### 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

### 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 90 Concept

The polygon_90 concept tag is polygon_90_concept

To register a user defined type as a model of polygon_90 concept, specialize the geometry concept meta-function for that type. In the example below CPolygon90 is registered as a model of polygon_90 concept.

template <>
struct geometry_concept<CPolygon90> { typedef polygon_90_concept type; };

The semantic of a polygon_90 is that it can provide iterators over the x and y coordinates that correspond to its horizontal and vertical sides, starting with an x coordinate. A mutable polygon_90 must also be able to set its geometry based on an interator range over such coordinates. Since most polygons use vertex points in internal storage iterator adaptors for converting to and from point sequences are provided in iterator_points_to_compact.hpp and iterator_compact_to_points.hpp to aid in the specialization of polygon_90_traits. A std::vector<int> or std::list<int> could be made models of polygon_90_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 the polygon_90_with_holes concept.

template <typename T>
struct polygon_90_traits {
typedef typename T::coordinate_type coordinate_type;
typedef typename T::compact_iterator_type compact_iterator_type;
static inline compact_iterator_type begin_compact(const T& t) {
return t.begin_compact();
}
static inline compact_iterator_type end_compact(const T& t) {
return t.end_compact();
}
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>
struct polygon_90_mutable_traits {
template <typename iT>
static inline T& set_compact(T& t, iT input_begin, iT input_end) {
t.set_compact(input_begin, input_end);
return t;
}
};

An object that is a model of polygon_90_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_90_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> compact_iterator_type begin_compact(const T& polygon) | Expects a model of polygon_90. Returns the begin iterator over the range of coordinates that correspond to horizontal and vertical edges.
template <typename T> compact_iterator_type end_compact(const T& polygon) | Expects a model of polygon_90. Returns the end iterator over the range of coordinates that correspond to horizontal and vertical edges.
template <typename T> point_iterator_type begin_points(const T& polygon) | Expects a model of polygon_90. 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_90. Returns the end iterator over the range of points that correspond to vertices of the polygon.
template <typename T, typename iterator> void set_compact(T& polygon, iterator b, iterator e) | Expects a model of polygon_90. Sets the polygon to the coordinate data range [b,e) that corresponds to .horizontal and vertical edges.
template <typename T, typename iterator> void set_points(T& polygon, iterator b, iterator e) | Expects a model of polygon_90. Sets the polygon to the point data range [b,e) that corresponds to vertices of a manhattan polygon. Non-manhattan edges between successive input points results in undefined behavior.
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_90 into left object that models polygon_90.
template <typename T, typename point_type> bool contains(const T&, const point_type& point, bool consider_touch=true) | Given an object that models polygon_90 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_90. 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_90 and returns true. Returns false and leaves bbox unchanged if polygon is empty. Linear wrt. vertices.
template <typename T> manhattan_area_type area(const T& polygon) | Returns the area of an object that models polygon_90. Linear wrt. vertices.
template <typename T> direction_1d winding(const T& polygon) | Returns the winding direction of an object that models polygon_90, LOW == CLOCKWISE, HIGH = COUNTERCLOCKWISE. Complexity depends upon winding trait.
template <typename T> coordinate_difference perimeter(const T& polygon) | Returns the perimeter length of an object that models polygon_90. 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_90 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_90 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_90 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_90 . 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_90. Linear wrt. vertices.

# Polygon 90 Data

The library provides a model of polygon 90 concept declared template<typename T> polygon_90_data where T is the coordinate type.

This data type is used internally when a Manhattan 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_90_concept
coordinate_type | T
iterator_type | Iterator over vertices point_data<T> vertices of polygon
compact_iterator_type | Iterator over non-redundant coordinates of the polygon, alternating x, y, x, y starting with an x, where each x corresponds to a vertical edge and each y corresponds to a horizontal edge.
polygon_90_data() | Default constructs the polygon.
polygon_90_data(const polygon_90_data& that) | Copy construct
polygon_90_data& operator=(const polygon_90_data& that) | Assignment operator.
template <typename T2> polygon_90_data& operator=(const T2& that) const | Assign from an object that is a model of polygon 90.
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.
compact_iterator_type begin_compact() const | Get the begin compact iterator over non-redundant coordinates of the polygon.
compact_iterator_type end_compact() const | Get the end compact iterator over non-redundant coordinates 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 a Manhattan figure, every other x and y value of the points is used to initialize the polygon.
template <typename iT> void set_compact(iT begin_coords, iT end_coords) | Sets the polygon to the iterator range of coordinates. These coordinates correspond to the x values of vertical edges and y values of horizontal edges. It is expected that the sequence start with an x value and proceed x then y then x then y.

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)