\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Straight Skeleton and Polygon Offsetting

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Straight_skeleton_2/Low_level_API.cpp
#include<vector>
#include<iterator>
#include<iostream>
#include<iomanip>
#include<string>
#include<boost/shared_ptr.hpp>
#include<CGAL/Polygon_2.h>
#include<CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include<CGAL/Straight_skeleton_builder_2.h>
#include<CGAL/Polygon_offset_builder_2.h>
#include<CGAL/compute_outer_frame_margin.h>
#include "print.h"
//
// This example illustrates how to use the CGAL Straight Skeleton package
// to construct an offset contour on the outside of a polygon
//
// This is the recommended kernel
typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
typedef Kernel::Point_2 Point_2;
typedef CGAL::Polygon_2<Kernel> Contour;
typedef boost::shared_ptr<Contour> ContourPtr;
typedef std::vector<ContourPtr> ContourSequence ;
typedef CGAL::Straight_skeleton_2<Kernel> Ss;
typedef Ss::Halfedge_iterator Halfedge_iterator;
typedef Ss::Halfedge_handle Halfedge_handle;
typedef Ss::Vertex_handle Vertex_handle;
typedef CGAL::Straight_skeleton_builder_traits_2<Kernel> SsBuilderTraits;
typedef CGAL::Straight_skeleton_builder_2<SsBuilderTraits,Ss> SsBuilder;
typedef CGAL::Polygon_offset_builder_traits_2<Kernel> OffsetBuilderTraits;
typedef CGAL::Polygon_offset_builder_2<Ss,OffsetBuilderTraits,Contour> OffsetBuilder;
int main()
{
// A start-shaped polygon, oriented counter-clockwise as required for outer contours.
Point_2 pts[] = { Point_2(-1,-1)
, Point_2(0,-12)
, Point_2(1,-1)
, Point_2(12,0)
, Point_2(1,1)
, Point_2(0,12)
, Point_2(-1,1)
, Point_2(-12,0)
} ;
std::vector<Point_2> star(pts,pts+8);
// We want an offset contour in the outside.
// Since the package doesn't support that operation directly, we use the following trick:
// (1) Place the polygon as a hole of a big outer frame.
// (2) Construct the skeleton on the interior of that frame (with the polygon as a hole)
// (3) Construc the offset contours
// (4) Identify the offset contour that corresponds to the frame and remove it from the result
double offset = 3 ; // The offset distance
// First we need to determine the proper separation between the polygon and the frame.
// We use this helper function provided in the package.
boost::optional<double> margin = CGAL::compute_outer_frame_margin(star.begin(),star.end(),offset);
// Proceed only if the margin was computed (an extremely sharp corner might cause overflow)
if ( margin )
{
// Get the bbox of the polygon
CGAL::Bbox_2 bbox = CGAL::bbox_2(star.begin(),star.end());
// Compute the boundaries of the frame
double fxmin = bbox.xmin() - *margin ;
double fxmax = bbox.xmax() + *margin ;
double fymin = bbox.ymin() - *margin ;
double fymax = bbox.ymax() + *margin ;
// Create the rectangular frame
Point_2 frame[4]= { Point_2(fxmin,fymin)
, Point_2(fxmax,fymin)
, Point_2(fxmax,fymax)
, Point_2(fxmin,fymax)
} ;
// Instantiate the skeleton builder
SsBuilder ssb ;
// Enter the frame
ssb.enter_contour(frame,frame+4);
// Enter the polygon as a hole of the frame (NOTE: as it is a hole we insert it in the opposite orientation)
ssb.enter_contour(star.rbegin(),star.rend());
// Construct the skeleton
boost::shared_ptr<Ss> ss = ssb.construct_skeleton();
// Proceed only if the skeleton was correctly constructed.
if ( ss )
{
print_straight_skeleton(*ss);
// Instantiate the container of offset contours
ContourSequence offset_contours ;
// Instantiate the offset builder with the skeleton
OffsetBuilder ob(*ss);
// Obtain the offset contours
ob.construct_offset_contours(offset, std::back_inserter(offset_contours));
// Locate the offset contour that corresponds to the frame
// That must be the outmost offset contour, which in turn must be the one
// with the largetst unsigned area.
ContourSequence::iterator f = offset_contours.end();
double lLargestArea = 0.0 ;
for (ContourSequence::iterator i = offset_contours.begin(); i != offset_contours.end(); ++ i )
{
double lArea = CGAL_NTS abs( (*i)->area() ) ; //Take abs() as Polygon_2::area() is signed.
if ( lArea > lLargestArea )
{
f = i ;
lLargestArea = lArea ;
}
}
// Remove the offset contour that corresponds to the frame.
offset_contours.erase(f);
print_polygons(offset_contours);
}
}
return 0;
}