### Contents

- Boost.Polygon Main Page
- Design Overview
- Isotropy
- Coordinate Concept
- Interval Concept
- Point Concept
- Segment Concept
- Rectangle Concept
- Polygon 90 Concept
- Polygon 90 With Holes Concept
- Polygon 45 Concept
- Polygon 45 With Holes Concept
- Polygon Concept
- Polygon With Holes Concept
- Polygon 90 Set Concept
- Polygon 45 Set Concept
- Polygon Set Concept
- Connectivity Extraction 90
- Connectivity Extraction 45
- Connectivity Extraction
- Property Merge 90
- Property Merge 45
- Property Merge
- Voronoi Main Page
- Voronoi Benchmark
- Voronoi Builder
- Voronoi Diagram
- Voronoi Predicates
- Voronoi Robust FPT

### Other Resources

- GTL Boostcon 2009 Paper
- GTL Boostcon 2009 Presentation
- Performance Analysis
- Layout Versus Schematic Tutorial
- Minkowski Sum Tutorial
- Voronoi Basic Tutorial
- Voronoi Advanced Tutorial

### Polygon Sponsor

# Polygon 45 Concept

The polygon_45 concept tag is polygon_45_concept

To register a user defined type as a model of polygon_45 concept, specialize the geometry concept meta-function for that type. In the example below CPolygon45 is registered as a model of polygon_45 concept.

template <>
struct geometry_concept<CPolygon45> { typedef polygon_45_concept type; };

The semantic of a polygon_45 is that it can provide iterators over the points that represent its vertices, angles formed as these vertices must be multiple of 45-degree relative to the coordinate axis. It is acceptable to have the last edge explict with the first and last point equal to each other or implied by this segement that would connect the first and last point. A mutable polygon_45 must also be able to set its geometry based on an interator range over such points. A std::vector<point_data<int> > or std::list<point_data<int> > could be made models of polygon_45_concept by simply providing access to their iterators through traits. Library functions that create polygon objects require that those objects provide a default constructor.

Below is shown the default polygon traits. Specialization of these traits is required for types that don't conform to the default behavior. Note that these traits are also used by several other polygon concepts through SFINAE enable template parameter. The SFINAE enable parameter also allows the library to provide default specialization that work for any object that models the 90 degree polygon concepts.

template <typename T, typename enable = gtl_yes>
struct polygon_traits {};
template <typename T>
struct polygon_traits<T,
typename gtl_or_4<
typename gtl_same_type<typename geometry_concept<T>::type, polygon_concept>::type,
typename gtl_same_type<typename geometry_concept<T>::type, polygon_45_concept>::type,
typename gtl_same_type<typename geometry_concept<T>::type, polygon_with_holes_concept>::type,
typename gtl_same_type<typename geometry_concept<T>::type, polygon_45_with_holes_concept>::type
>::type> {
typedef typename T::coordinate_type coordinate_type;
typedef typename T::iterator_type iterator_type;
typedef typename T::point_type point_type;
static inline iterator_type begin_points(const T& t) {
return t.begin();
}
static inline iterator_type end_points(const T& t) {
return t.end();
}
static inline unsigned int size(const T& t) {
return t.size();
}
static inline winding_direction winding(const T& t) {
return unknown_winding;
}
};

template <typename T, typename enable = void>
struct polygon_mutable_traits {
template <typename iT>
static inline T& set_points(T& t, iT input_begin, iT input_end) {
t.set(input_begin, input_end);
return t;
}
};

An object that is a model of polygon_45_concept can be viewed as a model of any of its refinements if it is determined at runtime to conform to the restriction of those concepts. This concept casting is accomplished through the view_as<>() function.

view_as<rectangle_concept>(polygon_45_object)
view_as<polygon_90_concept>(polygon_45_object)

The return value of view_as<>() can be passed into any interface that expects an object of the conceptual type specified in its template parameter.

## Functions

template <typename T> point_iterator_type begin_points(const T& polygon) | Expects a model of polygon_45. Returns the begin iterator over the range of points that correspond to vertices of the polygon.
template <typename T> point_iterator_type end_points(const T& polygon) | Expects a model of polygon_45. Returns the end iterator over the range of points that correspond to vertices of the polygon.
template <typename T, typename iterator> void set_points(T& polygon, iterator b, iterator e) | Expects a model of polygon_45. Sets the polygon to the point data range [b,e) that corresponds to vertices of a polygon. Non-45 edges between successive input points is disallowed.
template <typename T> unsigned int size(const T& polygon) | Returns the number of edges in the polygon.
template <typename T1, typename T2> T1& assign(T1& left, const T2& right) | Copies data from right object that models polygon_45 into left object that models polygon_45.
template <typename T, typename point_type> bool contains(const T&, const point_type& point, bool consider_touch=true) | Given an object that models polygon_45 and an object that models point, returns true if the polygon contains the point. If the consider_touch flag is true will return true if the point lies along the boundary of the polygon. Linear wrt. vertices.
// get the center coordinate template <typename T, typename point_type> void center(point_type& p, const T& polygon) | Sets object that models point to the center point of the bounding box of an object that models polygon_45. Linear wrt. vertices.
template <typename T, typename rectangle_type> bool extents(rectangle_type& bbox, const T& polygon) | Sets object that models rectangle to the bounding box of an object that models polygon_45 and returns true. Returns false and leaves bbox unchanged if polygon is empty. Linear wrt. vertices.
template <typename T> area_type area(const T& polygon) | Returns the area of an object that models polygon_45. Linear wrt. vertices.
template <typename T> direction_1d winding(const T& polygon) | Returns the winding direction of an object that models polygon_45, LOW == CLOCKWISE, HIGH = COUNTERCLOCKWISE. Complexity depends upon winding trait.
template <typename T> coordinate_distance perimeter(const T& polygon) | Returns the perimeter length of an object that models polygon_45. Linear wrt. vertices.
template <typename T, typename transform_type> T& transform(T& polygon, const transform_type&) | Applies transform() on the vertices of polygon and sets the polygon to that described by the result of transforming its vertices. Linear wrt. vertices.
template <typename T> T& scale_up(T& polygon, unsigned_area_type factor) | Scales up coordinate of an object that models polygon_45 by unsigned factor. Linear wrt. vertices.
template <typename T> T& scale_down(T& polygon, unsigned_area_type factor) | Scales down coordinates of an object that models polygon_45 by unsigned factor. Linear wrt. vertices.
template <typename T, scaling_type> T& scale(T& rectangle, double scaling) | Scales coordinates of an object that models polygon_45 by floating point factor. Linear wrt. vertices.
template <typename T> T& move(T& polygon, orientation_2d, coordinate_difference displacement) | Adds displacement value to coordinate indicated by orientation_2d of vertices of an object that models polygon_45. Linear wrt. vertices.
template <typename polygon_type, typename point_type> polygon_type& convolve(polygon_type& polygon, const point_type& point) | Convolves coordinate values of point with vertices of an object that models polygon_45. Linear wrt. vertices.

# Polygon 45 Data

The library provides a model of polygon 45 concept declared template<typename T> polygon_45_data where T is the coordinate type.

This data type is used internally when a 45-degree polygon is needed and is available to the library user who finds it convenient to use a library polygon data type instead of providing their own. The data type is implemented to be convenient to use with the library traits.

## Members

geometry_type | polygon_45_concept
coordinate_type | T
iterator_type | Iterator over vertices point_data<T> vertices of polygon
polygon_45_data() | Default constructs the polygon.
polygon_45_data(const polygon_45_data& that) | Copy construct
polygon_45_data& operator=(const polygon_45_data& that) | Assignment operator.
template <typename T2> polygon_45_data& operator=(const T2& that) const | Assign from an object that is a model of polygon 45.
iterator_type begin() const | Get the begin iterator over vertices of the polygon.
iterator_type end() const | Get the end iterator over vertices of the polygon.
std::size_t size() const | Get the number of elements in the sequence stored to the polygon, usually equal to the number of edges of the polygon.
template <typename iT> void set(iT begin_points, iT end_points) | Sets the polygon to the iterator range of points. No check is performed to ensure the points describe corners that are multiples of 45 degrees relative to the coordinate axis.

Copyright: | Copyright © Intel Corporation 2008-2010.
License: | Distributed under the Boost Software License, Version 1.0. (See accompanying file `LICENSE_1_0.txt` or copy at http://www.boost.org/LICENSE_1_0.txt)