1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Polygon Concept</title> 5<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../../index.html" title="Chapter 1. Geometry"> 8<link rel="up" href="../concepts.html" title="Concepts"> 9<link rel="prev" href="concept_linestring.html" title="Linestring Concept"> 10<link rel="next" href="concept_multi_point.html" title="MultiPoint Concept"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="concept_linestring.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="concept_multi_point.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h4 class="title"> 27<a name="geometry.reference.concepts.concept_polygon"></a><a class="link" href="concept_polygon.html" title="Polygon Concept">Polygon 28 Concept</a> 29</h4></div></div></div> 30<h6> 31<a name="geometry.reference.concepts.concept_polygon.h0"></a> 32 <span class="phrase"><a name="geometry.reference.concepts.concept_polygon.description"></a></span><a class="link" href="concept_polygon.html#geometry.reference.concepts.concept_polygon.description">Description</a> 33 </h6> 34<p> 35 The Polygon Concept describes the requirements for a polygon type. All 36 algorithms in Boost.Geometry will check any geometry arguments against 37 the concept requirements. 38 </p> 39<p> 40 A polygon is <span class="emphasis"><em>A polygon is a planar surface defined by one exterior 41 boundary and zero or more interior boundaries</em></span> (<a href="http://www.opengeospatial.org/standards/sfa" target="_top">OGC 42 Simple Feature Specification</a>). 43 </p> 44<p> 45 So the definition of a Boost.Geometry polygon differs a bit from e.g. Wiki, 46 where a polygon does not have holes. A polygon of Boost.Geometry is a polygon 47 with or without holes. <span class="emphasis"><em>(A polygon without holes is a <span class="emphasis"><em>helper 48 geometry</em></span> within Boost.Geometry, and referred to as a ring.)</em></span> 49 </p> 50<h6> 51<a name="geometry.reference.concepts.concept_polygon.h1"></a> 52 <span class="phrase"><a name="geometry.reference.concepts.concept_polygon.concept_definition"></a></span><a class="link" href="concept_polygon.html#geometry.reference.concepts.concept_polygon.concept_definition">Concept 53 Definition</a> 54 </h6> 55<p> 56 The Polygon Concept is defined as following: 57 </p> 58<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 59<li class="listitem"> 60 there must be a specialization of <code class="computeroutput"><span class="identifier">traits</span><span class="special">::</span><span class="identifier">tag</span></code> 61 defining <code class="computeroutput"><span class="identifier">polygon_tag</span></code> 62 as type 63 </li> 64<li class="listitem"> 65 there must be a specialization of <code class="computeroutput"><span class="identifier">traits</span><span class="special">::</span><span class="identifier">ring_type</span></code> 66 defining the type of its exterior ring and interior rings as type 67 </li> 68<li class="listitem"> 69 this type defined by <code class="computeroutput"><span class="identifier">ring_type</span></code> 70 must fulfill the <a class="link" href="concept_ring.html" title="Ring Concept">Ring 71 Concept</a> 72 </li> 73<li class="listitem"> 74 there must be a specialization of <code class="computeroutput"><span class="identifier">traits</span><span class="special">::</span><span class="identifier">interior_type</span></code> 75 defining the type of the collection of its interior rings as type; 76 this collection itself must fulfill a Boost.Range Random Access Range 77 Concept 78 </li> 79<li class="listitem"> 80 there must be a specialization of <code class="computeroutput"><span class="identifier">traits</span><span class="special">::</span><span class="identifier">exterior_ring</span></code> 81 with two functions named <code class="computeroutput"><span class="identifier">get</span></code>, 82 returning the exterior ring, one being const, the other being non const 83 </li> 84<li class="listitem"> 85 there must be a specialization of <code class="computeroutput"><span class="identifier">traits</span><span class="special">::</span><span class="identifier">interior_rings</span></code> 86 with two functions named <code class="computeroutput"><span class="identifier">get</span></code>, 87 returning the interior rings, one being const, the other being non 88 const 89 </li> 90</ul></div> 91<h6> 92<a name="geometry.reference.concepts.concept_polygon.h2"></a> 93 <span class="phrase"><a name="geometry.reference.concepts.concept_polygon.rules"></a></span><a class="link" href="concept_polygon.html#geometry.reference.concepts.concept_polygon.rules">Rules</a> 94 </h6> 95<p> 96 Besides the Concepts, which are checks on compile-time, there are some 97 other rules that valid polygons must fulfill. This follows the opengeospatial 98 rules (see link above). 99 </p> 100<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 101<li class="listitem"> 102 Polygons are simple geometric objects (See also <a href="http://en.wikipedia.org/wiki/Simple_polygon" target="_top">wiki</a> 103 but holes are allowed in Boost.Geometry polygons). 104 </li> 105<li class="listitem"> 106 If the polygons underlying <code class="computeroutput"><span class="identifier">ring_type</span></code> 107 is defined as clockwise, the exterior ring must have the clockwise 108 orientation, and any interior ring must be reversed w.r.t. the defined 109 orientation (so: counter clockwise for clockwise exterior rings). If 110 the <code class="computeroutput"><span class="identifier">ring_type</span></code> is defined 111 counter clockwise, it is vice versa. 112 </li> 113<li class="listitem"> 114 If the polygons underlying <code class="computeroutput"><span class="identifier">ring_type</span></code> 115 is defined as closed, all rings must be closed: the first point must 116 be spatially equal to the last point. 117 </li> 118<li class="listitem"> 119 The interior is a connected point set. 120 </li> 121<li class="listitem"> 122 There should be no self intersections, but self tangencies (between 123 exterior/interior rings) are allowed (as long as the interior is a 124 connected point set. 125 </li> 126<li class="listitem"> 127 There should be no cut lines, spikes or punctures. 128 </li> 129<li class="listitem"> 130 The interior rings should be located within the exterior ring. Interior 131 rings may not be located within each other. 132 </li> 133</ul></div> 134<p> 135 The algorithms such as intersection, area, centroid, union, etc. do not 136 check validity. There will be an algorithm is_valid which checks for validity 137 against these rules, at runtime, and which can be called (by the library 138 user) before. 139 </p> 140<p> 141 If the input is invalid, the output might be invalid too. For example: 142 if a polygon which should be closed is not closed, the area will be incorrect. 143 </p> 144<h6> 145<a name="geometry.reference.concepts.concept_polygon.h3"></a> 146 <span class="phrase"><a name="geometry.reference.concepts.concept_polygon.available_models"></a></span><a class="link" href="concept_polygon.html#geometry.reference.concepts.concept_polygon.available_models">Available 147 Models</a> 148 </h6> 149<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 150<li class="listitem"> 151 <a class="link" href="../models/model_polygon.html" title="model::polygon">polygon</a> 152 </li> 153<li class="listitem"> 154 a Boost.Polygon polygon_with_holes_data (requires <code class="computeroutput"><span class="preprocessor">#include</span> 155 <span class="identifier">boost</span><span class="special">/</span><span class="identifier">geometry</span><span class="special">/</span><span class="identifier">geometries</span><span class="special">/</span><span class="identifier">adapted</span><span class="special">/</span><span class="identifier">boost_polygon</span><span class="special">/</span><span class="identifier">polygon</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code>) 156 </li> 157</ul></div> 158</div> 159<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 160<td align="left"></td> 161<td align="right"><div class="copyright-footer">Copyright © 2009-2019 Barend Gehrels, Bruno Lalande, Mateusz Loskot, Adam 162 Wulkiewicz, Oracle and/or its affiliates<p> 163 Distributed under the Boost Software License, Version 1.0. (See accompanying 164 file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) 165 </p> 166</div></td> 167</tr></table> 168<hr> 169<div class="spirit-nav"> 170<a accesskey="p" href="concept_linestring.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="concept_multi_point.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 171</div> 172</body> 173</html> 174
