@@ -123,7 +123,7 @@ <h1>2D ellipse<a class="headerlink" href="#d-ellipse" title="Link to this headin
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">perim</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
 <span class="go">(2, 20)</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="2d_ellipse.html#spatialmath.geom2d.Ellipse.FromPerimeter" title="spatialmath.geom2d.Ellipse.FromPerimeter"><span class="n">Ellipse</span><span class="o">.</span><span class="n">FromPerimeter</span></a><span class="p">(</span><span class="n">perim</span><span class="p">)</span>
-<span class="go">Ellipse(radii=[1.+0.j 2.-0.j], centre=[3. 4.], theta=0.785398163397435)</span>
+<span class="go">Ellipse(radii=[1.+0.j 2.-0.j], centre=[3. 4.], theta=0.7853981633974343)</span>
 </pre></div>
 </div>
 <dl class="field-list simple">
 
@@ -716,11 +716,11 @@ <h1>se(2) twist<a class="headerlink" href="#se-2-twist" title="Link to this head
 <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="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">Twist3</span></a>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">S</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">Twist3</span></a><span class="p">(</span><span class="n">SE3</span><span class="o">.</span><span class="n">Rand</span><span class="p">())</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">S</span></a>
-<span class="go">Twist3([-0.47232, -1.479, 0.36317, -0.27707, 0.61083, -1.3003])</span>
+<span class="go">Twist3([1.3108, -0.98343, 0.16131, -0.45989, 0.79975, 2.8087])</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3.inv" title="spatialmath.twist.Twist3.inv"><span class="n">S</span><span class="o">.</span><span class="n">inv</span></a><span class="p">()</span>
-<span class="go">Twist3([0.47232, 1.479, -0.36317, 0.27707, -0.61083, 1.3003])</span>
+<span class="go">Twist3([-1.3108, 0.98343, -0.16131, 0.45989, -0.79975, -2.8087])</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">S</span></a> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3.inv" title="spatialmath.twist.Twist3.inv"><span class="n">S</span><span class="o">.</span><span class="n">inv</span></a><span class="p">()</span>
-<span class="go">Twist3([0, -1.1102e-16, 1.1102e-16, 0, 0, 0])</span>
+<span class="go">Twist3([5.5511e-16, -5.235e-33, 2.7756e-16, -1.0719e-17, 1.3878e-17, 1.3501e-17])</span>
 </pre></div>
 </div>
 </dd></dl>
 
@@ -490,9 +490,9 @@ <h1>SO(3) matrix<a class="headerlink" href="#so-3-matrix" title="Link to this he
 <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="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="3d_orient_SO3.html#spatialmath.pose3d.SO3" title="spatialmath.pose3d.SO3"><span class="n">SO3</span></a>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_orient_SO3.html#spatialmath.pose3d.SO3" title="spatialmath.pose3d.SO3"><span class="n">x</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="3d_orient_SO3.html#spatialmath.pose3d.SO3.Rand" title="spatialmath.pose3d.SO3.Rand"><span class="n">SO3</span><span class="o">.</span><span class="n">Rand</span></a><span class="p">()</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_orient_SO3.html#spatialmath.pose3d.SO3" title="spatialmath.pose3d.SO3"><span class="n">x</span></a>
-<span class="go">SO3(array([[-0.7462, -0.6606,  0.0823],</span>
-<span class="go">           [ 0.5962, -0.6082,  0.5241],</span>
-<span class="go">           [-0.2961,  0.4402,  0.8477]]))</span>
+<span class="go">SO3(array([[ 0.0048, -0.9778,  0.2097],</span>
+<span class="go">           [ 0.64  , -0.1581, -0.752 ],</span>
+<span class="go">           [ 0.7684,  0.1378,  0.625 ]]))</span>
 </pre></div>
 </div>
 <dl class="field-list simple">
 
@@ -453,11 +453,11 @@ <h1>Unit quaternion<a class="headerlink" href="#unit-quaternion" title="Link to
 <p>Example:</p>
 <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="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="3d_orient_unitquaternion.html#spatialmath.quaternion.UnitQuaternion" title="spatialmath.quaternion.UnitQuaternion"><span class="n">UnitQuaternion</span></a> <span class="k">as</span> <span class="n">UQ</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_orient_unitquaternion.html#spatialmath.quaternion.UnitQuaternion.Rand" title="spatialmath.quaternion.UnitQuaternion.Rand"><span class="n">UQ</span><span class="o">.</span><span class="n">Rand</span></a><span class="p">())</span>
-<span class="go"> 0.4414 &lt;&lt;  0.4585,  0.4210, -0.6463 &gt;&gt;</span>
+<span class="go"> 0.2470 &lt;&lt;  0.2336, -0.6851, -0.6443 &gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_orient_unitquaternion.html#spatialmath.quaternion.UnitQuaternion.Rand" title="spatialmath.quaternion.UnitQuaternion.Rand"><span class="n">UQ</span><span class="o">.</span><span class="n">Rand</span></a><span class="p">(</span><span class="mi">3</span><span class="p">))</span>
-<span class="go"> 0.2871 &lt;&lt;  0.4678,  0.6138, -0.5675 &gt;&gt;</span>
-<span class="go"> 0.9851 &lt;&lt; -0.1627,  0.0401, -0.0389 &gt;&gt;</span>
-<span class="go"> 0.4815 &lt;&lt; -0.1896,  0.6777,  0.5225 &gt;&gt;</span>
+<span class="go"> 0.0495 &lt;&lt; -0.2713, -0.0115, -0.9612 &gt;&gt;</span>
+<span class="go"> 0.3422 &lt;&lt; -0.2874,  0.7003,  0.5566 &gt;&gt;</span>
+<span class="go"> 0.7967 &lt;&lt;  0.3023,  0.0947,  0.5147 &gt;&gt;</span>
 </pre></div>
 </div>
 <dl class="field-list simple">
 
@@ -588,13 +588,13 @@ <h1>SE(3) matrix<a class="headerlink" href="#se-3-matrix" title="Link to this he
 <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="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="3d_pose_SE3.html#spatialmath.pose3d.SE3" title="spatialmath.pose3d.SE3"><span class="n">SE3</span></a>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_SE3.html#spatialmath.pose3d.SE3.Rand" title="spatialmath.pose3d.SE3.Rand"><span class="n">SE3</span><span class="o">.</span><span class="n">Rand</span></a><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
 <span class="go">SE3([</span>
-<span class="go">array([[ 0.3748, -0.7344,  0.5659, -0.9502],</span>
-<span class="go">       [-0.92  , -0.3701,  0.129 ,  0.7533],</span>
-<span class="go">       [ 0.1147, -0.569 , -0.8143, -0.5263],</span>
+<span class="go">array([[-0.7056, -0.3312,  0.6265,  0.351 ],</span>
+<span class="go">       [ 0.2319,  0.7275,  0.6458,  0.9865],</span>
+<span class="go">       [-0.6696,  0.6009, -0.4365,  0.5077],</span>
 <span class="go">       [ 0.    ,  0.    ,  0.    ,  1.    ]]),</span>
-<span class="go">array([[ 0.2094,  0.5213, -0.8273, -0.1144],</span>
-<span class="go">       [ 0.1691,  0.814 ,  0.5557, -0.951 ],</span>
-<span class="go">       [ 0.9631, -0.2562,  0.0823,  0.4297],</span>
+<span class="go">array([[ 0.1885,  0.0534,  0.9806,  0.3439],</span>
+<span class="go">       [-0.9555, -0.2208,  0.1957, -0.6524],</span>
+<span class="go">       [ 0.2269, -0.9739,  0.0094,  0.4882],</span>
 <span class="go">       [ 0.    ,  0.    ,  0.    ,  1.    ]]) ])</span>
 </pre></div>
 </div>
 
@@ -143,17 +143,17 @@ <h1>Unit dual quaternion<a class="headerlink" href="#unit-dual-quaternion" title
 <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="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="3d_pose_dualquaternion.html#spatialmath.DualQuaternion.UnitDualQuaternion" title="spatialmath.DualQuaternion.UnitDualQuaternion"><span class="n">UnitDualQuaternion</span></a><span class="p">,</span> <a class="sphinx-codeautolink-a" href="3d_pose_SE3.html#spatialmath.pose3d.SE3" title="spatialmath.pose3d.SE3"><span class="n">SE3</span></a>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_SE3.html#spatialmath.pose3d.SE3" title="spatialmath.pose3d.SE3"><span class="n">T</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="3d_pose_SE3.html#spatialmath.pose3d.SE3.Rand" title="spatialmath.pose3d.SE3.Rand"><span class="n">SE3</span><span class="o">.</span><span class="n">Rand</span></a><span class="p">()</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_pose_SE3.html#spatialmath.pose3d.SE3" title="spatialmath.pose3d.SE3"><span class="n">T</span></a><span class="p">)</span>
-<span class="go">   0.9101   -0.1421    0.3892   -0.3657    </span>
-<span class="go">  -0.3762    0.1098    0.92      0.7416    </span>
-<span class="go">  -0.1735   -0.9837    0.04646  -0.5227    </span>
+<span class="go">  -0.2771   -0.9511   -0.1367   -0.0973    </span>
+<span class="go">   0.02782  -0.1501    0.9883    0.7142    </span>
+<span class="go">  -0.9604    0.27      0.06806   0.6237    </span>
 <span class="go">   0         0         0         1</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_dualquaternion.html#spatialmath.DualQuaternion.UnitDualQuaternion" title="spatialmath.DualQuaternion.UnitDualQuaternion"><span class="n">d</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="3d_pose_dualquaternion.html#spatialmath.DualQuaternion.UnitDualQuaternion" title="spatialmath.DualQuaternion.UnitDualQuaternion"><span class="n">UnitDualQuaternion</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_pose_SE3.html#spatialmath.pose3d.SE3" title="spatialmath.pose3d.SE3"><span class="n">T</span></a><span class="p">)</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_pose_dualquaternion.html#spatialmath.DualQuaternion.UnitDualQuaternion" title="spatialmath.DualQuaternion.UnitDualQuaternion"><span class="n">d</span></a><span class="p">)</span>
-<span class="go"> 0.7187 &lt;&lt; -0.6622,  0.1957, -0.0814 &gt;&gt; + ε -0.2149 &lt; -0.1105,  0.4247,  0.0219 &gt;</span>
+<span class="go"> 0.4003 &lt;&lt; -0.4486,  0.5145,  0.6114 &gt;&gt; + ε -0.3962 &lt;  0.0384,  0.0328,  0.2600 &gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_pose_dualquaternion.html#spatialmath.DualQuaternion.UnitDualQuaternion.SE3" title="spatialmath.DualQuaternion.UnitDualQuaternion.SE3"><span class="n">d</span><span class="o">.</span><span class="n">SE3</span></a><span class="p">())</span>
-<span class="go">   0.9101   -0.1421    0.3892   -0.3657    </span>
-<span class="go">  -0.3762    0.1098    0.92      0.7416    </span>
-<span class="go">  -0.1735   -0.9837    0.04646  -0.5227    </span>
+<span class="go">  -0.2771   -0.9511   -0.1367   -0.0973    </span>
+<span class="go">   0.02782  -0.1501    0.9883    0.7142    </span>
+<span class="go">  -0.9604    0.27      0.06806   0.6237    </span>
 <span class="go">   0         0         0         1</span>
 </pre></div>
 </div>
@@ -200,13 +200,13 @@ <h1>Unit dual quaternion<a class="headerlink" href="#unit-dual-quaternion" title
 <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="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="3d_pose_dualquaternion.html#spatialmath.DualQuaternion.UnitDualQuaternion" title="spatialmath.DualQuaternion.UnitDualQuaternion"><span class="n">UnitDualQuaternion</span></a><span class="p">,</span> <a class="sphinx-codeautolink-a" href="3d_pose_SE3.html#spatialmath.pose3d.SE3" title="spatialmath.pose3d.SE3"><span class="n">SE3</span></a>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_SE3.html#spatialmath.pose3d.SE3" title="spatialmath.pose3d.SE3"><span class="n">T</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="3d_pose_SE3.html#spatialmath.pose3d.SE3.Rand" title="spatialmath.pose3d.SE3.Rand"><span class="n">SE3</span><span class="o">.</span><span class="n">Rand</span></a><span class="p">()</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_pose_SE3.html#spatialmath.pose3d.SE3" title="spatialmath.pose3d.SE3"><span class="n">T</span></a><span class="p">)</span>
-<span class="go">   0.9029   -0.2608    0.3418    0.2754    </span>
-<span class="go">  -0.239     0.3562    0.9033    0.4623    </span>
-<span class="go">  -0.3573   -0.8973    0.2592    0.3923    </span>
+<span class="go">  -0.3023    0.9513    0.06007   0.6794    </span>
+<span class="go">  -0.9496   -0.2951   -0.1056   -0.1114    </span>
+<span class="go">  -0.08273  -0.08897   0.9926    0.5953    </span>
 <span class="go">   0         0         0         1</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_dualquaternion.html#spatialmath.DualQuaternion.UnitDualQuaternion" title="spatialmath.DualQuaternion.UnitDualQuaternion"><span class="n">d</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="3d_pose_dualquaternion.html#spatialmath.DualQuaternion.UnitDualQuaternion" title="spatialmath.DualQuaternion.UnitDualQuaternion"><span class="n">UnitDualQuaternion</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_pose_SE3.html#spatialmath.pose3d.SE3" title="spatialmath.pose3d.SE3"><span class="n">T</span></a><span class="p">)</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_pose_dualquaternion.html#spatialmath.DualQuaternion.UnitDualQuaternion" title="spatialmath.DualQuaternion.UnitDualQuaternion"><span class="n">d</span></a><span class="p">)</span>
-<span class="go"> 0.7934 &lt;&lt; -0.5673,  0.2203,  0.0069 &gt;&gt; + ε  0.0259 &lt;  0.0677,  0.0712,  0.3171 &gt;</span>
+<span class="go">-0.5906 &lt;&lt; -0.0070, -0.0605,  0.8047 &gt;&gt; + ε -0.2405 &lt; -0.2275, -0.2425, -0.1967 &gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">type</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_pose_dualquaternion.html#spatialmath.DualQuaternion.UnitDualQuaternion" title="spatialmath.DualQuaternion.UnitDualQuaternion"><span class="n">d</span></a><span class="p">)</span>
 <span class="go">&lt;class 'spatialmath.DualQuaternion.UnitDualQuaternion'&gt;</span>
 </pre></div>
 
@@ -272,8 +272,8 @@ <h1>se(3) twist<a class="headerlink" href="#se-3-twist" title="Link to this head
 <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="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">Twist3</span></a>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3.Rand" title="spatialmath.twist.Twist3.Rand"><span class="n">Twist3</span><span class="o">.</span><span class="n">Rand</span></a><span class="p">(</span><span class="n">N</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
 <span class="go">Twist3([</span>
-<span class="go">  [-0.39482, 0.3723, -0.25871, 0.43681, 1.1773, 1.1857],</span>
-<span class="go">  [0.54222, 0.63569, 0.62347, 0.71304, -2.8807, 0.32338]</span>
+<span class="go">  [0.4726, -0.76985, 0.67827, 2.1538, -0.46039, -1.1215],</span>
+<span class="go">  [-1.1132, -0.6118, -0.60572, -1.9322, 0.031522, 0.59082]</span>
 <span class="go">])</span>
 </pre></div>
 </div>
@@ -1066,11 +1066,11 @@ <h1>se(3) twist<a class="headerlink" href="#se-3-twist" title="Link to this head
 <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="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">Twist3</span></a>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">S</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">Twist3</span></a><span class="p">(</span><span class="n">SE3</span><span class="o">.</span><span class="n">Rand</span><span class="p">())</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">S</span></a>
-<span class="go">Twist3([0.38159, -0.87725, -0.68071, 0.9069, 2.7033, 0.6204])</span>
+<span class="go">Twist3([0.29984, 1.2274, 0.11771, -1.0095, 0.24427, -1.3597])</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3.inv" title="spatialmath.twist.Twist3.inv"><span class="n">S</span><span class="o">.</span><span class="n">inv</span></a><span class="p">()</span>
-<span class="go">Twist3([-0.38159, 0.87725, 0.68071, -0.9069, -2.7033, -0.6204])</span>
+<span class="go">Twist3([-0.29984, -1.2274, -0.11771, 1.0095, -0.24427, 1.3597])</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">S</span></a> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3.inv" title="spatialmath.twist.Twist3.inv"><span class="n">S</span><span class="o">.</span><span class="n">inv</span></a><span class="p">()</span>
-<span class="go">Twist3([2.2204e-16, 0, 2.2204e-16, 0, 0, 0])</span>
+<span class="go">Twist3([0, 0, 2.7756e-16, 0, 0, 0])</span>
 </pre></div>
 </div>
 </dd></dl>