Boost ::几何联合简化 - 它是如何工作的？

Question

Boost中有很好的几何图形库。它还允许绘制SVG图像。我想在我的某个项目中使用它，但它对我来说真的很奇怪（见下图）。

所以我们在2d空间中有3个像素点表示为方形poligons

 1 1
 0 1

pic 1

我们希望从他们那里得到一个联合并简化它，这样当我们缩放它时，我们会得到一个像

这样的三角形

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

但我们得到了这个：

其中黄色虚线为联合，绿色为简化。

源码：

#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 );
}

至少需要来自boost/geometry/extensions/io/svg/

的1.47.0和3个文件

那么如何让它简化，就像我想要形成像pic 2一样的形状？

更新

创建新代码，正常运行，经过充分测试：

#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 );
}

此代码创建了这样的图像：

对于3分，它会返回相似的图像@J. Calleja回答：

Answer 1

我认为代码有几个问题：

• 您定义的多边形是：

  

1 1
    1 0

那是：

three two
one    -

因此预期结果与pic2不同。

• 多边形应该关​​闭，顺时针方向。

您缺少关闭点，第三个多边形不是顺时针方向。看一下correct方法。在此示例中，您应该为您定义的每个多边形调用它。

• 使用 _union 时，不能对输入和输出使用相同的参数。

您应该使用临时变量：

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

• 您的预期结果可能不是算法结果。

执行更正的代码后，结果为：

这可能是多边形的有效简化。请参阅Ramer–Douglas–Peucker algorithm。

执行这些修改后，下面是生成的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 ); 
}