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2d_ellipse-1.pdf

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2d_ellipse.html

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<p>&#169; Copyright 2020-, Peter Corke..
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2d_line.html

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<p>&#169; Copyright 2020-, Peter Corke..
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<span class="lastupdated">Last updated on 18-Apr-2024.
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2d_linesegment.html

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<span class="lastupdated">Last updated on 18-Apr-2024.
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<span class="lastupdated">Last updated on 13-May-2024.
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2d_orient_SO2-1.pdf

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2d_orient_SO2.html

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<p>&#169; Copyright 2020-, Peter Corke..
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<span class="lastupdated">Last updated on 13-May-2024.
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2d_polygon-1.pdf

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2d_polygon.html

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<p>&#169; Copyright 2020-, Peter Corke..
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<span class="lastupdated">Last updated on 18-Apr-2024.
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<span class="lastupdated">Last updated on 13-May-2024.
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2d_pose_SE2-1.pdf

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2d_pose_SE2.html

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<p>&#169; Copyright 2020-, Peter Corke..
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<span class="lastupdated">Last updated on 18-Apr-2024.
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<span class="lastupdated">Last updated on 13-May-2024.
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2d_pose_twist.html

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@@ -701,11 +701,11 @@ <h1>se(2) twist<a class="headerlink" href="#se-2-twist" title="Permalink to this
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<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">spatialmath</span> <span class="kn">import</span> <span class="n">Twist3</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="n">S</span> <span class="o">=</span> <span class="n">Twist3</span><span class="p">(</span><span class="n">SE3</span><span class="o">.</span><span class="n">Rand</span><span class="p">())</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="n">S</span>
704-
<span class="go">Twist3([-0.91017, -0.55606, 0.82654, -0.17246, -2.3463, -0.56793])</span>
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<span class="go">Twist3([-0.0096108, 0.13661, 1.2874, -1.8586, -1.2044, -0.043502])</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="n">S</span><span class="o">.</span><span class="n">inv</span><span class="p">()</span>
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<span class="go">Twist3([0.91017, 0.55606, -0.82654, 0.17246, 2.3463, 0.56793])</span>
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<span class="go">Twist3([0.0096108, -0.13661, -1.2874, 1.8586, 1.2044, 0.043502])</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="n">S</span> <span class="o">*</span> <span class="n">S</span><span class="o">.</span><span class="n">inv</span><span class="p">()</span>
708-
<span class="go">Twist3([-2.2204e-16, -8.3267e-17, -3.3307e-16, 0, 0, 0])</span>
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<span class="go">Twist3([-5.5511e-17, -1.1102e-16, -3.8858e-16, 0, 0, 0])</span>
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</pre></div>
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</div>
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</dd></dl>
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<p>&#169; Copyright 2020-, Peter Corke..
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<span class="lastupdated">Last updated on 18-Apr-2024.
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<span class="lastupdated">Last updated on 13-May-2024.
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3d_dualquaternion.html

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<div role="contentinfo">
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<p>&#169; Copyright 2020-, Peter Corke..
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<span class="lastupdated">Last updated on 18-Apr-2024.
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3d_line.html

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<p>&#169; Copyright 2020-, Peter Corke..
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<span class="lastupdated">Last updated on 18-Apr-2024.
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<span class="lastupdated">Last updated on 13-May-2024.
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3d_orient_SO3-1.pdf

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3d_orient_SO3.html

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@@ -504,9 +504,9 @@ <h1>SO(3) matrix<a class="headerlink" href="#so-3-matrix" title="Permalink to th
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<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">spatialmath</span> <span class="kn">import</span> <span class="n">SO3</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="n">x</span> <span class="o">=</span> <span class="n">SO3</span><span class="o">.</span><span class="n">Rand</span><span class="p">()</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="n">x</span>
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<span class="go">SO3(array([[-0.768 , 0.636 , 0.0755],</span>
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<span class="go"> [ 0.3237, 0.2837, 0.9026],</span>
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<span class="go"> [ 0.5526, 0.7177, -0.4238]]))</span>
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<span class="go">SO3(array([[ 0.3721, -0.5191, -0.7694],</span>
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<span class="go"> [ 0.371 , -0.6767, 0.636 ],</span>
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<span class="go"> [-0.8508, -0.5221, -0.0592]]))</span>
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</pre></div>
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</div>
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<dl class="field-list simple">
@@ -651,6 +651,28 @@ <h1>SO(3) matrix<a class="headerlink" href="#so-3-matrix" title="Permalink to th
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</dl>
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</dd></dl>
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<dl class="py method">
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<dt class="sig sig-object py" id="spatialmath.pose3d.SO3.UnitQuaternion">
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<span class="sig-name descname"><span class="pre">UnitQuaternion</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/pose3d.html#SO3.UnitQuaternion"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.pose3d.SO3.UnitQuaternion" title="Permalink to this definition"></a></dt>
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<dd><p>SO3 as a unit quaternion instance</p>
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<dl class="field-list simple">
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<dt class="field-odd">Returns</dt>
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<dd class="field-odd"><p>a unit quaternion representation</p>
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</dd>
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<dt class="field-even">Return type</dt>
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<dd class="field-even"><p>UnitQuaternion instance</p>
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</dd>
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</dl>
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<p><code class="docutils literal notranslate"><span class="pre">R.UnitQuaternion()</span></code> is an <code class="docutils literal notranslate"><span class="pre">UnitQuaternion</span></code> instance representing the same rotation
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as the SO3 rotation <code class="docutils literal notranslate"><span class="pre">R</span></code>.</p>
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<p>Example:</p>
669+
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">spatialmath</span> <span class="kn">import</span> <span class="n">SO3</span>
670+
<span class="gp">&gt;&gt;&gt; </span><span class="n">SO3</span><span class="o">.</span><span class="n">Rz</span><span class="p">(</span><span class="mf">0.3</span><span class="p">)</span><span class="o">.</span><span class="n">UnitQuaternion</span><span class="p">()</span>
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<span class="go">UnitQuaternion(array([0.9888, 0. , 0. , 0.1494]))</span>
672+
</pre></div>
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</div>
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</dd></dl>
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<dl class="py method">
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<dt class="sig sig-object py" id="spatialmath.pose3d.SO3.__add__">
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<span class="sig-name descname"><span class="pre">__add__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">right</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#spatialmath.pose3d.SO3.__add__" title="Permalink to this definition"></a></dt>
@@ -3009,7 +3031,7 @@ <h1>SO(3) matrix<a class="headerlink" href="#so-3-matrix" title="Permalink to th
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<div role="contentinfo">
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<p>&#169; Copyright 2020-, Peter Corke..
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<span class="lastupdated">Last updated on 18-Apr-2024.
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<span class="lastupdated">Last updated on 13-May-2024.
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3d_orient_unitquaternion.html

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<p>Example:</p>
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<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">spatialmath</span> <span class="kn">import</span> <span class="n">UnitQuaternion</span> <span class="k">as</span> <span class="n">UQ</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">UQ</span><span class="o">.</span><span class="n">Rand</span><span class="p">())</span>
454-
<span class="go"> 0.1630 &lt;&lt; -0.1271, 0.7775, 0.5939 &gt;&gt;</span>
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<span class="go"> 0.4535 &lt;&lt; 0.0997, -0.7699, 0.4378 &gt;&gt;</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">UQ</span><span class="o">.</span><span class="n">Rand</span><span class="p">(</span><span class="mi">3</span><span class="p">))</span>
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<span class="go"> 0.2822 &lt;&lt; 0.2440, -0.8064, -0.4589 &gt;&gt;</span>
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<span class="go"> 0.7041 &lt;&lt; -0.6589, -0.2637, -0.0242 &gt;&gt;</span>
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<span class="go"> 0.5300 &lt;&lt; 0.6432, 0.3893, -0.3922 &gt;&gt;</span>
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<span class="go"> 0.0689 &lt;&lt; -0.0831, -0.9847, 0.1367 &gt;&gt;</span>
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<span class="go"> 0.4568 &lt;&lt; 0.8859, 0.0708, -0.0390 &gt;&gt;</span>
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<span class="go"> 0.7968 &lt;&lt; -0.4355, -0.2317, -0.3491 &gt;&gt;</span>
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</pre></div>
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<dl class="field-list simple">
@@ -2484,7 +2484,7 @@ <h1>Unit quaternion<a class="headerlink" href="#unit-quaternion" title="Permalin
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<span class="lastupdated">Last updated on 13-May-2024.
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3d_plane.html

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<span class="lastupdated">Last updated on 13-May-2024.
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3d_pose_SE3-1.pdf

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3d_pose_SE3.html

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@@ -618,13 +618,13 @@ <h1>SE(3) matrix<a class="headerlink" href="#se-3-matrix" title="Permalink to th
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<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">spatialmath</span> <span class="kn">import</span> <span class="n">SE3</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="n">SE3</span><span class="o">.</span><span class="n">Rand</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
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<span class="go">SE3([</span>
621-
<span class="go">array([[ 0.5805, -0.1663, -0.7971, 0.9158],</span>
622-
<span class="go"> [-0.3364, 0.8425, -0.4207, 0.6684],</span>
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<span class="go"> [ 0.7415, 0.5124, 0.4331, -0.0256],</span>
621+
<span class="go">array([[ 0.6971, -0.3436, 0.6293, 0.6429],</span>
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<span class="go"> [ 0.0836, -0.8327, -0.5473, -0.565 ],</span>
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<span class="go"> [ 0.7121, 0.4342, -0.5517, 0.6927],</span>
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<span class="go"> [ 0. , 0. , 0. , 1. ]]),</span>
625-
<span class="go">array([[-0.0059, 0.5239, 0.8518, -0.6303],</span>
626-
<span class="go"> [-0.9852, -0.1492, 0.085 , -0.7984],</span>
627-
<span class="go"> [ 0.1716, -0.8386, 0.517 , 0.2132],</span>
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<span class="go">array([[ 0.5934, 0.7317, -0.3356, -0.6947],</span>
626+
<span class="go"> [ 0.2724, 0.2098, 0.939 , -0.0829],</span>
627+
<span class="go"> [ 0.7575, -0.6486, -0.0748, 0.0196],</span>
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<span class="go"> [ 0. , 0. , 0. , 1. ]]) ])</span>
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</pre></div>
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</div>
@@ -1032,6 +1032,28 @@ <h1>SE(3) matrix<a class="headerlink" href="#se-3-matrix" title="Permalink to th
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</dl>
10331033
</dd></dl>
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1035+
<dl class="py method">
1036+
<dt class="sig sig-object py" id="spatialmath.pose3d.SE3.UnitQuaternion">
1037+
<span class="sig-name descname"><span class="pre">UnitQuaternion</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#spatialmath.pose3d.SE3.UnitQuaternion" title="Permalink to this definition"></a></dt>
1038+
<dd><p>SO3 as a unit quaternion instance</p>
1039+
<dl class="field-list simple">
1040+
<dt class="field-odd">Returns</dt>
1041+
<dd class="field-odd"><p>a unit quaternion representation</p>
1042+
</dd>
1043+
<dt class="field-even">Return type</dt>
1044+
<dd class="field-even"><p>UnitQuaternion instance</p>
1045+
</dd>
1046+
</dl>
1047+
<p><code class="docutils literal notranslate"><span class="pre">R.UnitQuaternion()</span></code> is an <code class="docutils literal notranslate"><span class="pre">UnitQuaternion</span></code> instance representing the same rotation
1048+
as the SO3 rotation <code class="docutils literal notranslate"><span class="pre">R</span></code>.</p>
1049+
<p>Example:</p>
1050+
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">spatialmath</span> <span class="kn">import</span> <span class="n">SO3</span>
1051+
<span class="gp">&gt;&gt;&gt; </span><span class="n">SO3</span><span class="o">.</span><span class="n">Rz</span><span class="p">(</span><span class="mf">0.3</span><span class="p">)</span><span class="o">.</span><span class="n">UnitQuaternion</span><span class="p">()</span>
1052+
<span class="go">UnitQuaternion(array([0.9888, 0. , 0. , 0.1494]))</span>
1053+
</pre></div>
1054+
</div>
1055+
</dd></dl>
1056+
10351057
<dl class="py method">
10361058
<dt class="sig sig-object py" id="spatialmath.pose3d.SE3.__add__">
10371059
<span class="sig-name descname"><span class="pre">__add__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">right</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#spatialmath.pose3d.SE3.__add__" title="Permalink to this definition"></a></dt>
@@ -3460,7 +3482,7 @@ <h1>SE(3) matrix<a class="headerlink" href="#se-3-matrix" title="Permalink to th
34603482

34613483
<div role="contentinfo">
34623484
<p>&#169; Copyright 2020-, Peter Corke..
3463-
<span class="lastupdated">Last updated on 18-Apr-2024.
3485+
<span class="lastupdated">Last updated on 13-May-2024.
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</span></p>
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</div>
34663488

3d_pose_dualquaternion.html

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@@ -201,14 +201,14 @@ <h1>Unit dual quaternion<a class="headerlink" href="#unit-dual-quaternion" title
201201
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">spatialmath</span> <span class="kn">import</span> <span class="n">UnitDualQuaternion</span><span class="p">,</span> <span class="n">SE3</span>
202202
<span class="gp">&gt;&gt;&gt; </span><span class="n">T</span> <span class="o">=</span> <span class="n">SE3</span><span class="o">.</span><span class="n">Rand</span><span class="p">()</span>
203203
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
204-
<span class="go"> 0.9814 0.001594 -0.1922 -0.3993 </span>
205-
<span class="go"> -0.03561 0.9842 -0.1737 -0.5439 </span>
206-
<span class="go"> 0.1888 0.1773 0.9659 0.1066 </span>
204+
<span class="go"> 0.9614 -0.02782 -0.2737 -0.6802 </span>
205+
<span class="go"> 0.2708 0.2718 0.9235 -0.4805 </span>
206+
<span class="go"> 0.0487 -0.962 0.2688 0.8108 </span>
207207
<span class="go"> 0 0 0 1 </span>
208208

209209
<span class="gp">&gt;&gt;&gt; </span><span class="n">d</span> <span class="o">=</span> <span class="n">UnitDualQuaternion</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
210210
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
211-
<span class="go"> 0.9914 &lt;&lt; 0.0885, -0.0961, -0.0094 &gt;&gt; + ε -0.0080 &lt; -0.1903, -0.2667, 0.0961 &gt;</span>
211+
<span class="go"> 0.7909 &lt;&lt; -0.5960, -0.1019, 0.0944 &gt;&gt; + ε -0.2655 &lt; -0.2504, -0.3995, 0.2121 &gt;</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="nb">type</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
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<span class="go">&lt;class &#39;spatialmath.DualQuaternion.UnitDualQuaternion&#39;&gt;</span>
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</pre></div>
@@ -387,7 +387,7 @@ <h1>Unit dual quaternion<a class="headerlink" href="#unit-dual-quaternion" title
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<div role="contentinfo">
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<p>&#169; Copyright 2020-, Peter Corke..
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<span class="lastupdated">Last updated on 18-Apr-2024.
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<span class="lastupdated">Last updated on 13-May-2024.
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3d_pose_twist.html

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<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">spatialmath</span> <span class="kn">import</span> <span class="n">Twist3</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="n">Twist3</span><span class="o">.</span><span class="n">Rand</span><span class="p">(</span><span class="n">N</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
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<span class="go">Twist3([</span>
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<span class="go"> [0.70324, -0.20353, 0.53189, 0.12834, 0.42283, -1.768],</span>
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<span class="go"> [0.16965, 0.8109, 0.38997, 2.0537, 0.69441, 0.46064]</span>
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<span class="go"> [-0.89074, -0.088516, 0.77379, -0.73406, -0.3762, 0.61722],</span>
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<span class="go"> [-0.013092, 1.3491, -0.89224, 1.4434, 2.2282, 1.5603]</span>
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<span class="go">])</span>
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</pre></div>
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</div>
@@ -1081,11 +1081,11 @@ <h1>se(3) twist<a class="headerlink" href="#se-3-twist" title="Permalink to this
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<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">spatialmath</span> <span class="kn">import</span> <span class="n">Twist3</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="n">S</span> <span class="o">=</span> <span class="n">Twist3</span><span class="p">(</span><span class="n">SE3</span><span class="o">.</span><span class="n">Rand</span><span class="p">())</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="n">S</span>
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<span class="go">Twist3([-0.36425, -0.022578, 1.1753, -1.1929, 0.58508, -2.4692])</span>
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<span class="go">Twist3([-1.2288, -1.2813, -0.58902, -1.3462, -1.0936, 2.6115])</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="n">S</span><span class="o">.</span><span class="n">inv</span><span class="p">()</span>
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<span class="go">Twist3([0.36425, 0.022578, -1.1753, 1.1929, -0.58508, 2.4692])</span>
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<span class="go">Twist3([1.2288, 1.2813, 0.58902, 1.3462, 1.0936, -2.6115])</span>
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<span class="gp">&gt;&gt;&gt; </span><span class="n">S</span> <span class="o">*</span> <span class="n">S</span><span class="o">.</span><span class="n">inv</span><span class="p">()</span>
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<span class="go">Twist3([5.5511e-17, 0, -1.1102e-16, 0, 0, 0])</span>
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<span class="go">Twist3([-2.2204e-16, -1.1102e-16, -1.1102e-16, 0, 0, 0])</span>
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</pre></div>
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</div>
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</dd></dl>
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<p>&#169; Copyright 2020-, Peter Corke..
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3d_quaternion.html

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<div role="contentinfo">
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<p>&#169; Copyright 2020-, Peter Corke..
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<span class="lastupdated">Last updated on 18-Apr-2024.
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<span class="lastupdated">Last updated on 13-May-2024.
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</span></p>
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