1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>cross_product</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="../arithmetic.html" title="Arithmetic"> 9<link rel="prev" href="cross_product_2.html" title="cross_product"> 10<link rel="next" href="divide_point.html" title="divide_point"> 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="cross_product_2.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../arithmetic.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="divide_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.arithmetic.cross_product_2_0"></a><a class="link" href="cross_product_2_0.html" title="cross_product">cross_product</a> 28</h4></div></div></div> 29<p> 30 <a class="indexterm" name="idm45635686019616"></a> 31Computes the cross product of two vectors. 32 </p> 33<h6> 34<a name="geometry.reference.arithmetic.cross_product_2.h5"></a> 35 <span class="phrase"><a name="geometry.reference.arithmetic.cross_product_2.description0"></a></span><a class="link" href="cross_product_2_0.html#geometry.reference.arithmetic.cross_product_2.description0">Description</a> 36 </h6> 37<p> 38 All vectors should have the same dimension, 3 or 2. 39 </p> 40<h6> 41<a name="geometry.reference.arithmetic.cross_product_2.h6"></a> 42 <span class="phrase"><a name="geometry.reference.arithmetic.cross_product_2.synopsis0"></a></span><a class="link" href="cross_product_2_0.html#geometry.reference.arithmetic.cross_product_2.synopsis0">Synopsis</a> 43 </h6> 44<p> 45</p> 46<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">P</span><span class="special">></span> 47<span class="identifier">P</span> <span class="identifier">cross_product</span><span class="special">(</span><span class="identifier">P</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">p1</span><span class="special">,</span> <span class="identifier">P</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">p2</span><span class="special">)</span></pre> 48<p> 49 </p> 50<h6> 51<a name="geometry.reference.arithmetic.cross_product_2.h7"></a> 52 <span class="phrase"><a name="geometry.reference.arithmetic.cross_product_2.parameters0"></a></span><a class="link" href="cross_product_2_0.html#geometry.reference.arithmetic.cross_product_2.parameters0">Parameters</a> 53 </h6> 54<div class="informaltable"><table class="table"> 55<colgroup> 56<col> 57<col> 58<col> 59<col> 60</colgroup> 61<thead><tr> 62<th> 63 <p> 64 Type 65 </p> 66 </th> 67<th> 68 <p> 69 Concept 70 </p> 71 </th> 72<th> 73 <p> 74 Name 75 </p> 76 </th> 77<th> 78 <p> 79 Description 80 </p> 81 </th> 82</tr></thead> 83<tbody> 84<tr> 85<td> 86 <p> 87 P const & 88 </p> 89 </td> 90<td> 91 </td> 92<td> 93 <p> 94 p1 95 </p> 96 </td> 97<td> 98 <p> 99 first vector 100 </p> 101 </td> 102</tr> 103<tr> 104<td> 105 <p> 106 P const & 107 </p> 108 </td> 109<td> 110 </td> 111<td> 112 <p> 113 p2 114 </p> 115 </td> 116<td> 117 <p> 118 second vector 119 </p> 120 </td> 121</tr> 122</tbody> 123</table></div> 124<h6> 125<a name="geometry.reference.arithmetic.cross_product_2.h8"></a> 126 <span class="phrase"><a name="geometry.reference.arithmetic.cross_product_2.returns0"></a></span><a class="link" href="cross_product_2_0.html#geometry.reference.arithmetic.cross_product_2.returns0">Returns</a> 127 </h6> 128<p> 129 the cross product vector 130 </p> 131<h6> 132<a name="geometry.reference.arithmetic.cross_product_2.h9"></a> 133 <span class="phrase"><a name="geometry.reference.arithmetic.cross_product_2.header0"></a></span><a class="link" href="cross_product_2_0.html#geometry.reference.arithmetic.cross_product_2.header0">Header</a> 134 </h6> 135<p> 136 <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">geometry</span><span class="special">/</span><span class="identifier">arithmetic</span><span class="special">/</span><span class="identifier">cross_product</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> 137 </p> 138<h6> 139<a name="geometry.reference.arithmetic.cross_product_2.h10"></a> 140 <span class="phrase"><a name="geometry.reference.arithmetic.cross_product_2.examples"></a></span><a class="link" href="cross_product_2_0.html#geometry.reference.arithmetic.cross_product_2.examples">Examples</a> 141 </h6> 142<p> 143 Calculate the cross product of two points 144 </p> 145<p> 146</p> 147<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> 148<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">geometry</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> 149<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">geometry</span><span class="special">/</span><span class="identifier">arithmetic</span><span class="special">/</span><span class="identifier">cross_product</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> 150 151<span class="keyword">namespace</span> <span class="identifier">bg</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">geometry</span><span class="special">;</span> <a class="co" name="geometry.reference.arithmetic.cross_product_2.c0" href="cross_product_2_0.html#geometry.reference.arithmetic.cross_product_2.c1"><img src="../../../../../../../doc/src/images/callouts/1.png" alt="1" border="0"></a> 152 153<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> 154<span class="special">{</span> 155 <span class="comment">//Example 1 2D Vector</span> 156 157 <span class="identifier">bg</span><span class="special">::</span><span class="identifier">model</span><span class="special">::</span><span class="identifier">point</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">bg</span><span class="special">::</span><span class="identifier">cs</span><span class="special">::</span><span class="identifier">cartesian</span><span class="special">></span> <span class="identifier">p1</span><span class="special">(</span><span class="number">7.0</span><span class="special">,</span> <span class="number">2.0</span><span class="special">);</span> 158 <span class="identifier">bg</span><span class="special">::</span><span class="identifier">model</span><span class="special">::</span><span class="identifier">point</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">bg</span><span class="special">::</span><span class="identifier">cs</span><span class="special">::</span><span class="identifier">cartesian</span><span class="special">></span> <span class="identifier">p2</span><span class="special">(</span><span class="number">4.0</span><span class="special">,</span> <span class="number">5.0</span><span class="special">);</span> 159 160 <span class="identifier">bg</span><span class="special">::</span><span class="identifier">model</span><span class="special">::</span><span class="identifier">point</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">bg</span><span class="special">::</span><span class="identifier">cs</span><span class="special">::</span><span class="identifier">cartesian</span><span class="special">></span> <span class="identifier">r1</span><span class="special">;</span> 161 162 <span class="identifier">r1</span> <span class="special">=</span> <span class="identifier">bg</span><span class="special">::</span><span class="identifier">cross_product</span><span class="special">(</span><span class="identifier">p1</span><span class="special">,</span><span class="identifier">p2</span><span class="special">);</span> 163 164 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Cross Product 1: "</span><span class="special"><<</span> <span class="identifier">r1</span><span class="special">.</span><span class="identifier">get</span><span class="special"><</span><span class="number">0</span><span class="special">>()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">//Note that the second point (r1.get<1>) would be undefined in this case</span> 165 166 <span class="comment">//Example 2 - 3D Vector </span> 167 168 <span class="identifier">bg</span><span class="special">::</span><span class="identifier">model</span><span class="special">::</span><span class="identifier">point</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="number">3</span><span class="special">,</span> <span class="identifier">bg</span><span class="special">::</span><span class="identifier">cs</span><span class="special">::</span><span class="identifier">cartesian</span><span class="special">></span> <span class="identifier">p3</span><span class="special">(</span><span class="number">4.0</span><span class="special">,</span> <span class="number">6.0</span><span class="special">,</span> <span class="number">5.0</span><span class="special">);</span> 169 <span class="identifier">bg</span><span class="special">::</span><span class="identifier">model</span><span class="special">::</span><span class="identifier">point</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="number">3</span><span class="special">,</span> <span class="identifier">bg</span><span class="special">::</span><span class="identifier">cs</span><span class="special">::</span><span class="identifier">cartesian</span><span class="special">></span> <span class="identifier">p4</span><span class="special">(</span><span class="number">7.0</span><span class="special">,</span> <span class="number">2.0</span><span class="special">,</span> <span class="number">3.0</span><span class="special">);</span> 170 171 <span class="identifier">bg</span><span class="special">::</span><span class="identifier">model</span><span class="special">::</span><span class="identifier">point</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="number">3</span><span class="special">,</span> <span class="identifier">bg</span><span class="special">::</span><span class="identifier">cs</span><span class="special">::</span><span class="identifier">cartesian</span><span class="special">></span> <span class="identifier">r2</span><span class="special">;</span> 172 173 <span class="identifier">r2</span> <span class="special">=</span> <span class="identifier">bg</span><span class="special">::</span><span class="identifier">cross_product</span><span class="special">(</span><span class="identifier">p3</span><span class="special">,</span><span class="identifier">p4</span><span class="special">);</span> 174 175 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Cross Product 2: ("</span><span class="special"><<</span> <span class="identifier">r2</span><span class="special">.</span><span class="identifier">get</span><span class="special"><</span><span class="number">0</span><span class="special">>()</span> <span class="special"><<</span><span class="string">","</span><span class="special"><<</span> <span class="identifier">r2</span><span class="special">.</span><span class="identifier">get</span><span class="special"><</span><span class="number">1</span><span class="special">>()</span> <span class="special"><<</span><span class="string">","</span><span class="special"><<</span> <span class="identifier">r2</span><span class="special">.</span><span class="identifier">get</span><span class="special"><</span><span class="number">2</span><span class="special">>()</span> <span class="special"><<</span> <span class="string">")"</span><span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> 176 177 <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> 178<span class="special">}</span> 179</pre> 180<p> 181 </p> 182<div class="calloutlist"><table border="0" summary="Callout list"><tr> 183<td width="5%" valign="top" align="left"><p><a name="geometry.reference.arithmetic.cross_product_2.c1"></a><a href="#geometry.reference.arithmetic.cross_product_2.c0"><img src="../../../../../../../doc/src/images/callouts/1.png" alt="1" border="0"></a> </p></td> 184<td valign="top" align="left"><p> 185 Convenient namespace alias 186 </p></td> 187</tr></table></div> 188<p> 189 Output: 190 </p> 191<pre class="programlisting">Cross Product 1: 27 192Cross Product 2: (8,23,-34) 193</pre> 194</div> 195<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 196<td align="left"></td> 197<td align="right"><div class="copyright-footer">Copyright © 2009-2019 Barend Gehrels, Bruno Lalande, Mateusz Loskot, Adam 198 Wulkiewicz, Oracle and/or its affiliates<p> 199 Distributed under the Boost Software License, Version 1.0. (See accompanying 200 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>) 201 </p> 202</div></td> 203</tr></table> 204<hr> 205<div class="spirit-nav"> 206<a accesskey="p" href="cross_product_2.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../arithmetic.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="divide_point.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 207</div> 208</body> 209</html> 210
