There is great library for geometry in Boost. It allows also to draw SVG images. I want to use it in some project of mine but it works really strange for me (see image below).
So we have 3 pixel points represented as square poligons in 2d space
1 1
0 1
pic 1
we want to get from them a union and simplify it so that when we scale it we'd get a triangle like
1 1 1 1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
0 1 1 1 1 1
0 0 1 1 1 1
0 0 0 1 1 1
pic 2
but we get this:
where yellow doted line is union and green is simplification.
Sourcecode:
#include <iostream>
#include <fstream>
#include <boost/assign.hpp>
#include <boost/algorithm/string.hpp>
#include <boost/geometry/geometry.hpp>
#include <boost/geometry/geometries/geometries.hpp>
#include <boost/geometry/multi/geometries/multi_polygon.hpp>
#include <boost/geometry/algorithms/envelope.hpp>
#include <boost/geometry/extensions/io/svg/svg_mapper.hpp>
template <typename Geometry1, typename Geometry2>
void create_svg(std::string const& filename, Geometry1 const& a, Geometry2 const& b)
{
typedef typename boost::geometry::point_type<Geometry1>::type point_type;
std::ofstream svg(filename.c_str());
boost::geometry::svg_mapper<point_type> mapper(svg, 400, 400);
mapper.add(a);
mapper.add(b);
mapper.map(a, "fill-opacity:0.5;fill:rgb(153,204,0);stroke:rgb(153,204,0);stroke-width:2");
mapper.map(b, "opacity:0.8;fill:none;stroke:rgb(255,128,0);stroke-width:4;stroke-dasharray:1,7;stroke-linecap:round");
}
int main()
{
// create points (each point == square poligon)
boost::geometry::model::polygon<boost::geometry::model::d2::point_xy<double> > one, two, three;
boost::geometry::read_wkt(
"POLYGON((1 1, 1 0, 0 0, 0 1))", one);
boost::geometry::read_wkt(
"POLYGON((2 2, 2 1, 1 1, 1 2))", two);
boost::geometry::read_wkt(
"POLYGON((1 1, 1 2, 0 2, 0 1))", three);
// create a container for joined points structure
boost::geometry::model::multi_polygon< boost::geometry::model::polygon<boost::geometry::model::d2::point_xy<double> > > output, simpl;
// join points one by one (because one day we would have many=))
boost::geometry::union_(one, two, output);
boost::geometry::union_( output , three, output);
// simplify joined structure
boost::geometry::simplify(output, simpl, 0.5);
// create an svg image
create_svg("make_envelope.svg", simpl, output );
}
requires at least boost 1.47.0 and 3 files from boost/geometry/extensions/io/svg/
So how to make it simplify like I want meaning to get shape like pic 2
?
Created new code, works correctly, quite tested:
#include <iostream>
#include <fstream>
#include <boost/assign.hpp>
//Boost
#include <boost/algorithm/string.hpp>
#include <boost/geometry/geometry.hpp>
#include <boost/geometry/geometries/geometries.hpp>
#include <boost/geometry/multi/geometries/multi_polygon.hpp>
#include <boost/geometry/geometries/adapted/boost_tuple.hpp>
#include <boost/foreach.hpp>
//and this is why we use Boost Geometry from Boost trunk
#include <boost/geometry/extensions/io/svg/svg_mapper.hpp>
BOOST_GEOMETRY_REGISTER_BOOST_TUPLE_CS(cs::cartesian)
template <typename Geometry1, typename Geometry2>
void create_svg(std::string const& filename, Geometry1 const& a, Geometry2 const& b)
{
typedef typename boost::geometry::point_type<Geometry1>::type point_type;
std::ofstream svg(filename.c_str());
boost::geometry::svg_mapper<point_type> mapper(svg, 400, 400);
mapper.add(a);
mapper.add(b);
mapper.map(a, "fill-rule:nonzero;fill-opacity:0.5;fill:rgb(153,204,0);stroke:rgb(153,204,0);stroke-width:2;");
mapper.map(b, "opacity:0.8;fill:none;stroke:rgb(255,128,0);stroke-width:4;stroke-dasharray:1,7;stroke-linecap:round");
}
void make_point(int x, int y, boost::geometry::model::polygon<boost::geometry::model::d2::point_xy<double> > & ring)
{
using namespace boost::assign;
boost::geometry::append( ring, boost::geometry::model::d2::point_xy<double>(x-1, y-1));
boost::geometry::append( ring, boost::geometry::model::d2::point_xy<double>(x, y-1));
boost::geometry::append( ring, boost::geometry::model::d2::point_xy<double>(x, y));
boost::geometry::append( ring, boost::geometry::model::d2::point_xy<double>(x-1, y));
boost::geometry::append( ring, boost::geometry::model::d2::point_xy<double>(x-1, y-1));
boost::geometry::correct(ring);
}
void create_point(int x, int y, boost::geometry::model::multi_polygon< boost::geometry::model::polygon<boost::geometry::model::d2::point_xy<double> > > & mp)
{
boost::geometry::model::multi_polygon< boost::geometry::model::polygon<boost::geometry::model::d2::point_xy<double> > > temp;
boost::geometry::model::polygon<boost::geometry::model::d2::point_xy<double> > ring;
make_point(x, y, ring);
boost::geometry::union_(mp, ring, temp);
boost::geometry::correct(temp);
mp=temp;
}
int main()
{
using namespace boost::assign;
typedef boost::geometry::model::polygon
<
boost::geometry::model::d2::point_xy<double>
> polygon;
typedef boost::geometry::model::multi_polygon<polygon> mp;
polygon ring;
mp pol, simpl;
polygon exring;
create_point(1,1, pol);
create_point(2, 1, pol);
create_point(3, 1, pol);
create_point(4,1, pol);
create_point(5, 1, pol);
create_point(1,2, pol);
create_point(2, 2, pol);
create_point(3, 2, pol);
create_point(4,2, pol);
create_point(5, 2, pol);
create_point(2, 3, pol);
create_point(3, 3, pol);
create_point(5, 3, pol);
create_point(3, 4, pol);
create_point(5, 3, pol);
create_point(5, 5, pol);
//boost::geometry::dissolve(ring, pol); // Baad
boost::geometry::simplify(pol, simpl, 0.5); // Good
create_svg("make_envelope.svg",pol, simpl );
}
And this code creates such image:
And for 3 points it returns images alike @J. Calleja answer:
I think there are several problems with the code:
1 1
1 0
That is:
three two one -
So the expected result is different from pic2.
You are missing the closing point and the third polygon is not directed clockwise. Take a look at the correct method. On this example, you should call it for every polygon you define.
You should use a temporary variable:
boost::geometry::union_(one, two, outputTmp);
boost::geometry::union_( outputTmp, three, output);
After executing the corrected code, the result is:
This may be a valid simplifcation of your polygon. See the Ramer–Douglas–Peucker algorithm.
After performing those modifications, below is the resulting main()
int main()
{
// create points (each point == square poligon)
boost::geometry::model::polygon<boost::geometry::model::d2::point_xy<double> > one, two, three;
boost::geometry::read_wkt( "POLYGON((1 1, 1 0, 0 0, 0 1))", one);
boost::geometry::read_wkt( "POLYGON((2 2, 2 1, 1 1, 1 2))", two);
boost::geometry::read_wkt( "POLYGON((1 1, 1 2, 0 2, 0 1))", three);
boost::geometry::correct(one);
boost::geometry::correct(two);
boost::geometry::correct(three);
// create a container for joined points structure
boost::geometry::model::multi_polygon< boost::geometry::model::polygon<boost::geometry::model::d2::point_xy<double> > > outputTmp, output, simpl;
// join points one by one (because one day we would have many=))
boost::geometry::union_(one, two, outputTmp);
boost::geometry::union_( outputTmp, three, output);
// simplify joined structure
boost::geometry::simplify(output, simpl, 0.5);
// create an svg image
create_svg("make_envelope.svg", simpl, output );
}
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