if(assign(l, obj))
|
||
|
|
*o++ = make_object(Intersection_curve(project_xy(l, k), 1));
|
||
|
|
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
|
||
|
|
if(s1.is_all_plane() && !s2.is_all_plane())
|
||
|
|
{
|
||
|
|
Object obj = plane_half_plane_proj_intersection(h1,
|
||
|
|
h2,
|
||
|
|
s2.line(),
|
||
|
|
k);
|
||
|
|
if(obj.is_empty())
|
||
|
|
return o;
|
||
|
|
Line_2 temp_l;
|
||
|
|
if(assign(temp_l, obj))
|
||
|
|
{
|
||
|
|
*o++ = make_object(Intersection_curve(temp_l, 1));
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
Ray_2 ray;
|
||
|
|
if(assign(ray, obj))
|
||
|
|
{
|
||
|
|
*o++ = make_object(Intersection_curve(ray, 1));
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
if(!s2.is_all_plane() && s2.is_all_plane())
|
||
|
|
{
|
||
|
|
Object obj = plane_half_plane_proj_intersection(h2,
|
||
|
|
h1,
|
||
|
|
s1.line(),
|
||
|
|
k);
|
||
|
|
if(obj.is_empty())
|
||
|
|
return o;
|
||
|
|
Line_2 line;
|
||
|
|
if(assign(line, obj))
|
||
|
|
{
|
||
|
|
*o++ = make_object(Intersection_curve(line, 1));
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
Ray_2 ray;
|
||
|
|
if(assign(ray, obj))
|
||
|
|
{
|
||
|
|
*o++ = make_object(Intersection_curve(ray, 1));
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
return o;
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
CGAL_assertion(!s2.is_all_plane() && !s2.is_all_plane());
|
||
|
|
Object obj =
|
||
|
|
half_plane_half_plane_proj_intersection(h1, s1.line(), h2, s2.line(), k);
|
||
|
|
|
||
|
|
if(obj.is_empty())
|
||
|
|
return o;
|
||
|
|
Line_2 line;
|
||
|
|
if(assign(line, obj))
|
||
|
|
{
|
||
|
|
*o++ = make_object(Intersection_curve(line, 1));
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
Ray_2 ray;
|
||
|
|
if(assign(ray, obj))
|
||
|
|
{
|
||
|
|
*o++ = make_object(Intersection_curve(ray, 1));
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
|
||
|
|
Segment_2 seg;
|
||
|
|
if(assign(seg, obj))
|
||
|
|
{
|
||
|
|
*o++ = make_object(Intersection_curve(seg, 1));
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
|
||
|
|
Point_2 p;
|
||
|
|
if(assign(p, obj))
|
||
|
|
{
|
||
|
|
*o++ = make_object(p);
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
return o;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
Construct_projected_intersections_2
|
||
|
|
construct_projected_intersections_2_object() const
|
||
|
|
{
|
||
|
|
return Construct_projected_intersections_2();
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
} //namespace CGAL
|
||
|
|
|
||
|
|
#endif
|