-
Notifications
You must be signed in to change notification settings - Fork 2
/
Copy pathclassCGAL_1_1Ray__2.html
387 lines (370 loc) · 27.1 KB
/
classCGAL_1_1Ray__2.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<link rel="canonical" href="https://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Ray__2.html"/>
<link rel="icon" type="image/png" href="../Manual/g-196x196-doc.png">
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8">
<meta http-equiv="X-UA-Compatible" content="IE=11">
<meta name="generator" content="Doxygen 1.9.6">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>CGAL 6.1 - 2D and 3D Linear Geometry Kernel: CGAL::Ray_2< Kernel > Class Template Reference</title>
<!-- <link href="../Manual/tabs.css" rel="stylesheet" type="text/css"/> -->
<script type="text/javascript" src="../Manual/jquery.js"></script>
<script type="text/javascript" src="../Manual/dynsections.js"></script>
<script src="../Manual/hacks.js" type="text/javascript"></script>
<!-- Manually include treeview and search to avoid bloat and to fix
paths to the directory Manual . -->
<!-- $.treeview -->
<!-- $.search -->
<link href="navtree.css" rel="stylesheet" type="text/css">
<script type="text/javascript" src="../Manual/resize.js"></script>
<script type="text/javascript" src="navtreedata.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<script type="text/javascript">
$(document).ready(initResizable);
</script>
<link href="../Manual/search/search.css" rel="stylesheet" type="text/css">
<script type="text/javascript" src="../Manual/search/searchdata.js"></script>
<script type="text/javascript" src="../Manual/search/search.js"></script>
<script type="text/javascript">
$(document).ready(function() { init_search(); });
</script>
<link href="../Manual/search/search.css" rel="stylesheet" type="text/css">
<script type="text/javascript" src="../Manual/search/search.js"></script>
<!-- Manually done below. -->
<link href="../Manual/doxygen.css" rel="stylesheet" type="text/css">
<link href="../Manual/cgal_stylesheet.css" rel="stylesheet" type="text/css">
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
jax: ["input/TeX","output/HTML-CSS"],
});
//<![CDATA[
MathJax.Hub.Config(
{
TeX: {
Macros: {
qprel: [ "{\\gtreqless}", 0],
qpx: [ "{\\mathbf{x}}", 0],
qpl: [ "{\\mathbf{l}}", 0],
qpu: [ "{\\mathbf{u}}", 0],
qpc: [ "{\\mathbf{c}}", 0],
qpb: [ "{\\mathbf{b}}", 0],
qpy: [ "{\\mathbf{y}}", 0],
qpw: [ "{\\mathbf{w}}", 0],
qplambda: [ "{\\mathbf{\\lambda}}", 0],
ssWpoint: [ "{\\bf #1}", 1],
ssWeight: [ "{w_{#1}}", 1],
dabs: [ "{\\parallel\\! #1 \\!\\parallel}", 1],
E: [ "{\\mathrm{E}}", 0],
A: [ "{\\mathrm{A}}", 0],
R: [ "{\\mathrm{R}}", 0],
N: [ "{\\mathrm{N}}", 0],
Q: [ "{\\mathrm{Q}}", 0],
Z: [ "{\\mathrm{Z}}", 0],
ccSum: [ "{\\sum_{#1}^{#2}{#3}}", 3],
ccProd: [ "{\\prod_{#1}^{#2}{#3}}", 3],
pyr: [ "{\\operatorname{Pyr}}", 0],
aff: [ "{\\operatorname{aff}}", 0],
Ac: [ "{\\cal A}", 0],
Sc: [ "{\\cal S}", 0],
},
equationNumbers: { autoNumber: "AMS" }
}
}
);
MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () {
var PARSE = MathJax.InputJax.TeX.Parse,
TEXT = PARSE.prototype.InternalText;
PARSE.Augment({
InternalText: function (text,def) {
text = text.replace(/\\/g,"");
return TEXT.call(this,text,def);
}
});
});
//]]>
</script>
<script type="text/javascript" async="async" src="https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js"></script>
<script src="modules.js" type="text/javascript"></script>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="back-nav">
<ul>
<li><a href="https://www.cgal.org/">cgal.org</a></li>
<li><a href="../Manual/index.html">Top</a></li>
<li><a href="../Manual/general_intro.html">Getting Started</a></li>
<li><a href="../Manual/tutorials.html">Tutorials</a></li>
<li><a href="../Manual/packages.html">Package Overview</a></li>
<li><a href="../Manual/how_to_cite_cgal.html">Acknowledging CGAL</a></li>
</ul>
<!-- In a package SEARCHENGINE = false, so we cannot use
insertion. That's why we have to do it manually here. Notice
that we also take pngs from the Manual. -->
<div id="MSearchBox" class="MSearchBoxInactive">
<span class="left">
<span id="MSearchSelect" onmouseover="return searchBox.OnSearchSelectShow()" onmouseout="return searchBox.OnSearchSelectHide()">
</span>
<input type="text" id="MSearchField" value="" placeholder="Search" accesskey="S" onfocus="searchBox.OnSearchFieldFocus(true)" onblur="searchBox.OnSearchFieldFocus(false)" onkeyup="searchBox.OnSearchFieldChange(event)">
</span>
<span class="right">
<a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="../Manual/search/close.svg" alt=""></a>
</span>
</div>
</div>
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr id="projectrow">
<td id="projectalign">
<div id="projectname">CGAL 6.1 - 2D and 3D Linear Geometry Kernel
</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- Code below is usually inserted by doxygen when SEARCHENGINE =
true. Notice that the path to the search directory is adjusted to
the top-level.-->
<script type="text/javascript">
var searchBox = new SearchBox("searchBox", "../Manual/search/",'.html');
</script>
<!-- window showing the filter options -->
<div id="MSearchSelectWindow" onmouseover="return searchBox.OnSearchSelectShow()" onmouseout="return searchBox.OnSearchSelectHide()" onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<div id="MSearchResults">
<div class="SRPage">
<div id="SRIndex">
<div id="SRResults"></div>
<div class="SRStatus" id="Loading">Loading...</div>
<div class="SRStatus" id="Searching">Searching...</div>
<div class="SRStatus" id="NoMatches">No Matches</div>
</div>
</div>
</div>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.9.6 -->
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
<div id="nav-tree">
<div id="nav-tree-contents">
<div id="nav-sync" class="sync" style="display: none"></div>
</div>
</div>
<div id="splitbar" style="-moz-user-select:none;" class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
$(document).ready(function(){initNavTree('classCGAL_1_1Ray__2.html',''); initResizable(); });
/* @license-end */
</script>
<div id="doc-content">
<div class="header">
<div class="summary">
<a href="classCGAL_1_1Ray__2-members.html">List of all members</a> </div>
<div class="headertitle"><div class="title">CGAL::Ray_2< Kernel > Class Template Reference<div class="ingroups"><a class="el" href="group__PkgKernel23Ref.html">2D and 3D Linear Geometry Kernel Reference</a> » <a class="el" href="group__kernel__classes2.html">2D Kernel Objects</a></div></div></div>
</div><!--header-->
<div class="contents">
<p><code>#include <CGAL/Ray_2.h></code></p>
<a name="details" id="details"></a><h2 class="groupheader">Definition</h2>
<div class="textblock"><div class="compoundTemplParams">template<typename <a class="el" href="classKernel.html">Kernel</a>><br>
class CGAL::Ray_2< Kernel ></div><p>An object <code>r</code> of the data type <code><a class="el" href="classCGAL_1_1Ray__2.html" title="An object r of the data type Ray_2 is a directed straight ray in the two-dimensional Euclidean plane ...">Ray_2</a></code> is a directed straight ray in the two-dimensional Euclidean plane \( \E^2\). </p>
<p>It starts in a point called the <em>source</em> of <code>r</code> and goes to infinity.</p>
<dl>
<dt>Is model of</dt>
<dd><code><a class="el" href="classKernel_1_1Ray__2.html" title="A type representing rays in two dimensions.">Kernel::Ray_2</a></code> </dd>
</dl>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader">Creation</h2></td></tr>
<tr class="memitem:a01c6b5d3f0e223fefa896d4c8406ddbf"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Ray__2.html#a01c6b5d3f0e223fefa896d4c8406ddbf">Ray_2</a> (const <a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &p, const <a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &q)</td></tr>
<tr class="memdesc:a01c6b5d3f0e223fefa896d4c8406ddbf"><td class="mdescLeft"> </td><td class="mdescRight">introduces a ray <code>r</code> with source <code>p</code> and passing through point <code>q</code>. <br></td></tr>
<tr class="separator:a01c6b5d3f0e223fefa896d4c8406ddbf"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a438e5423ac125f2a6f636989ff46b6b8"><td class="memItemLeft" align="right" valign="top"><a id="a438e5423ac125f2a6f636989ff46b6b8" name="a438e5423ac125f2a6f636989ff46b6b8"></a>
</td><td class="memItemRight" valign="bottom"><b>Ray_2</b> (const <a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &p, const <a class="el" href="classCGAL_1_1Direction__2.html">Direction_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &d)</td></tr>
<tr class="memdesc:a438e5423ac125f2a6f636989ff46b6b8"><td class="mdescLeft"> </td><td class="mdescRight">introduces a ray <code>r</code> starting at source <code>p</code> with direction <code>d</code>. <br></td></tr>
<tr class="separator:a438e5423ac125f2a6f636989ff46b6b8"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af05a0a7b9c421e1fea00421acc0fad0a"><td class="memItemLeft" align="right" valign="top"><a id="af05a0a7b9c421e1fea00421acc0fad0a" name="af05a0a7b9c421e1fea00421acc0fad0a"></a>
</td><td class="memItemRight" valign="bottom"><b>Ray_2</b> (const <a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &p, const <a class="el" href="classCGAL_1_1Vector__2.html">Vector_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &v)</td></tr>
<tr class="memdesc:af05a0a7b9c421e1fea00421acc0fad0a"><td class="mdescLeft"> </td><td class="mdescRight">introduces a ray <code>r</code> starting at source <code>p</code> with the direction of <code>v</code>. <br></td></tr>
<tr class="separator:af05a0a7b9c421e1fea00421acc0fad0a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a5eb1f7f4592cf3b135472916a984eeaa"><td class="memItemLeft" align="right" valign="top"><a id="a5eb1f7f4592cf3b135472916a984eeaa" name="a5eb1f7f4592cf3b135472916a984eeaa"></a>
</td><td class="memItemRight" valign="bottom"><b>Ray_2</b> (const <a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &p, const <a class="el" href="classCGAL_1_1Line__2.html">Line_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &l)</td></tr>
<tr class="memdesc:a5eb1f7f4592cf3b135472916a984eeaa"><td class="mdescLeft"> </td><td class="mdescRight">introduces a ray <code>r</code> starting at source <code>p</code> with the same direction as <code>l</code>. <br></td></tr>
<tr class="separator:a5eb1f7f4592cf3b135472916a984eeaa"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader">Operations</h2></td></tr>
<tr class="memitem:a682abff02cf74bc364022c715454a2c6"><td class="memItemLeft" align="right" valign="top"><a id="a682abff02cf74bc364022c715454a2c6" name="a682abff02cf74bc364022c715454a2c6"></a>
bool </td><td class="memItemRight" valign="bottom"><b>operator==</b> (const <a class="el" href="classCGAL_1_1Ray__2.html">Ray_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &h) const</td></tr>
<tr class="memdesc:a682abff02cf74bc364022c715454a2c6"><td class="mdescLeft"> </td><td class="mdescRight">Test for equality: two rays are equal, iff they have the same source and the same direction. <br></td></tr>
<tr class="separator:a682abff02cf74bc364022c715454a2c6"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af897f164ef72c9aa864406f1c62a8d44"><td class="memItemLeft" align="right" valign="top"><a id="af897f164ef72c9aa864406f1c62a8d44" name="af897f164ef72c9aa864406f1c62a8d44"></a>
bool </td><td class="memItemRight" valign="bottom"><b>operator!=</b> (const <a class="el" href="classCGAL_1_1Ray__2.html">Ray_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &h) const</td></tr>
<tr class="memdesc:af897f164ef72c9aa864406f1c62a8d44"><td class="mdescLeft"> </td><td class="mdescRight">Test for inequality. <br></td></tr>
<tr class="separator:af897f164ef72c9aa864406f1c62a8d44"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a1df6a967cf44c7c1030f049751c18353"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Ray__2.html#a1df6a967cf44c7c1030f049751c18353">source</a> () const</td></tr>
<tr class="memdesc:a1df6a967cf44c7c1030f049751c18353"><td class="mdescLeft"> </td><td class="mdescRight">returns the source of <code>r</code>. <br></td></tr>
<tr class="separator:a1df6a967cf44c7c1030f049751c18353"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a00befcf4dae0c9847fccdf9ef2100a9a"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Ray__2.html#a00befcf4dae0c9847fccdf9ef2100a9a">point</a> (const Kernel::FT i) const</td></tr>
<tr class="memdesc:a00befcf4dae0c9847fccdf9ef2100a9a"><td class="mdescLeft"> </td><td class="mdescRight">returns a point on <code>r</code>. <br></td></tr>
<tr class="separator:a00befcf4dae0c9847fccdf9ef2100a9a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab0c6bdfcef7912dca5f49ab8567d81df"><td class="memItemLeft" align="right" valign="top"><a id="ab0c6bdfcef7912dca5f49ab8567d81df" name="ab0c6bdfcef7912dca5f49ab8567d81df"></a>
<a class="el" href="classCGAL_1_1Direction__2.html">Direction_2</a>< <a class="el" href="classKernel.html">Kernel</a> > </td><td class="memItemRight" valign="bottom"><b>direction</b> () const</td></tr>
<tr class="memdesc:ab0c6bdfcef7912dca5f49ab8567d81df"><td class="mdescLeft"> </td><td class="mdescRight">returns the direction of <code>r</code>. <br></td></tr>
<tr class="separator:ab0c6bdfcef7912dca5f49ab8567d81df"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:add1e63220f2eb43ae271826bf898bc3a"><td class="memItemLeft" align="right" valign="top"><a id="add1e63220f2eb43ae271826bf898bc3a" name="add1e63220f2eb43ae271826bf898bc3a"></a>
<a class="el" href="classCGAL_1_1Vector__2.html">Vector_2</a>< <a class="el" href="classKernel.html">Kernel</a> > </td><td class="memItemRight" valign="bottom"><b>to_vector</b> () const</td></tr>
<tr class="memdesc:add1e63220f2eb43ae271826bf898bc3a"><td class="mdescLeft"> </td><td class="mdescRight">returns a vector giving the direction of <code>r</code>. <br></td></tr>
<tr class="separator:add1e63220f2eb43ae271826bf898bc3a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a8b003ab6db366d9bffdfec7ecde35890"><td class="memItemLeft" align="right" valign="top"><a id="a8b003ab6db366d9bffdfec7ecde35890" name="a8b003ab6db366d9bffdfec7ecde35890"></a>
<a class="el" href="classCGAL_1_1Line__2.html">Line_2</a>< <a class="el" href="classKernel.html">Kernel</a> > </td><td class="memItemRight" valign="bottom"><b>supporting_line</b> () const</td></tr>
<tr class="memdesc:a8b003ab6db366d9bffdfec7ecde35890"><td class="mdescLeft"> </td><td class="mdescRight">returns the line supporting <code>r</code> which has the same direction. <br></td></tr>
<tr class="separator:a8b003ab6db366d9bffdfec7ecde35890"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a456590ff8dafb2c5bd9a2f1e811a1df9"><td class="memItemLeft" align="right" valign="top"><a id="a456590ff8dafb2c5bd9a2f1e811a1df9" name="a456590ff8dafb2c5bd9a2f1e811a1df9"></a>
<a class="el" href="classCGAL_1_1Ray__2.html">Ray_2</a>< <a class="el" href="classKernel.html">Kernel</a> > </td><td class="memItemRight" valign="bottom"><b>opposite</b> () const</td></tr>
<tr class="memdesc:a456590ff8dafb2c5bd9a2f1e811a1df9"><td class="mdescLeft"> </td><td class="mdescRight">returns the ray with the same source and the opposite direction. <br></td></tr>
<tr class="separator:a456590ff8dafb2c5bd9a2f1e811a1df9"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader">Predicates</h2></td></tr>
<tr class="memitem:a63b77c6bb2994ca418cfd0087b90d807"><td class="memItemLeft" align="right" valign="top"><a id="a63b77c6bb2994ca418cfd0087b90d807" name="a63b77c6bb2994ca418cfd0087b90d807"></a>
bool </td><td class="memItemRight" valign="bottom"><b>is_degenerate</b> () const</td></tr>
<tr class="memdesc:a63b77c6bb2994ca418cfd0087b90d807"><td class="mdescLeft"> </td><td class="mdescRight">ray <code>r</code> is degenerate, if the source and the second defining point fall together (that is if the direction is degenerate). <br></td></tr>
<tr class="separator:a63b77c6bb2994ca418cfd0087b90d807"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae2473d152571e13daabdad4c787a085e"><td class="memItemLeft" align="right" valign="top"><a id="ae2473d152571e13daabdad4c787a085e" name="ae2473d152571e13daabdad4c787a085e"></a>
bool </td><td class="memItemRight" valign="bottom"><b>is_horizontal</b> () const</td></tr>
<tr class="separator:ae2473d152571e13daabdad4c787a085e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab57b58ce052a0d585090c077ebc334b5"><td class="memItemLeft" align="right" valign="top"><a id="ab57b58ce052a0d585090c077ebc334b5" name="ab57b58ce052a0d585090c077ebc334b5"></a>
bool </td><td class="memItemRight" valign="bottom"><b>is_vertical</b> () const</td></tr>
<tr class="separator:ab57b58ce052a0d585090c077ebc334b5"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:afa01be9f470d364059c27c2e2c813369"><td class="memItemLeft" align="right" valign="top"><a id="afa01be9f470d364059c27c2e2c813369" name="afa01be9f470d364059c27c2e2c813369"></a>
bool </td><td class="memItemRight" valign="bottom"><b>has_on</b> (const <a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &p) const</td></tr>
<tr class="memdesc:afa01be9f470d364059c27c2e2c813369"><td class="mdescLeft"> </td><td class="mdescRight">A point is on <code>r</code>, iff it is equal to the source of <code>r</code>, or if it is in the interior of <code>r</code>. <br></td></tr>
<tr class="separator:afa01be9f470d364059c27c2e2c813369"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a8c43b53bdaece6927d91dcf86b0b423c"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Ray__2.html#a8c43b53bdaece6927d91dcf86b0b423c">collinear_has_on</a> (const <a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &p) const</td></tr>
<tr class="memdesc:a8c43b53bdaece6927d91dcf86b0b423c"><td class="mdescLeft"> </td><td class="mdescRight">checks if point <code>p</code> is on <code>r</code>. <br></td></tr>
<tr class="separator:a8c43b53bdaece6927d91dcf86b0b423c"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader">Miscellaneous</h2></td></tr>
<tr class="memitem:a5f589995661a753566d403a840694651"><td class="memItemLeft" align="right" valign="top"><a id="a5f589995661a753566d403a840694651" name="a5f589995661a753566d403a840694651"></a>
<a class="el" href="classCGAL_1_1Ray__2.html">Ray_2</a>< <a class="el" href="classKernel.html">Kernel</a> > </td><td class="memItemRight" valign="bottom"><b>transform</b> (const <a class="el" href="classCGAL_1_1Aff__transformation__2.html">Aff_transformation_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &t) const</td></tr>
<tr class="memdesc:a5f589995661a753566d403a840694651"><td class="mdescLeft"> </td><td class="mdescRight">returns the ray obtained by applying <code>t</code> on the source and on the direction of <code>r</code>. <br></td></tr>
<tr class="separator:a5f589995661a753566d403a840694651"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<h2 class="groupheader">Constructor & Destructor Documentation</h2>
<a id="a01c6b5d3f0e223fefa896d4c8406ddbf" name="a01c6b5d3f0e223fefa896d4c8406ddbf"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a01c6b5d3f0e223fefa896d4c8406ddbf">◆ </a></span>Ray_2()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
<table class="memname">
<tr>
<td class="memname"><a class="el" href="classCGAL_1_1Ray__2.html">CGAL::Ray_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::Ray_2 </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > & </td>
<td class="paramname"><em>p</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > & </td>
<td class="paramname"><em>q</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>introduces a ray <code>r</code> with source <code>p</code> and passing through point <code>q</code>. </p>
<dl class="section note">
<dt>Exactness</dt>
<dd>This construction is trivial and therefore always exact in <code><a class="el" href="classCGAL_1_1Exact__predicates__inexact__constructions__kernel.html" title="A typedef to a kernel that has the following properties:">Exact_predicates_inexact_constructions_kernel</a></code>.</dd>
</dl>
</div>
</div>
<h2 class="groupheader">Member Function Documentation</h2>
<a id="a8c43b53bdaece6927d91dcf86b0b423c" name="a8c43b53bdaece6927d91dcf86b0b423c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a8c43b53bdaece6927d91dcf86b0b423c">◆ </a></span>collinear_has_on()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
<table class="memname">
<tr>
<td class="memname">bool <a class="el" href="classCGAL_1_1Ray__2.html">CGAL::Ray_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::collinear_has_on </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > & </td>
<td class="paramname"><em>p</em></td><td>)</td>
<td> const</td>
</tr>
</table>
</div><div class="memdoc">
<p>checks if point <code>p</code> is on <code>r</code>. </p>
<p>This function is faster than function <code><a class="el" href="classCGAL_1_1Ray__2.html#afa01be9f470d364059c27c2e2c813369" title="A point is on r, iff it is equal to the source of r, or if it is in the interior of r.">has_on()</a></code> if the precondition checking is disabled. </p><dl class="section pre"><dt>Precondition</dt><dd><code>p</code> is on the supporting line of <code>r</code>. </dd></dl>
</div>
</div>
<a id="a00befcf4dae0c9847fccdf9ef2100a9a" name="a00befcf4dae0c9847fccdf9ef2100a9a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a00befcf4dae0c9847fccdf9ef2100a9a">◆ </a></span>point()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
<table class="memname">
<tr>
<td class="memname"><a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > <a class="el" href="classCGAL_1_1Ray__2.html">CGAL::Ray_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::point </td>
<td>(</td>
<td class="paramtype">const Kernel::FT </td>
<td class="paramname"><em>i</em></td><td>)</td>
<td> const</td>
</tr>
</table>
</div><div class="memdoc">
<p>returns a point on <code>r</code>. </p>
<p><code>point(0)</code> is the source, <code>point(i)</code>, with <code>i>0</code>, is different from the source. </p><dl class="section pre"><dt>Precondition</dt><dd><code>i >= 0</code>. </dd></dl>
</div>
</div>
<a id="a1df6a967cf44c7c1030f049751c18353" name="a1df6a967cf44c7c1030f049751c18353"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a1df6a967cf44c7c1030f049751c18353">◆ </a></span>source()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
<table class="memname">
<tr>
<td class="memname"><a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > <a class="el" href="classCGAL_1_1Ray__2.html">CGAL::Ray_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::source </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</td>
</tr>
</table>
</div><div class="memdoc">
<p>returns the source of <code>r</code>. </p>
<dl class="section note">
<dt>Exactness</dt>
<dd>This construction is trivial and therefore always exact in <code><a class="el" href="classCGAL_1_1Exact__predicates__inexact__constructions__kernel.html" title="A typedef to a kernel that has the following properties:">Exact_predicates_inexact_constructions_kernel</a></code>.</dd>
</dl>
</div>
</div>
</div><!-- contents -->
</div><!-- doc-content -->
<!-- HTML footer for doxygen 1.9.6-->
<!-- start footer part -->
<!-- The footer div is not part of the default but we require it to
move the footer to the bottom of the page. -->
<div id="footer">
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><b>CGAL</b></li><li class="navelem"><a class="el" href="classCGAL_1_1Ray__2.html">Ray_2</a></li>
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"></a> 1.9.6 </li>
</ul>
</div>
</div>
</body>
</html>