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// Copyright (c) 2006 Fernando Luis Cacciola Carballal. All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1.1/Straight_skeleton_2/include/CGAL/constructions/Polygon_offset_cons_ftC2.h $
// $Id: include/CGAL/constructions/Polygon_offset_cons_ftC2.h 08b27d3db14 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s) : Fernando Cacciola <fernando_cacciola@ciudad.com.ar>
//
#ifndef CGAL_POLYGON_OFFSET_CONS_FTC2_H
#define CGAL_POLYGON_OFFSET_CONS_FTC2_H 1
#include <CGAL/license/Straight_skeleton_2.h>
#include <CGAL/constructions/Straight_skeleton_cons_ftC2.h>
#include <optional>
namespace CGAL {
namespace CGAL_SS_i {
// Given an offset distance 't' and 2 oriented line segments e0 and e1, returns the coordinates (x,y)
// of the intersection of their offsets at the given distance.
//
// PRECONDITIONS:
// The line coefficients must be normalized: a²+b²==1 and (a,b) being the leftward normal vector
// The offsets at the given distance do intersect in a single point.
//
// POSTCONDITION: In case of overflow an empty optional is returned.
//
template<class K, class Caches>
std::optional< typename K::Point_2 >
construct_offset_pointC2 ( typename K::FT const& t,
Segment_2_with_ID<K> const& e0,
typename K::FT const& w0,
Segment_2_with_ID<K> const& e1,
typename K::FT const& w1,
Trisegment_2_ptr< Trisegment_2<K, Segment_2_with_ID<K> > > const& tri,
Caches& aCaches)
{
typedef typename K::FT FT ;
typedef typename K::Point_2 Point_2 ;
typedef typename K::Line_2 Line_2 ;
typedef std::optional<Point_2> Optional_point_2 ;
typedef std::optional<Line_2> Optional_line_2 ;
FT x(0.0),y(0.0) ;
CGAL_STSKEL_TRAITS_TRACE("Constructing offset point for t=" << t ) ;
CGAL_STSKEL_TRAITS_TRACE("Edges e0=" << s2str(e0) << "w = " << w0 ) ;
CGAL_STSKEL_TRAITS_TRACE(" e1=" << s2str(e1) << "w = " << w1 ) ;
CGAL_STSKEL_TRAITS_TRACE("Event:\n" << tri);
Optional_line_2 l0 = compute_normalized_line_coeffC2(e0, aCaches) ;
Optional_line_2 l1 = compute_normalized_line_coeffC2(e1, aCaches) ;
bool ok = false ;
if ( l0 && l1 )
{
FT den = l1->a() * l0->b() - l0->a() * l1->b() ;
if ( CGAL_NTS is_finite(den) )
{
if ( ! CGAL_NTS is_zero(den) )
{
FT numX = t * l1->b() / w0 - t * l0->b() / w1 + l0->b() * l1->c() - l1->b() * l0->c() ;
FT numY = t * l1->a() / w0 - t * l0->a() / w1 + l0->a() * l1->c() - l1->a() * l0->c() ;
x = -numX / den ;
y = numY / den ;
ok = CGAL_NTS is_finite(x) && CGAL_NTS is_finite(y) ;
}
else
{
CGAL_STSKEL_TRAITS_TRACE(" DEGENERATE case: Collinear segments involved. Seed event " << ( !tri ? " ABSENT" : " exists." ) ) ;
Optional_point_2 q = tri ? construct_offset_lines_isecC2(tri, aCaches)
: compute_oriented_midpoint(e0,e1) ;
if ( q )
{
CGAL_STSKEL_TRAITS_TRACE(" Seed point: " << p2str(*q) ) ;
FT px, py ;
line_project_pointC2(l0->a(),l0->b(),l0->c(),q->x(),q->y(),px,py);
CGAL_STSKEL_TRAITS_TRACE(" Projected seed point: (" << px << "," << py << ")" ) ;
// When reformulating the progression of the front using the line orthogonal
// to the input segment, the speed (weight) becomes inverted: a large weight
// in the coefficients of the line means the front moves slower
x = px + t * l0->a() / w0 ;
y = py + t * l0->b() / w0 ;
ok = CGAL_NTS is_finite(x) && CGAL_NTS is_finite(y) ;
}
}
}
}
CGAL_STSKEL_TRAITS_TRACE(" RESULT: (" << x << "," << y << ")" << ( ok ? "" : " NONE really" ) ) ;
return cgal_make_optional(ok,K().construct_point_2_object()(x,y)) ;
}
} // namespace CGAL_SS_i
} // end namespace CGAL
#endif // CGAL_POLYGON_OFFSET_CONS_FTC2_H //
// EOF //
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