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<a href="classCGAL_1_1Point__2-members.html">List of all members</a> |
<a href="#related">Related Functions</a> </div>
<div class="headertitle"><div class="title">CGAL::Point_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>
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<p><code>#include <CGAL/Point_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::Point_2< Kernel ></div><p>An object <code>p</code> of the class <code><a class="el" href="classCGAL_1_1Point__2.html" title="An object p of the class Point_2 is a point in the two-dimensional Euclidean plane .">Point_2</a></code> is a point in the two-dimensional Euclidean plane \( \E^2\). </p>
<p>Remember that <code>Kernel::RT</code> and <code>Kernel::FT</code> denote a <code><a class="elRef" href="../Algebraic_foundations/classRingNumberType.html">RingNumberType</a></code> and a <code><a class="elRef" href="../Algebraic_foundations/classFieldNumberType.html">FieldNumberType</a></code>, respectively. For the kernel model <code><a class="el" href="structCGAL_1_1Cartesian.html" title="A model for Kernel that uses Cartesian coordinates to represent the geometric objects.">Cartesian</a><NT></code>, the two types are the same. For the kernel model <code><a class="el" href="structCGAL_1_1Homogeneous.html" title="A model for a Kernel using homogeneous coordinates to represent the geometric objects.">Homogeneous</a><NT></code>, <code>Kernel::RT</code> is equal to <code>NT</code>, and <code>Kernel::FT</code> is equal to <code><a class="elRef" href="../Number_types/classCGAL_1_1Quotient.html">Quotient</a><NT></code>.</p>
<p><b>Example</b><br>
</p>
<p>The following declaration creates two points with Cartesian double coordinates.</p>
<div class="fragment"><div class="line"><a class="code hl_class" href="classCGAL_1_1Point__2.html">Point_2< Cartesian<double></a> > p, q(1.0, 2.0);</div>
<div class="ttc" id="aclassCGAL_1_1Point__2_html"><div class="ttname"><a href="classCGAL_1_1Point__2.html">CGAL::Point_2</a></div><div class="ttdoc">An object p of the class Point_2 is a point in the two-dimensional Euclidean plane .</div><div class="ttdef"><b>Definition:</b> Point_2.h:37</div></div>
</div><!-- fragment --><p>The variable <code>p</code> is uninitialized and should first be used on the left hand side of an assignment.</p>
<div class="fragment"><div class="line">p = q;</div>
<div class="line"> </div>
<div class="line">std::cout << p.<a class="code hl_function" href="classCGAL_1_1Point__2.html#a2d77e6a2b4ae36169e0cf4e2e9c35378">x</a>() << <span class="stringliteral">" "</span> << p.<a class="code hl_function" href="classCGAL_1_1Point__2.html#ac844c95dbfc2e70e82dc6ee1095871f4">y</a>() << std::endl;</div>
<div class="ttc" id="aclassCGAL_1_1Point__2_html_a2d77e6a2b4ae36169e0cf4e2e9c35378"><div class="ttname"><a href="classCGAL_1_1Point__2.html#a2d77e6a2b4ae36169e0cf4e2e9c35378">CGAL::Point_2::x</a></div><div class="ttdeci">Kernel::FT x() const</div><div class="ttdoc">returns the Cartesian coordinate, that is hx()/hw().</div></div>
<div class="ttc" id="aclassCGAL_1_1Point__2_html_ac844c95dbfc2e70e82dc6ee1095871f4"><div class="ttname"><a href="classCGAL_1_1Point__2.html#ac844c95dbfc2e70e82dc6ee1095871f4">CGAL::Point_2::y</a></div><div class="ttdeci">Kernel::FT y() const</div><div class="ttdoc">returns the Cartesian coordinate, that is hy()/hw().</div></div>
</div><!-- fragment --><dl>
<dt>Is model of</dt>
<dd><code><a class="el" href="classKernel_1_1Point__2.html" title="A type representing points in two dimensions.">Kernel::Point_2</a></code> </dd>
<dt></dt>
<dd><code><a class="elRef" href="../STL_Extension/classHashable.html">Hashable</a></code> if <code><a class="el" href="classKernel.html" title="The concept of a kernel is defined by a set of requirements on the provision of certain types and acc...">Kernel</a></code> is a cartesian kernel and if <code>Kernel::FT</code> is <code><a class="elRef" href="../STL_Extension/classHashable.html">Hashable</a></code></dd>
</dl>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="related" name="related"></a>
Related Functions</h2></td></tr>
<tr><td class="ititle" colspan="2"><p>(Note that these are not member functions.) </p>
</td></tr>
<tr class="memitem:ab95ced18112a90aba4b88a5180dd4f68"><td class="memItemLeft" align="right" valign="top"><a id="ab95ced18112a90aba4b88a5180dd4f68" name="ab95ced18112a90aba4b88a5180dd4f68"></a>
bool </td><td class="memItemRight" valign="bottom"><b>operator<</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_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &q)</td></tr>
<tr class="memdesc:ab95ced18112a90aba4b88a5180dd4f68"><td class="mdescLeft"> </td><td class="mdescRight">returns true iff <code>p</code> is lexicographically smaller than <code>q</code>, i.e. either if <code>p.x() < q.x()</code> or if <code>p.x() == q.x()</code> and <code>p.y() < q.y()</code>. <br></td></tr>
<tr class="separator:ab95ced18112a90aba4b88a5180dd4f68"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ac0cb9a24bbd0d9353768f1e17b7b0702"><td class="memItemLeft" align="right" valign="top"><a id="ac0cb9a24bbd0d9353768f1e17b7b0702" name="ac0cb9a24bbd0d9353768f1e17b7b0702"></a>
bool </td><td class="memItemRight" valign="bottom"><b>operator></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_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &q)</td></tr>
<tr class="memdesc:ac0cb9a24bbd0d9353768f1e17b7b0702"><td class="mdescLeft"> </td><td class="mdescRight">returns true iff <code>p</code> is lexicographically greater than <code>q</code>. <br></td></tr>
<tr class="separator:ac0cb9a24bbd0d9353768f1e17b7b0702"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a1c1498fc0e1b7309920830542f8536ea"><td class="memItemLeft" align="right" valign="top"><a id="a1c1498fc0e1b7309920830542f8536ea" name="a1c1498fc0e1b7309920830542f8536ea"></a>
bool </td><td class="memItemRight" valign="bottom"><b>operator<=</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_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &q)</td></tr>
<tr class="memdesc:a1c1498fc0e1b7309920830542f8536ea"><td class="mdescLeft"> </td><td class="mdescRight">returns true iff <code>p</code> is lexicographically smaller or equal to <code>q</code>. <br></td></tr>
<tr class="separator:a1c1498fc0e1b7309920830542f8536ea"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a54d75f0356d4a3681e53098ccfdc96ab"><td class="memItemLeft" align="right" valign="top"><a id="a54d75f0356d4a3681e53098ccfdc96ab" name="a54d75f0356d4a3681e53098ccfdc96ab"></a>
bool </td><td class="memItemRight" valign="bottom"><b>operator>=</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_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &q)</td></tr>
<tr class="memdesc:a54d75f0356d4a3681e53098ccfdc96ab"><td class="mdescLeft"> </td><td class="mdescRight">returns true iff <code>p</code> is lexicographically greater or equal to <code>q</code>. <br></td></tr>
<tr class="separator:a54d75f0356d4a3681e53098ccfdc96ab"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a84b6abfccf34b2ac0b07063c12c7d336"><td class="memItemLeft" align="right" valign="top"><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"><a class="el" href="classCGAL_1_1Point__2.html#a84b6abfccf34b2ac0b07063c12c7d336">operator-</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:a84b6abfccf34b2ac0b07063c12c7d336"><td class="mdescLeft"> </td><td class="mdescRight">returns the difference vector between <code>q</code> and <code>p</code>. <br></td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader">Types</h2></td></tr>
<tr class="memitem:abd267a9e192755c434fdca0e684a985d"><td class="memItemLeft" align="right" valign="top"><a id="abd267a9e192755c434fdca0e684a985d" name="abd267a9e192755c434fdca0e684a985d"></a>
typedef <a class="elRef" href="../Manual/classunspecified__type.html">unspecified_type</a> </td><td class="memItemRight" valign="bottom"><b>Cartesian_const_iterator</b></td></tr>
<tr class="memdesc:abd267a9e192755c434fdca0e684a985d"><td class="mdescLeft"> </td><td class="mdescRight">An iterator for enumerating the Cartesian coordinates of a point. <br></td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader">Creation</h2></td></tr>
<tr class="memitem:a361f8abdb70edd957f965f9e5e876af7"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Point__2.html#a361f8abdb70edd957f965f9e5e876af7">Point_2</a> (const <a class="el" href="classCGAL_1_1Origin.html">Origin</a> &<a class="el" href="group__kernel__enums.html#ga9d272a8e3a8080b851741b6d3a44afdc">ORIGIN</a>)</td></tr>
<tr class="memdesc:a361f8abdb70edd957f965f9e5e876af7"><td class="mdescLeft"> </td><td class="mdescRight">introduces a variable <code>p</code> with Cartesian coordinates \( (0,0)\). <br></td></tr>
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<tr class="memitem:a08b3e53d4272b0b87418c95eccaf8984"><td class="memItemLeft" align="right" valign="top"><a id="a08b3e53d4272b0b87418c95eccaf8984" name="a08b3e53d4272b0b87418c95eccaf8984"></a>
</td><td class="memItemRight" valign="bottom"><b>Point_2</b> (int <a class="el" href="classCGAL_1_1Point__2.html#a2d77e6a2b4ae36169e0cf4e2e9c35378">x</a>, int <a class="el" href="classCGAL_1_1Point__2.html#ac844c95dbfc2e70e82dc6ee1095871f4">y</a>)</td></tr>
<tr class="memdesc:a08b3e53d4272b0b87418c95eccaf8984"><td class="mdescLeft"> </td><td class="mdescRight">introduces a point <code>p</code> initialized to <code>(x,y)</code>. <br></td></tr>
<tr class="separator:a08b3e53d4272b0b87418c95eccaf8984"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af37827b476db6a63cd095ed0a89af57f"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Point__2.html#af37827b476db6a63cd095ed0a89af57f">Point_2</a> (double <a class="el" href="classCGAL_1_1Point__2.html#a2d77e6a2b4ae36169e0cf4e2e9c35378">x</a>, double <a class="el" href="classCGAL_1_1Point__2.html#ac844c95dbfc2e70e82dc6ee1095871f4">y</a>)</td></tr>
<tr class="memdesc:af37827b476db6a63cd095ed0a89af57f"><td class="mdescLeft"> </td><td class="mdescRight">introduces a point <code>p</code> initialized to <code>(x,y)</code> provided <code>RT</code> supports construction from <code>double</code>. <br></td></tr>
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<tr class="memitem:aac7161df759fa58f4b1c8cd336f9d44d"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Point__2.html#aac7161df759fa58f4b1c8cd336f9d44d">Point_2</a> (const Kernel::RT &<a class="el" href="classCGAL_1_1Point__2.html#a7b738e73d56c94d74ae77207eed88c4f">hx</a>, const Kernel::RT &<a class="el" href="classCGAL_1_1Point__2.html#a70c1aeead596d438247b9f5f583584ea">hy</a>, const Kernel::RT &<a class="el" href="classCGAL_1_1Point__2.html#ab878c738c78d66cb19047f558c4daaee">hw</a>=RT(1))</td></tr>
<tr class="memdesc:aac7161df759fa58f4b1c8cd336f9d44d"><td class="mdescLeft"> </td><td class="mdescRight">introduces a point <code>p</code> initialized to <code>(hx/hw,hy/hw)</code>. <br></td></tr>
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<tr class="memitem:ae86ad08ceefb6b2d9aac560c7ddc34ef"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Point__2.html#ae86ad08ceefb6b2d9aac560c7ddc34ef">Point_2</a> (const Kernel::FT &<a class="el" href="classCGAL_1_1Point__2.html#a2d77e6a2b4ae36169e0cf4e2e9c35378">x</a>, const Kernel::FT &<a class="el" href="classCGAL_1_1Point__2.html#ac844c95dbfc2e70e82dc6ee1095871f4">y</a>)</td></tr>
<tr class="memdesc:ae86ad08ceefb6b2d9aac560c7ddc34ef"><td class="mdescLeft"> </td><td class="mdescRight">introduces a point <code>p</code> initialized to <code>(x,y)</code>. <br></td></tr>
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<tr class="memitem:aae8dd158f6d63eb1a612a0068864e3f1"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Point__2.html#aae8dd158f6d63eb1a612a0068864e3f1">Point_2</a> (const Kernel::Weighted_point_2 &wp)</td></tr>
<tr class="memdesc:aae8dd158f6d63eb1a612a0068864e3f1"><td class="mdescLeft"> </td><td class="mdescRight">introduces a point from a weighted point. <br></td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader">Operations</h2></td></tr>
<tr class="memitem:a9aef233897ead320f39ce6739a5482d8"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Point__2.html#a9aef233897ead320f39ce6739a5482d8">operator==</a> (const <a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &q) const</td></tr>
<tr class="memdesc:a9aef233897ead320f39ce6739a5482d8"><td class="mdescLeft"> </td><td class="mdescRight">Test for equality. <br></td></tr>
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<tr class="memitem:a2b2542b533541a4575225cc25865e9b0"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Point__2.html#a2b2542b533541a4575225cc25865e9b0">operator!=</a> (const <a class="el" href="classCGAL_1_1Point__2.html">Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> > &q) const</td></tr>
<tr class="memdesc:a2b2542b533541a4575225cc25865e9b0"><td class="mdescLeft"> </td><td class="mdescRight">Test for inequality. <br></td></tr>
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<tr class="memitem:a24e99d35bd525056bad0c30330e610d7"><td class="memItemLeft" align="right" valign="top"><a id="a24e99d35bd525056bad0c30330e610d7" name="a24e99d35bd525056bad0c30330e610d7"></a>
<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"><b>operator+=</b> (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:a24e99d35bd525056bad0c30330e610d7"><td class="mdescLeft"> </td><td class="mdescRight">translates the point by the vector <code>v</code>. <br></td></tr>
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<tr class="memitem:a452b64bb546a08e814299f49f120d187"><td class="memItemLeft" align="right" valign="top"><a id="a452b64bb546a08e814299f49f120d187" name="a452b64bb546a08e814299f49f120d187"></a>
<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"><b>operator-=</b> (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:a452b64bb546a08e814299f49f120d187"><td class="mdescLeft"> </td><td class="mdescRight">translates the point by the vector -<code>v</code>. <br></td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader">Coordinate Access</h2></td></tr>
<tr><td class="ititle" colspan="2"><p>There are two sets of coordinate access functions, namely to the homogeneous and to the Cartesian coordinates.</p>
<p>They can be used independently from the chosen kernel model. Note that you do not lose information with the homogeneous representation, because the <code><a class="elRef" href="../Algebraic_foundations/classFieldNumberType.html">FieldNumberType</a></code> is a quotient. </p>
</td></tr>
<tr class="memitem:a7b738e73d56c94d74ae77207eed88c4f"><td class="memItemLeft" align="right" valign="top"><a id="a7b738e73d56c94d74ae77207eed88c4f" name="a7b738e73d56c94d74ae77207eed88c4f"></a>
Kernel::RT </td><td class="memItemRight" valign="bottom"><b>hx</b> () const</td></tr>
<tr class="memdesc:a7b738e73d56c94d74ae77207eed88c4f"><td class="mdescLeft"> </td><td class="mdescRight">returns the homogeneous \( x\) coordinate. <br></td></tr>
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<tr class="memitem:a70c1aeead596d438247b9f5f583584ea"><td class="memItemLeft" align="right" valign="top"><a id="a70c1aeead596d438247b9f5f583584ea" name="a70c1aeead596d438247b9f5f583584ea"></a>
Kernel::RT </td><td class="memItemRight" valign="bottom"><b>hy</b> () const</td></tr>
<tr class="memdesc:a70c1aeead596d438247b9f5f583584ea"><td class="mdescLeft"> </td><td class="mdescRight">returns the homogeneous \( y\) coordinate. <br></td></tr>
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<tr class="memitem:ab878c738c78d66cb19047f558c4daaee"><td class="memItemLeft" align="right" valign="top"><a id="ab878c738c78d66cb19047f558c4daaee" name="ab878c738c78d66cb19047f558c4daaee"></a>
Kernel::RT </td><td class="memItemRight" valign="bottom"><b>hw</b> () const</td></tr>
<tr class="memdesc:ab878c738c78d66cb19047f558c4daaee"><td class="mdescLeft"> </td><td class="mdescRight">returns the homogenizing coordinate. <br></td></tr>
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<tr class="memitem:a2d77e6a2b4ae36169e0cf4e2e9c35378"><td class="memItemLeft" align="right" valign="top">Kernel::FT </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Point__2.html#a2d77e6a2b4ae36169e0cf4e2e9c35378">x</a> () const</td></tr>
<tr class="memdesc:a2d77e6a2b4ae36169e0cf4e2e9c35378"><td class="mdescLeft"> </td><td class="mdescRight">returns the Cartesian \( x\) coordinate, that is <code><a class="el" href="classCGAL_1_1Point__2.html#a7b738e73d56c94d74ae77207eed88c4f" title="returns the homogeneous coordinate.">hx()</a></code>/<code><a class="el" href="classCGAL_1_1Point__2.html#ab878c738c78d66cb19047f558c4daaee" title="returns the homogenizing coordinate.">hw()</a></code>. <br></td></tr>
<tr class="separator:a2d77e6a2b4ae36169e0cf4e2e9c35378"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ac844c95dbfc2e70e82dc6ee1095871f4"><td class="memItemLeft" align="right" valign="top">Kernel::FT </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Point__2.html#ac844c95dbfc2e70e82dc6ee1095871f4">y</a> () const</td></tr>
<tr class="memdesc:ac844c95dbfc2e70e82dc6ee1095871f4"><td class="mdescLeft"> </td><td class="mdescRight">returns the Cartesian \( y\) coordinate, that is <code><a class="el" href="classCGAL_1_1Point__2.html#a70c1aeead596d438247b9f5f583584ea" title="returns the homogeneous coordinate.">hy()</a></code>/<code><a class="el" href="classCGAL_1_1Point__2.html#ab878c738c78d66cb19047f558c4daaee" title="returns the homogenizing coordinate.">hw()</a></code>. <br></td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader">Convenience Operations</h2></td></tr>
<tr><td class="ititle" colspan="2"><p>The following operations are for convenience and for compatibility with higher dimensional points.</p>
<p>Again they come in a Cartesian and in a homogeneous flavor. </p>
</td></tr>
<tr class="memitem:a97e9d520869b12caa7edab8a7f97a932"><td class="memItemLeft" align="right" valign="top">Kernel::RT </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Point__2.html#a97e9d520869b12caa7edab8a7f97a932">homogeneous</a> (int i) const</td></tr>
<tr class="memdesc:a97e9d520869b12caa7edab8a7f97a932"><td class="mdescLeft"> </td><td class="mdescRight">returns the i'th homogeneous coordinate of <code>p</code>. <br></td></tr>
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<tr class="memitem:aad9e9d84474250ad0984762fc8d180c0"><td class="memItemLeft" align="right" valign="top">Kernel::FT </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Point__2.html#aad9e9d84474250ad0984762fc8d180c0">cartesian</a> (int i) const</td></tr>
<tr class="memdesc:aad9e9d84474250ad0984762fc8d180c0"><td class="mdescLeft"> </td><td class="mdescRight">returns the i'th Cartesian coordinate of <code>p</code>. <br></td></tr>
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<tr class="memitem:a7edf8f8333bd3f8b1cd0c0335dbbe929"><td class="memItemLeft" align="right" valign="top">Kernel::FT </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Point__2.html#a7edf8f8333bd3f8b1cd0c0335dbbe929">operator[]</a> (int i) const</td></tr>
<tr class="memdesc:a7edf8f8333bd3f8b1cd0c0335dbbe929"><td class="mdescLeft"> </td><td class="mdescRight">returns <code>cartesian(i)</code>. <br></td></tr>
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<tr class="memitem:a163ff0e42a0726d8275af15d0f4b2968"><td class="memItemLeft" align="right" valign="top"><a id="a163ff0e42a0726d8275af15d0f4b2968" name="a163ff0e42a0726d8275af15d0f4b2968"></a>
<a class="el" href="classCGAL_1_1Point__2.html#abd267a9e192755c434fdca0e684a985d">Cartesian_const_iterator</a> </td><td class="memItemRight" valign="bottom"><b>cartesian_begin</b> () const</td></tr>
<tr class="memdesc:a163ff0e42a0726d8275af15d0f4b2968"><td class="mdescLeft"> </td><td class="mdescRight">returns an iterator to the Cartesian coordinates of <code>p</code>, starting with the 0th coordinate. <br></td></tr>
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<tr class="memitem:a6d8d28a004d9c08cd23957fc3af89c8b"><td class="memItemLeft" align="right" valign="top"><a id="a6d8d28a004d9c08cd23957fc3af89c8b" name="a6d8d28a004d9c08cd23957fc3af89c8b"></a>
<a class="el" href="classCGAL_1_1Point__2.html#abd267a9e192755c434fdca0e684a985d">Cartesian_const_iterator</a> </td><td class="memItemRight" valign="bottom"><b>cartesian_end</b> () const</td></tr>
<tr class="memdesc:a6d8d28a004d9c08cd23957fc3af89c8b"><td class="mdescLeft"> </td><td class="mdescRight">returns an off the end iterator to the <a class="el" href="structCGAL_1_1Cartesian.html" title="A model for Kernel that uses Cartesian coordinates to represent the geometric objects.">Cartesian</a> coordinates of <code>p</code>. <br></td></tr>
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<tr class="memitem:a6694a2aa77151abae4672d34ba252db7"><td class="memItemLeft" align="right" valign="top"><a id="a6694a2aa77151abae4672d34ba252db7" name="a6694a2aa77151abae4672d34ba252db7"></a>
int </td><td class="memItemRight" valign="bottom"><b>dimension</b> () const</td></tr>
<tr class="memdesc:a6694a2aa77151abae4672d34ba252db7"><td class="mdescLeft"> </td><td class="mdescRight">returns the dimension (the constant 2). <br></td></tr>
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<tr class="memitem:a808350922ee124a5ee2c8f2691311d2f"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classCGAL_1_1Bbox__2.html">Bbox_2</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classCGAL_1_1Point__2.html#a808350922ee124a5ee2c8f2691311d2f">bbox</a> () const</td></tr>
<tr class="memdesc:a808350922ee124a5ee2c8f2691311d2f"><td class="mdescLeft"> </td><td class="mdescRight">returns a bounding box containing <code>p</code>. <br></td></tr>
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<tr class="memitem:af2decacd0356adfa2e22ebb76176d523"><td class="memItemLeft" align="right" valign="top"><a id="af2decacd0356adfa2e22ebb76176d523" name="af2decacd0356adfa2e22ebb76176d523"></a>
<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"><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:af2decacd0356adfa2e22ebb76176d523"><td class="mdescLeft"> </td><td class="mdescRight">returns the point obtained by applying <code>t</code> on <code>p</code>. <br></td></tr>
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<tr class="memitem:ga7be1ffd6b3e12cbe03575d932420c672"><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"><b>operator+</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:ga7be1ffd6b3e12cbe03575d932420c672"><td class="mdescLeft"> </td><td class="mdescRight">returns the point obtained by translating <code>p</code> by the vector <code>v</code>. <br></td></tr>
<tr class="separator:ga7be1ffd6b3e12cbe03575d932420c672"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gaf6b6f30efbc1bbca5d00c8e8b33a3fb2"><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"><b>operator-</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:gaf6b6f30efbc1bbca5d00c8e8b33a3fb2"><td class="mdescLeft"> </td><td class="mdescRight">returns the point obtained by translating <code>p</code> by the vector -<code>v</code>. <br></td></tr>
<tr class="separator:gaf6b6f30efbc1bbca5d00c8e8b33a3fb2"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<h2 class="groupheader">Constructor & Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a361f8abdb70edd957f965f9e5e876af7">◆ </a></span>Point_2() <span class="overload">[1/5]</span></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">CGAL::Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::Point_2 </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="classCGAL_1_1Origin.html">Origin</a> & </td>
<td class="paramname"><em>ORIGIN</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>introduces a variable <code>p</code> with Cartesian coordinates \( (0,0)\). </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>
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</div>
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<h2 class="memtitle"><span class="permalink"><a href="#af37827b476db6a63cd095ed0a89af57f">◆ </a></span>Point_2() <span class="overload">[2/5]</span></h2>
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template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
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<td class="memname"><a class="el" href="classCGAL_1_1Point__2.html">CGAL::Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::Point_2 </td>
<td>(</td>
<td class="paramtype">double </td>
<td class="paramname"><em>x</em>, </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double </td>
<td class="paramname"><em>y</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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</div><div class="memdoc">
<p>introduces a point <code>p</code> initialized to <code>(x,y)</code> provided <code>RT</code> supports construction from <code>double</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>
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<h2 class="memtitle"><span class="permalink"><a href="#aac7161df759fa58f4b1c8cd336f9d44d">◆ </a></span>Point_2() <span class="overload">[3/5]</span></h2>
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<div class="memproto">
<div class="memtemplate">
template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
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<tr>
<td class="memname"><a class="el" href="classCGAL_1_1Point__2.html">CGAL::Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::Point_2 </td>
<td>(</td>
<td class="paramtype">const Kernel::RT & </td>
<td class="paramname"><em>hx</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Kernel::RT & </td>
<td class="paramname"><em>hy</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Kernel::RT & </td>
<td class="paramname"><em>hw</em> = <code>RT(1)</code> </td>
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<td>)</td>
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<p>introduces a point <code>p</code> initialized to <code>(hx/hw,hy/hw)</code>. </p>
<dl class="section pre"><dt>Precondition</dt><dd><code>hw != Kernel::RT(0)</code>. </dd></dl>
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<h2 class="memtitle"><span class="permalink"><a href="#ae86ad08ceefb6b2d9aac560c7ddc34ef">◆ </a></span>Point_2() <span class="overload">[4/5]</span></h2>
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<div class="memtemplate">
template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
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<tr>
<td class="memname"><a class="el" href="classCGAL_1_1Point__2.html">CGAL::Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::Point_2 </td>
<td>(</td>
<td class="paramtype">const Kernel::FT & </td>
<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Kernel::FT & </td>
<td class="paramname"><em>y</em> </td>
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<td></td>
<td>)</td>
<td></td><td></td>
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<p>introduces a point <code>p</code> initialized to <code>(x,y)</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>
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</div>
<a id="aae8dd158f6d63eb1a612a0068864e3f1" name="aae8dd158f6d63eb1a612a0068864e3f1"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aae8dd158f6d63eb1a612a0068864e3f1">◆ </a></span>Point_2() <span class="overload">[5/5]</span></h2>
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<div class="memproto">
<div class="memtemplate">
template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="classCGAL_1_1Point__2.html">CGAL::Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::Point_2 </td>
<td>(</td>
<td class="paramtype">const Kernel::Weighted_point_2 & </td>
<td class="paramname"><em>wp</em></td><td>)</td>
<td></td>
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<span class="mlabels"><span class="mlabel">explicit</span></span> </td>
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<p>introduces a point from a weighted point. </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>
<dl class="section warning"><dt>Warning</dt><dd>The <code>explicit</code> keyword is used to avoid accidental implicit conversions between <a class="el" href="classCGAL_1_1Point__2.html" title="An object p of the class Point_2 is a point in the two-dimensional Euclidean plane .">Point_2</a> and <a class="el" href="classCGAL_1_1Weighted__point__2.html" title="An object of the class Weighted_point_2 is a tuple of a two-dimensional point and a scalar weight.">Weighted_point_2</a>. </dd></dl>
</div>
</div>
<h2 class="groupheader">Member Function Documentation</h2>
<a id="a808350922ee124a5ee2c8f2691311d2f" name="a808350922ee124a5ee2c8f2691311d2f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a808350922ee124a5ee2c8f2691311d2f">◆ </a></span>bbox()</h2>
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<div class="memtemplate">
template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
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<td class="memname"><a class="el" href="classCGAL_1_1Bbox__2.html">Bbox_2</a> <a class="el" href="classCGAL_1_1Point__2.html">CGAL::Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::bbox </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</td>
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</table>
</div><div class="memdoc">
<p>returns a bounding box containing <code>p</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>
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</div>
<a id="aad9e9d84474250ad0984762fc8d180c0" name="aad9e9d84474250ad0984762fc8d180c0"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aad9e9d84474250ad0984762fc8d180c0">◆ </a></span>cartesian()</h2>
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<div class="memtemplate">
template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
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<td class="memname">Kernel::FT <a class="el" href="classCGAL_1_1Point__2.html">CGAL::Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::cartesian </td>
<td>(</td>
<td class="paramtype">int </td>
<td class="paramname"><em>i</em></td><td>)</td>
<td> const</td>
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<p>returns the i'th Cartesian coordinate of <code>p</code>. </p>
<dl class="section pre"><dt>Precondition</dt><dd><code>0 <= i <= 1</code>.</dd></dl>
<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>
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<h2 class="memtitle"><span class="permalink"><a href="#a97e9d520869b12caa7edab8a7f97a932">◆ </a></span>homogeneous()</h2>
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<div class="memtemplate">
template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
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<tr>
<td class="memname">Kernel::RT <a class="el" href="classCGAL_1_1Point__2.html">CGAL::Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::homogeneous </td>
<td>(</td>
<td class="paramtype">int </td>
<td class="paramname"><em>i</em></td><td>)</td>
<td> const</td>
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<p>returns the i'th homogeneous coordinate of <code>p</code>. </p>
<dl class="section pre"><dt>Precondition</dt><dd><code>0 <= i <= 2</code>. </dd></dl>
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</div>
<a id="a2b2542b533541a4575225cc25865e9b0" name="a2b2542b533541a4575225cc25865e9b0"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a2b2542b533541a4575225cc25865e9b0">◆ </a></span>operator!=()</h2>
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template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
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<td class="memname">bool <a class="el" href="classCGAL_1_1Point__2.html">CGAL::Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::operator!= </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><td>)</td>
<td> const</td>
</tr>
</table>
</div><div class="memdoc">
<p>Test for inequality. </p>
<p>The point can be compared with <code>ORIGIN</code>. </p>
</div>
</div>
<a id="a9aef233897ead320f39ce6739a5482d8" name="a9aef233897ead320f39ce6739a5482d8"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a9aef233897ead320f39ce6739a5482d8">◆ </a></span>operator==()</h2>
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template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
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<td class="memname">bool <a class="el" href="classCGAL_1_1Point__2.html">CGAL::Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::operator== </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><td>)</td>
<td> const</td>
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<p>Test for equality. </p>
<p>Two points are equal, iff their \( x\) and \( y\) coordinates are equal. The point can be compared with <code>ORIGIN</code>. </p>
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<h2 class="memtitle"><span class="permalink"><a href="#a7edf8f8333bd3f8b1cd0c0335dbbe929">◆ </a></span>operator[]()</h2>
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<div class="memtemplate">
template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
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<td class="memname">Kernel::FT <a class="el" href="classCGAL_1_1Point__2.html">CGAL::Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::operator[] </td>
<td>(</td>
<td class="paramtype">int </td>
<td class="paramname"><em>i</em></td><td>)</td>
<td> const</td>
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<p>returns <code>cartesian(i)</code>. </p>
<dl class="section pre"><dt>Precondition</dt><dd><code>0 <= i <= 1</code>.</dd></dl>
<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>
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</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a2d77e6a2b4ae36169e0cf4e2e9c35378">◆ </a></span>x()</h2>
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<div class="memproto">
<div class="memtemplate">
template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
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<tr>
<td class="memname">Kernel::FT <a class="el" href="classCGAL_1_1Point__2.html">CGAL::Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::x </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</td>
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<p>returns the Cartesian \( x\) coordinate, that is <code><a class="el" href="classCGAL_1_1Point__2.html#a7b738e73d56c94d74ae77207eed88c4f" title="returns the homogeneous coordinate.">hx()</a></code>/<code><a class="el" href="classCGAL_1_1Point__2.html#ab878c738c78d66cb19047f558c4daaee" title="returns the homogenizing coordinate.">hw()</a></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>
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<a id="ac844c95dbfc2e70e82dc6ee1095871f4" name="ac844c95dbfc2e70e82dc6ee1095871f4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac844c95dbfc2e70e82dc6ee1095871f4">◆ </a></span>y()</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">Kernel::FT <a class="el" href="classCGAL_1_1Point__2.html">CGAL::Point_2</a>< <a class="el" href="classKernel.html">Kernel</a> >::y </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</td>
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</table>
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<p>returns the Cartesian \( y\) coordinate, that is <code><a class="el" href="classCGAL_1_1Point__2.html#a70c1aeead596d438247b9f5f583584ea" title="returns the homogeneous coordinate.">hy()</a></code>/<code><a class="el" href="classCGAL_1_1Point__2.html#ab878c738c78d66cb19047f558c4daaee" title="returns the homogenizing coordinate.">hw()</a></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">Friends And Related Function Documentation</h2>
<a id="a84b6abfccf34b2ac0b07063c12c7d336" name="a84b6abfccf34b2ac0b07063c12c7d336"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a84b6abfccf34b2ac0b07063c12c7d336">◆ </a></span>operator-()</h2>
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<div class="memproto">
<div class="memtemplate">
template<typename <a class="el" href="classKernel.html">Kernel</a> > </div>
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<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="classCGAL_1_1Vector__2.html">Vector_2</a>< <a class="el" href="classKernel.html">Kernel</a> > operator- </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>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">related</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>returns the difference vector between <code>q</code> and <code>p</code>. </p>
<p>You can substitute <code>ORIGIN</code> for either <code>p</code> or <code>q</code>, but not for both. </p>
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<li class="navelem"><b>CGAL</b></li><li class="navelem"><a class="el" href="classCGAL_1_1Point__2.html">Point_2</a></li>
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