### Include Boost.Geometry headers and use namespace

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/quickstart

Basic setup for using Boost.Geometry library. Include the main header and geometry-specific headers for point and polygon types, then use the boost::geometry namespace. Boost.Geometry is header-only, requiring no library linking.

```cpp
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp>
#include <boost/geometry/geometries/polygon.hpp>

using namespace boost::geometry;
```

--------------------------------

### Boost.Geometry R-tree Setup and Includes (C++)

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/spatial_indexes/rtree_quickstart

This snippet includes the necessary Boost.Geometry headers for R-tree operations, defining common namespaces and data structures. It sets up the foundation for spatial indexing by including point, box, and R-tree specific headers, along with utilities for output and storing query results.

```cpp
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point.hpp>
#include <boost/geometry/geometries/box.hpp>

#include <boost/geometry/index/rtree.hpp>

// to store queries results
#include <vector>

// just for output
#include <iostream>
#include <boost/foreach.hpp>

namespace bg = boost::geometry;
namespace bgi = boost::geometry::index;

```

--------------------------------

### Register Boost.Tuple as point type

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/quickstart

Register Boost.Tuple coordinate system with Boost.Geometry to use tuples as point objects. Enables seamless integration of Boost.Tuple with geometry algorithms.

```cpp
#include <boost/geometry/geometries/adapted/boost_tuple.hpp>

BOOST_GEOMETRY_REGISTER_BOOST_TUPLE_CS(cs::cartesian)
```

--------------------------------

### Boost.Geometry R-tree Data Insertion (C++)

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/spatial_indexes/rtree_quickstart

Populates the R-tree by creating and inserting several box-value pairs. This example illustrates the use of the `insert()` method and the creation of box objects, assuming `geometry::envelope()` might be used in more complex scenarios. It demonstrates a basic loop for generating and adding data.

```cpp
// create some values
for ( unsigned i = 0 ; i < 10 ; ++i )
{
    // create a box
    box b(point(i + 0.0f, i + 0.0f), point(i + 0.5f, i + 0.5f));
    // insert new value
    rtree.insert(std::make_pair(b, i));
}

```

--------------------------------

### Boost Geometry transform example with translation, scaling, and rotation

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/algorithms/transform/transform_3_with_strategy

An example demonstrating the use of Boost.Geometry's transform algorithm with various strategies including translation, scaling, and rotation. It shows how to transform points and print the results.

```cpp
#include <iostream>
#include <boost/geometry.hpp>

int main()
{
    namespace trans = boost::geometry::strategy::transform;
    using boost::geometry::dsv;

    using point_type = boost::geometry::model::point<double, 2, boost::geometry::cs::cartesian>;

    point_type p1(1.0, 1.0);

    // Translate over (1.5, 1.5)
    point_type p2;
    trans::translate_transformer<double, 2, 2> translate(1.5, 1.5);
    boost::geometry::transform(p1, p2, translate);

    // Scale with factor 3.0
    point_type p3;
    trans::scale_transformer<double, 2, 2> scale(3.0);
    boost::geometry::transform(p1, p3, scale);

    // Rotate with respect to the origin (0,0) over 90 degrees (clockwise)
    point_type p4;
    trans::rotate_transformer<boost::geometry::degree, double, 2, 2> rotate(90.0);
    boost::geometry::transform(p1, p4, rotate);

    std::cout
        << "p1: " << dsv(p1) << std::endl
        << "p2: " << dsv(p2) << std::endl
        << "p3: " << dsv(p3) << std::endl
        << "p4: " << dsv(p4) << std::endl;

    return 0;
}

```

--------------------------------

### Boost.Geometry box_view Example

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/views/box_view

Demonstrates the usage of boost::geometry::box_view to iterate over the corners of a box and calculate its area. This example requires the Boost.Geometry library and shows how to adapt a box to the Boost.Range concept.

```cpp
#include <iostream>

#include <boost/geometry.hpp>


int main()
{
    using box_type = boost::geometry::model::box
        <
            boost::geometry::model::point<double, 2, boost::geometry::cs::cartesian>
        >;

    // Define the Boost.Range compatible type:
    using box_view = boost::geometry::box_view<box_type>;

    box_type box;
    boost::geometry::assign_values(box, 0, 0, 4, 4);

    box_view view(box);

    // Iterating in clockwise direction over the points of this box
    for (boost::range_iterator<box_view const>::type it = boost::begin(view);
        it != boost::end(view); ++it)
    {
        std::cout << " " << boost::geometry::dsv(*it);
    }
    std::cout << std::endl;

    // Note that a box_view is tagged as a ring, so supports area etc.
    std::cout << "Area: " << boost::geometry::area(view) << std::endl;

    return 0;
}

```

--------------------------------

### Boost.Geometry model::linestring Example

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/models/model_linestring

An example demonstrating the declaration and use of Boost.Geometry's model::linestring, including creating linestrings, appending points, and calculating the length. It utilizes C++11 initializer list syntax and the bg::append and bg::length functions.

```cpp
#include <iostream>
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/geometries.hpp>

namespace bg = boost::geometry;

int main()
{
    using point_t = bg::model::point<double, 2, bg::cs::cartesian>;
    using linestring_t = bg::model::linestring<point_t>;

    linestring_t ls1; 
    linestring_t ls2{{0.0, 0.0}, {1.0, 0.0}, {1.0, 2.0}}; 

    bg::append(ls1, point_t(0.0, 0.0)); 
    bg::append(ls1, point_t(1.0, 0.0));
    bg::append(ls1, point_t(1.0, 2.0));

    double l = bg::length(ls1);

    std::cout << l << std::endl;

    return 0;
}

```

--------------------------------

### Boost.Geometry R-tree K-Nearest Neighbor Query (C++)

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/spatial_indexes/rtree_quickstart

Executes a k-nearest neighbor (k-nn) query to find a specified number of values closest to a given point. This example uses `bgi::nearest()` to find the 5 nearest values to the point (0, 0) and stores them in a vector. The order of results is not guaranteed.

```cpp
// find 5 nearest values to a point
std::vector<value> result_n;
rtree.query(bgi::nearest(point(0, 0), 5), std::back_inserter(result_n));

```

--------------------------------

### Boost.Geometry model::ring Example in C++

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/models/model_ring

This C++ example demonstrates the declaration and usage of `boost::geometry::model::ring`. It shows how to create rings using both default and initializer list constructors, append points using `bg::append`, calculate the area using `bg::area`, and print the result. It requires including the necessary Boost.Geometry headers.

```cpp
#include <iostream>
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/geometries.hpp>

namespace bg = boost::geometry;

int main()
{
    using point_t = bg::model::point<double, 2, bg::cs::cartesian>;
    using ring_t = bg::model::ring<point_t>; 

    ring_t ring1; 
    ring_t ring2{{0.0, 0.0}, {0.0, 5.0}, {5.0, 5.0}, {5.0, 0.0}, {0.0, 0.0}}; 

    bg::append(ring1, point_t(0.0, 0.0)); 
    bg::append(ring1, point_t(0.0, 5.0));
    bg::append(ring1, point_t(5.0, 5.0));
    bg::append(ring1, point_t(5.0, 0.0));
    bg::append(ring1, point_t(0.0, 0.0));

    double a = bg::area(ring1);

    std::cout << a << std::endl;

    return 0;
}


```

--------------------------------

### Set Point Coordinates Example - Boost.Geometry C++

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/access/set/set_2

Practical example demonstrating how to create a 2D point and set its x and y coordinates using the set function. The example creates a point_xy object, sets dimension 0 (x-coordinate) to 1 and dimension 1 (y-coordinate) to 2, then outputs the point using the dsv function. Requires boost/geometry headers and the boost::geometry namespace.

```cpp
#include <iostream>

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp>

namespace bg = boost::geometry;

int main()
{
    bg::model::d2::point_xy<double> point;

    bg::set<0>(point, 1);
    bg::set<1>(point, 2);

    std::cout << "Location: " << bg::dsv(point) << std::endl;

    return 0;
}

```

--------------------------------

### Boost.Geometry Tag Dispatching Example

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/core/tag

Demonstrates the tag dispatching mechanism in Boost.Geometry. This C++ example shows how to use the 'tag' metafunction to apply different logic based on the geometry type (point, polygon, multipolygon). It utilizes custom 'dispatch' structs and free functions like 'get' and 'dsv'.

```cpp
#include <iostream>

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/polygon.hpp>
#include <boost/geometry/geometries/multi_polygon.hpp>
#include <boost/geometry/geometries/adapted/boost_tuple.hpp>

BOOST_GEOMETRY_REGISTER_BOOST_TUPLE_CS(cs::cartesian)

template <typename Tag> struct dispatch {};

// Specialization for points
template <> struct dispatch<boost::geometry::point_tag>
{
    template <typename Point>
    static inline void apply(Point const& p)
    {
        // Use the Boost.Geometry free function "get"
        // working on all supported point types
        std::cout << "Hello POINT, you are located at: "
            << boost::geometry::get<0>(p) << ", "
            << boost::geometry::get<1>(p)
            << std::endl;
    }
};

// Specialization for polygons
template <> struct dispatch<boost::geometry::polygon_tag>
{
    template <typename Polygon>
    static inline void apply(Polygon const& p)
    {
        // Use the Boost.Geometry manipulator "dsv"
        // working on all supported geometries
        std::cout << "Hello POLYGON, you look like: "
            << boost::geometry::dsv(p)
            << std::endl;
    }
};

// Specialization for multipolygons
template <> struct dispatch<boost::geometry::multi_polygon_tag>
{
    template <typename MultiPolygon>
    static inline void apply(MultiPolygon const& m)
    {
        // Use the Boost.Range free function "size" because all
        // multigeometries comply to Boost.Range
        std::cout << "Hello MULTIPOLYGON, you contain: "
            << boost::size(m) << " polygon(s)"
            << std::endl;
    }
};

template <typename Geometry>
inline void hello(Geometry const& geometry)
{
    // Call the metafunction "tag" to dispatch, and call method (here "apply")
    dispatch
        <
            typename boost::geometry::tag<Geometry>::type
        >::apply(geometry);
}

int main()
{
    // Define polygon type (here: based on a Boost.Tuple)
    using polygon_type = boost::geometry::model::polygon<boost::tuple<int, int>>;

    // Declare and fill a polygon and a multipolygon
    polygon_type poly;
    boost::geometry::exterior_ring(poly) = {{0, 0}, {0, 10}, {10, 5}, {0, 0}};

    boost::geometry::model::multi_polygon<polygon_type> multi;
    multi.push_back(poly);

    // Call "hello" for point, polygon, multipolygon
    hello(boost::make_tuple(2, 3));
    hello(poly);
    hello(multi);

    return 0;
}

```

--------------------------------

### Boost.Geometry model::multi_point Usage Example

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/models/model_multi_point

A complete C++ example showcasing the declaration and use of `boost::geometry::model::multi_point`. It demonstrates creating multi-points using default and initializer list constructors, appending individual points, and retrieving the total number of points. This code requires the Boost.Geometry library.

```cpp
#include <iostream>
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/geometries.hpp>

namespace bg = boost::geometry;

int main()
{
    using point_t = bg::model::point<double, 2, bg::cs::cartesian>;
    using mpoint_t = bg::model::multi_point<point_t>;

    mpoint_t mpt1; 
    mpoint_t mpt2{{{0.0, 0.0}, {1.0, 1.0}, {2.0, 2.0}}}; 

    bg::append(mpt1, point_t(0.0, 0.0)); 
    bg::append(mpt1, point_t(1.0, 1.0));
    bg::append(mpt1, point_t(2.0, 2.0));

    std::size_t count = bg::num_points(mpt1);

    std::cout << count << std::endl;

    return 0;
}
```

--------------------------------

### Boost.Geometry R-tree Quick Start

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/spatial_indexes/rtree_examples/quick_start

Demonstrates the creation and usage of a Boost.Geometry R-tree for spatial indexing. It includes inserting boxes, performing spatial intersection queries, and nearest neighbor queries. This snippet requires Boost.Geometry and standard C++ libraries.

```cpp
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point.hpp>
#include <boost/geometry/geometries/box.hpp>
#include <boost/geometry/index/rtree.hpp>
#include <vector>
#include <iostream>
#include <boost/foreach.hpp>

namespace bg = boost::geometry;
namespace bgi = boost::geometry::index;

int main()
{
    typedef bg::model::point<float, 2, bg::cs::cartesian> point;
    typedef bg::model::box<point> box;
    typedef std::pair<box, unsigned> value;

    bgi::rtree< value, bgi::quadratic<16> > rtree;

    for ( unsigned i = 0 ; i < 10 ; ++i )
    {
        box b(point(i + 0.0f, i + 0.0f), point(i + 0.5f, i + 0.5f));
        rtree.insert(std::make_pair(b, i));
    }

    box query_box(point(0, 0), point(5, 5));
    std::vector<value> result_s;
    rtree.query(bgi::intersects(query_box), std::back_inserter(result_s));

    std::vector<value> result_n;
    rtree.query(bgi::nearest(point(0, 0), 5), std::back_inserter(result_n));

    std::cout << "spatial query box:" << std::endl;
    std::cout << bg::wkt<box>(query_box) << std::endl;
    std::cout << "spatial query result:" << std::endl;
    BOOST_FOREACH(value const& v, result_s)
        std::cout << bg::wkt<box>(v.first) << " - " << v.second << std::endl;

    std::cout << "knn query point:" << std::endl;
    std::cout << bg::wkt<point>(point(0, 0)) << std::endl;
    std::cout << "knn query result:" << std::endl;
    BOOST_FOREACH(value const& v, result_n)
        std::cout << bg::wkt<box>(v.first) << " - " << v.second << std::endl;

    return 0;
}

```

--------------------------------

### Boost.Range Sliced Adaptor Example with Linestring (C++)

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/adapted/boost_range/sliced

Demonstrates how to use the Boost.Range sliced adaptor to create a sub-range (slice) of a Boost.Geometry linestring. This example includes necessary headers, defines a linestring, applies the sliced adaptor with specified start and end indices, and prints the resulting slice.

```cpp
#include <iostream>

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/linestring.hpp>
#include <boost/geometry/geometries/point_xy.hpp>
#include <boost/geometry/geometries/adapted/boost_range/sliced.hpp>

int main()
{
    using xy = boost::geometry::model::d2::point_xy<int>;
    boost::geometry::model::linestring<xy> line = {{0, 0}, {1, 1}, {2, 2}, {3, 3}, {4, 4}};

    std::cout
        << boost::geometry::dsv(line | boost::adaptors::sliced(1, 3)) << std::endl;

    return 0;
}

```

--------------------------------

### Boost.Geometry model::point Declaration and Usage Example

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/models/model_point

This C++ example demonstrates the declaration and basic usage of the Boost.Geometry model::point class. It shows how to create points with different coordinate types and dimensions, set individual coordinates using both generic and class-specific methods, and retrieve coordinates.

```cpp
#include <iostream>
#include <boost/geometry.hpp>

namespace bg = boost::geometry;

int main()
{
    bg::model::point<double, 2, bg::cs::cartesian> point1;
    bg::model::point<double, 3, bg::cs::cartesian> point2(1.0, 2.0, 3.0); 

    bg::set<0>(point1, 1.0); 
    point1.set<1>(2.0); 

    double x = bg::get<0>(point1); 
    double y = point1.get<1>(); 

    std::cout << x << ", " << y << std::endl;
    return 0;
}

```

--------------------------------

### Boost.Geometry Index Query Examples

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/spatial_indexes/group__rtree__functions/query_rtree______const____predicates_const____outiter_

Examples demonstrating various ways to use the `query` function with different predicate combinations in Boost.Geometry. These include spatial queries, custom satisfies predicates, and nearest neighbor searches.

```cpp
// return elements intersecting box
bgi::query(tree, bgi::intersects(box), std::back_inserter(result));
// return elements intersecting poly but not within box
bgi::query(tree, bgi::intersects(poly) && !bgi::within(box), std::back_inserter(result));
// return elements overlapping box and meeting my_fun value predicate
bgi::query(tree, bgi::overlaps(box) && bgi::satisfies(my_fun), std::back_inserter(result));
// return 5 elements nearest to pt and elements are intersecting box
bgi::query(tree, bgi::nearest(pt, 5) && bgi::intersects(box), std::back_inserter(result));

// For each found value do_something (it is a type of function object)
tree.query(bgi::intersects(box),
           boost::make_function_output_iterator(do_something()));
```

--------------------------------

### Boost.Geometry Index Query Examples

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/spatial_indexes/boost__geometry__index__rtree/query_predicates_const____outiter_

Code examples demonstrating the usage of the Boost.Geometry index `query` function with various predicates, including spatial, satisfies, and nearest neighbor searches. It also shows how to connect multiple predicates and use different output iterator types like `std::back_inserter` and custom function output iterators.

```cpp
// return elements intersecting box
tree.query(bgi::intersects(box), std::back_inserter(result));
// return elements intersecting poly but not within box
tree.query(bgi::intersects(poly) && !bgi::within(box), std::back_inserter(result));
// return elements overlapping box and meeting my_fun unary predicate
tree.query(bgi::overlaps(box) && bgi::satisfies(my_fun), std::back_inserter(result));
// return 5 elements nearest to pt and elements are intersecting box
tree.query(bgi::nearest(pt, 5) && bgi::intersects(box), std::back_inserter(result));

// For each found value do_something (it is a type of function object)
tree.query(bgi::intersects(box),
           boost::make_function_output_iterator(do_something()));

// For each value stored in the rtree do_something
// always_true is a type of function object always returning true
tree.query(bgi::satisfies(always_true()),
           boost::make_function_output_iterator(do_something()));

// C++11 (lambda expression)
tree.query(bgi::intersects(box),
           boost::make_function_output_iterator([](value_type const& val){
               // do something
           }));

// C++14 (generic lambda expression)
tree.query(bgi::intersects(box),
           boost::make_function_output_iterator([](auto const& val){
               // do something
           }));
```

--------------------------------

### Boost.Geometry point_square Buffer Strategy Example (C++)

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/strategies/strategy_buffer_point_square

This example demonstrates how to use the `strategy::buffer::point_square` as a `PointStrategy` for the `buffer` algorithm in Boost.Geometry. It shows the creation of square buffers around a multipoint geometry using various buffer strategies (distance, side, join, end) along with the point_square strategy. The code requires Boost.Geometry headers for geometries and strategies.

```cpp
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp>
#include <boost/geometry/geometries/geometries.hpp>


int main()
{
    using point = boost::geometry::model::d2::point_xy<double>;
    using polygon = boost::geometry::model::polygon<point>;

    // Declare the point_square strategy
    boost::geometry::strategy::buffer::point_square point_strategy;

    // Declare other strategies
    boost::geometry::strategy::buffer::distance_symmetric<double> distance_strategy(0.5);
    boost::geometry::strategy::buffer::join_round join_strategy;
    boost::geometry::strategy::buffer::end_round end_strategy;
    boost::geometry::strategy::buffer::side_straight side_strategy;

    // Declare/fill of a multi point
    boost::geometry::model::multi_point<point> mp;
    boost::geometry::read_wkt("MULTIPOINT((3 3),(3 4),(4 4),(7 3))", mp);

    // Create the buffer of a multi point
    boost::geometry::model::multi_polygon<polygon> result;
    boost::geometry::buffer(mp, result,
                distance_strategy, side_strategy,
                join_strategy, end_strategy, point_strategy);


    return 0;
}

```

--------------------------------

### Register and use C arrays as points

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/quickstart

Register C array coordinate system with Boost.Geometry to use plain C arrays as point types. After registration, C arrays can be used directly with Boost.Geometry algorithms like distance calculation.

```cpp
#include <boost/geometry/geometries/adapted/c_array.hpp>

BOOST_GEOMETRY_REGISTER_C_ARRAY_CS(cs::cartesian)
```

```cpp
int a[2] = {1,1};
int b[2] = {2,3};
double d = distance(a, b);
std::cout << "Distance a-b is: " << d << std::endl;
```

--------------------------------

### Boost.Geometry R-tree Initialization (C++)

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/spatial_indexes/rtree_quickstart

Initializes an R-tree using the quadratic insertion algorithm with a maximum of 16 elements per node. This demonstrates how to configure the R-tree with specific parameters for performance tuning, such as choosing an appropriate algorithm and node capacity.

```cpp
// create the rtree using default constructor
bgi::rtree< value, bgi::quadratic<16> > rtree;

```

--------------------------------

### Box Construction and Manipulation Example

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/models/model_box

Demonstrates the declaration and usage of the Boost.Geometry model::box. It covers default construction, construction with corner points (including C++11 initialization), setting individual coordinates using both generic and class-specific methods, and retrieving coordinates.

```cpp
#include <iostream>
#include <boost/geometry.hpp>

namespace bg = boost::geometry;

int main()
{
    using point_t = bg::model::point<double, 2, bg::cs::cartesian>;
    using box_t = bg::model::box<point_t>;

    box_t box1; 
    box_t box2(point_t(0.0, 0.0), point_t(5.0, 5.0)); 
    box_t box3{{0.0, 0.0}, {5.0, 5.0}}; 

    bg::set<bg::min_corner, 0>(box1, 1.0); 
    bg::set<bg::min_corner, 1>(box1, 2.0);
    box1.max_corner().set<0>(3.0); 
    box1.max_corner().set<1>(4.0);

    double min_x = bg::get<bg::min_corner, 0>(box1); 
    double min_y = bg::get<bg::min_corner, 1>(box1);
    double max_x = box1.max_corner().get<0>(); 
    double max_y = box1.max_corner().get<1>();

    std::cout << min_x << ", " << min_y << ", " << max_x << ", " << max_y << std::endl;

    return 0;
}

```

--------------------------------

### Boost.Geometry point_order Example: Polygon Winding Order

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/core/point_order

An example demonstrating how to use the Boost.Geometry point_order metafunction to examine the winding order of a polygon. This code includes necessary headers for geometry types and prints the order value along with constants for clockwise and counterclockwise.

```cpp
#include <iostream>

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/polygon.hpp>
#include <boost/geometry/geometries/point_xy.hpp>

int main()
{
    using point_type = boost::geometry::model::d2::point_xy<double>;
    using polygon_type = boost::geometry::model::polygon<point_type, false>;

    boost::geometry::order_selector order = boost::geometry::point_order<polygon_type>::value;

    std::cout << "order: " << order << std::endl
        << "(clockwise = " << boost::geometry::clockwise
        << ", counterclockwise = " << boost::geometry::counterclockwise
        << ") " << std::endl;

    return 0;
}

```

--------------------------------

### Boost Geometry equals Example with Polygon and Box

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/algorithms/equals/equals_3_with_strategy

Complete example demonstrating the equals function comparing two polygons and a polygon with a box. Creates polygon and box geometries using boost tuples, registers the cartesian coordinate system, and outputs whether geometries are spatially equal. Shows practical usage with multiple geometry type combinations.

```cpp
#include <iostream>

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/polygon.hpp>
#include <boost/geometry/geometries/adapted/boost_tuple.hpp>

BOOST_GEOMETRY_REGISTER_BOOST_TUPLE_CS(cs::cartesian)

int main()
{
    using point = boost::tuple<int, int>;

    boost::geometry::model::polygon<point> poly1, poly2;
    boost::geometry::exterior_ring(poly1) = {{0, 0}, {0, 5}, {5, 5}, {5, 0}, {0, 0}};
    boost::geometry::exterior_ring(poly2) = {{5, 0}, {0, 0}, {0, 5}, {5, 5}, {5, 0}};

    std::cout
        << "polygons are spatially "
        << (boost::geometry::equals(poly1, poly2) ? "equal" : "not equal")
        << std::endl;

    boost::geometry::model::box<point> box;
    boost::geometry::assign_values(box, 0, 0, 5, 5);

    std::cout
        << "polygon and box are spatially "
        << (boost::geometry::equals(box, poly2) ? "equal" : "not equal")
        << std::endl;

    return 0;
}
```

--------------------------------

### Boost Geometry strategy::distance::cross_track Constructor Examples

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/strategies/strategy_distance_cross_track

Examples of constructors for the strategy::distance::cross_track class. The default constructor is shown, along with constructors that accept a radius type and a specific strategy instance.

```cpp
cross_track()
cross_track(typename Strategy::radius_type const & r)
cross_track(Strategy const & s)
```

--------------------------------

### Example: Register Legacy Point and Calculate Distance

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/adapted/register/boost_geometry_register_point_2d

Complete example demonstrating how to register a custom legacy_point struct with Boost.Geometry and use library functions like assign_values and distance. The example shows defining a point structure, registering it with the macro, assigning values, and calculating the distance between two points.

```C++
#include <iostream>
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/register/point.hpp>


struct legacy_point
{
    double x, y;
};

BOOST_GEOMETRY_REGISTER_POINT_2D(legacy_point, double, cs::cartesian, x, y)

int main()
{
    legacy_point p1, p2;

    namespace bg = boost::geometry;

    
    bg::assign_values(p1, 1, 1);
    bg::assign_values(p2, 2, 2);

    double d = bg::distance(p1, p2);

    std::cout << "Distance: " << d << std::endl;

    return 0;
}
```

--------------------------------

### Perform k-NN Queries with Boost.Geometry.Index (C++)

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/spatial_indexes/queries

Illustrates how to perform k-Nearest Neighbors (k-NN) queries using the `bgi::nearest` predicate. Examples show querying for the `k` closest values to a Point, Box, and Segment. For non-point indexables, `bg::comparable_distance` is used.

```cpp
std::vector<Value> returned_values;
Point pt(/*...*/);
rt.query(bgi::nearest(pt, k), std::back_inserter(returned_values));

Box box(/*...*/);
rt.query(bgi::nearest(box, k), std::back_inserter(returned_values));

Segment seg(/*...*/);
rt.query(bgi::nearest(seg, k), std::back_inserter(returned_values));

```

--------------------------------

### Boost.Geometry segment_view Example

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/views/segment_view

Demonstrates the usage of segment_view to iterate over the points of a segment and calculate its length. It adapts a segment to the Boost.Range concept, enabling linestring operations.

```cpp
#include <iostream>

#include <boost/geometry.hpp>


int main()
{
    using segment_type = boost::geometry::model::segment
        <
            boost::geometry::model::point<double, 2, boost::geometry::cs::cartesian>
        >;

    using segment_view = boost::geometry::segment_view<segment_type>;

    segment_type segment;
    boost::geometry::assign_values(segment, 0, 0, 1, 1);

    segment_view view(segment);

    // Iterating over the points of this segment
    for (boost::range_iterator<segment_view const>::type it = boost::begin(view);
        it != boost::end(view); ++it)
    {
        std::cout << " " << boost::geometry::dsv(*it);
    }
    std::cout << std::endl;

    // Note that a segment_view is tagged as a linestring, so supports length etc.
    std::cout << "Length: " << boost::geometry::length(view) << std::endl;

    return 0;
}

```

--------------------------------

### Create R-tree with Range Adaptors in Boost.Geometry C++

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/spatial_indexes/rtree_examples/range_adaptors

Complete example demonstrating how to construct a Boost.Geometry R-tree spatial index using Boost.Range adaptors to transform a vector of boxes. The indexed adaptor assigns indices to elements, while the transformed adaptor applies a function object to convert elements into key-value pairs. The example creates 10 boxes, builds an R-tree, and queries it using the first box as a search criterion.

```cpp
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point.hpp>
#include <boost/geometry/geometries/box.hpp>
#include <boost/geometry/index/rtree.hpp>
#include <boost/range.hpp>
#include <boost/range/adaptor/indexed.hpp>
#include <boost/range/adaptor/transformed.hpp>
#include <vector>
#include <iostream>

namespace bg = boost::geometry;
namespace bgi = boost::geometry::index;

template <typename First, typename Second>
struct pair_maker
{
    typedef std::pair<First, Second> result_type;
    template<typename T>
    inline result_type operator()(T const& v) const
    {
        return result_type(v.value(), v.index());
    }
};

int main()
{
    typedef bg::model::point<float, 2, bg::cs::cartesian> point;
    typedef bg::model::box<point> box;
    typedef std::vector<box> container;
    typedef container::size_type size_type;
    typedef std::pair<box, size_type> value;

    container boxes;
    for ( size_type i = 0 ; i < 10 ; ++i )
    {
        box b(point(i + 0.0f, i + 0.0f), point(i + 0.5f, i + 0.5f));
        boxes.push_back(b);
    }

    bgi::rtree< value, bgi::quadratic<16> >
        rtree(boxes | boost::adaptors::indexed()
                    | boost::adaptors::transformed(pair_maker<box, size_type>()));

    std::cout << rtree.count(boxes[0]) << std::endl;

    return 0;
}
```

--------------------------------

### Boost.Geometry join_round Strategy Example

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/strategies/strategy_buffer_join_round

Demonstrates how to use the join_round strategy with the buffer algorithm to create buffered geometries featuring rounded corners. This involves setting up various buffer strategies, defining geometry objects, and then applying the buffer operation.

```cpp
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp>
#include <boost/geometry/geometries/geometries.hpp>


int main()
{
    using point = boost::geometry::model::d2::point_xy<double>;
    using polygon = boost::geometry::model::polygon<point>;

    // Declare the join_round strategy with 72 points for a full circle
    boost::geometry::strategy::buffer::join_round join_strategy(72);

    // Declare other strategies
    boost::geometry::strategy::buffer::distance_symmetric<double> distance_strategy(1.0);
    boost::geometry::strategy::buffer::end_flat end_strategy;
    boost::geometry::strategy::buffer::side_straight side_strategy;
    boost::geometry::strategy::buffer::point_circle point_strategy;

    // Declare/fill a multi polygon
    boost::geometry::model::multi_polygon<polygon> mp;
    boost::geometry::read_wkt("MULTIPOLYGON(((5 5,7 8,9 5,5 5)),((8 7,8 10,11 10,11 7,8 7)))", mp);

    // Create the buffered geometry with rounded corners
    boost::geometry::model::multi_polygon<polygon> result;
    boost::geometry::buffer(mp, result,
                distance_strategy, side_strategy,
                join_strategy, end_strategy, point_strategy);


    return 0;
}

```

--------------------------------

### Calculate polygon area

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/quickstart

Compute the area of a polygon using Boost.Geometry's area function. Works with any registered polygon type and coordinate system.

```cpp
std::cout << "Area: " << area(poly) << std::endl;
```

--------------------------------

### Calculate distance between mixed point types

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/quickstart

Demonstrate Boost.Geometry's flexibility by calculating distance between points of different types (C array and Boost.Tuple). The template library automatically handles type conversions.

```cpp
double d2 = distance(a, p);
std::cout << "Distance a-p is: " << d2 << std::endl;
```

--------------------------------

### Define and use spherical coordinate points

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/quickstart

Create points in spherical coordinate system (with equatorial and degree units) and calculate great-circle distance between them. Demonstrates non-Cartesian geometry support where the library automatically applies spherical distance calculations.

```cpp
using spherical_point = boost::geometry::model::point
    <
        double, 2, boost::geometry::cs::spherical_equatorial<boost::geometry::degree>
    >;

spherical_point amsterdam(4.90, 52.37);
spherical_point paris(2.35, 48.86);

double const earth_radius = 3959; // miles
std::cout << "Distance in miles: " << distance(amsterdam, paris) * earth_radius << std::endl;
```

--------------------------------

### Check point-in-polygon using within algorithm

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/quickstart

Determine whether a point (Boost.Tuple) is located within a polygon. Demonstrates the `within` function which performs point-in-polygon testing by comparing the point against polygon boundaries defined by C array coordinates.

```cpp
double points[][2] = {{2.0, 1.3}, {4.1, 3.0}, {5.3, 2.6}, {2.9, 0.7}, {2.0, 1.3}};
model::polygon<model::d2::point_xy<double>> poly;
append(poly, points);
boost::tuple<double, double> p = boost::make_tuple(3.7, 2.0);
std::cout << "Point p is in polygon? " << std::boolalpha << within(p, poly) << std::endl;
```

--------------------------------

### Calculate distance between two Cartesian points

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/quickstart

Compute the Euclidean distance between two 2D points using Boost.Geometry's point_xy type. The distance function automatically applies the appropriate distance formula based on the coordinate system.

```cpp
model::d2::point_xy<int> p1(1, 1), p2(2, 2);
std::cout << "Distance p1-p2 is: " << distance(p1, p2) << std::endl;
```

--------------------------------

### Initialize and Use Boost.Geometry Polyhedral Surface (C++)

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/models/model_polyhedral_surface

This C++ code snippet demonstrates how to declare and use the Boost.Geometry model::polyhedral_surface. It covers initialization via default constructor, list initialization, manual appending of points, and reading from Well-Known Text (WKT) format. The example also shows how to output the polyhedral surface in WKT format.

```cpp
#include <iostream>
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/geometries.hpp>

namespace bg = boost::geometry;

int main()
{
    using point_t = bg::model::point<double, 3, bg::cs::cartesian>;
    using polygon_t = bg::model::polygon<point_t>;
    using polyhedral_t = bg::model::polyhedral_surface<polygon_t>;

    polyhedral_t polyhedral0; 

    polyhedral_t polyhedral1 = {{{{0, 0, 0}, {0, 1, 0}, {1, 1, 0}, {1, 0, 0}, {0, 0, 0}}},
                                {{{0, 0, 0}, {0, 1, 0}, {0, 1, 1}, {0, 0, 1}, {0, 0, 0}}},
                                {{{0, 0, 0}, {1, 0, 0}, {1, 0, 1}, {0, 0, 1}, {0, 0, 0}}},
                                {{{1, 1, 1}, {1, 0, 1}, {0, 0, 1}, {0, 1, 1}, {1, 1, 1}}},
                                {{{1, 1, 1}, {1, 0, 1}, {1, 0, 0}, {1, 1, 0}, {1, 1, 1}}},
                                {{{1, 1, 1}, {1, 1, 0}, {0, 1, 0}, {0, 1, 1}, {1, 1, 1}}}}; 


    polyhedral0.resize(4);
    bg::append(polyhedral0[0].outer(), point_t(0.0, 0.0, 0.0));
    bg::append(polyhedral0[0].outer(), point_t(5.0, 0.0, 0.0));
    bg::append(polyhedral0[0].outer(), point_t(0.0, 5.0, 0.0));
    bg::append(polyhedral0[1].outer(), point_t(0.0, 0.0, 0.0));
    bg::append(polyhedral0[1].outer(), point_t(0.0, 5.0, 0.0));
    bg::append(polyhedral0[1].outer(), point_t(0.0, 0.0, 5.0));
    bg::append(polyhedral0[2].outer(), point_t(0.0, 0.0, 0.0));
    bg::append(polyhedral0[2].outer(), point_t(5.0, 0.0, 0.0));
    bg::append(polyhedral0[2].outer(), point_t(0.0, 0.0, 5.0));
    bg::append(polyhedral0[3].outer(), point_t(5.0, 0.0, 0.0));
    bg::append(polyhedral0[3].outer(), point_t(0.0, 5.0, 0.0));
    bg::append(polyhedral0[3].outer(), point_t(0.0, 0.0, 5.0)); 

    polyhedral_t polyhedral2;
    bg::read_wkt("POLYHEDRALSURFACE(((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)),\
                                    ((0 0 0, 0 1 0, 0 1 1, 0 0 1, 0 0 0)),\
                                    ((0 0 0, 1 0 0, 1 0 1, 0 0 1, 0 0 0)),\
                                    ((1 1 1, 1 0 1, 0 0 1, 0 1 1, 1 1 1)),\
                                    ((1 1 1, 1 0 1, 1 0 0, 1 1 0, 1 1 1)),\
                                    ((1 1 1, 1 1 0, 0 1 0, 0 1 1, 1 1 1))", polyhedral2);

    std::cout << bg::wkt(polyhedral0) << std::endl; 
    std::cout << bg::wkt(polyhedral1) << std::endl;
    std::cout << bg::wkt(polyhedral2) << std::endl;

    return 0;
}

```

--------------------------------

### Get Coordinate Type of Polygon (C++)

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/core/coordinate_type

This example demonstrates how to use the boost::geometry::coordinate_type metafunction to retrieve the coordinate type of a polygon. It requires including the necessary Boost.Geometry headers for points and polygons. The output shows the name of the coordinate type.

```cpp
#include <iostream>
#include <typeinfo>

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/polygon.hpp>
#include <boost/geometry/geometries/point_xy.hpp>

int main()
{
    using point_type = boost::geometry::model::d2::point_xy<double>;
    using polygon_type = boost::geometry::model::polygon<point_type>;

    using ctype = boost::geometry::coordinate_type<polygon_type>::type;

    std::cout << "type: " << typeid(ctype).name() << std::endl;

    return 0;
}
```

--------------------------------

### Check rectangle overlap and reassign Qt objects

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/quickstart

Detect if two Qt rectangles overlap using Boost.Geometry's overlaps function, then reassign the second rectangle's values. Demonstrates how Qt classes can be adapted and used with Boost.Geometry after proper registration.

```cpp
QRect r1(100, 200, 15, 15);
QRect r2(110, 210, 20, 20);
if (overlaps(r1, r2))
{
    assign_values(r2, 200, 300, 220, 320);
}
```

--------------------------------

### qbegin() Usage Example - Iterative rtree Query with Nearest Predicate

Source: https://www.boost.org/doc/libs/latest/libs/geometry/doc/html/geometry/reference/spatial_indexes/group__rtree__functions/qbegin_rtree______const____predicates_const___

Demonstrates iterative querying on an rtree using qbegin() with a nearest() predicate to find the 3 nearest points to a given point, then applying do_something() to each result using std::for_each.

```cpp
std::for_each(bgi::qbegin(tree, bgi::nearest(pt, 3)), bgi::qend(tree), do_something());
```