Boost::Geometry union simplification - how it works?

Question

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?

Update

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:

Answer 1

I think there are several problems with the code:

• The polygons you are defining are:

1 1
1 0

That is:

three two
one    -

So the expected result is different from pic2.

• Polygons should be closed, and directed clockwise.

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 cannot use the same argument for input and output when using _union.

You should use a temporary variable:

  boost::geometry::union_(one, two, outputTmp);    
  boost::geometry::union_( outputTmp, three, output);  

• Your expected result may not be the algorithm result.

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 ); 
}