@@ -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=0.7853981633974343)</span>
+<span class="go">Ellipse(radii=[1.+0.j 2.-0.j], centre=[3. 4.], theta=0.785398163397435)</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([1.0696, 0.3719, 0.76054, 2.012, -1.1901, 0.54468])</span>
+<span class="go">Twist3([-0.47232, -1.479, 0.36317, -0.27707, 0.61083, -1.3003])</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([-1.0696, -0.3719, -0.76054, -2.012, 1.1901, -0.54468])</span>
+<span class="go">Twist3([0.47232, 1.479, -0.36317, 0.27707, -0.61083, 1.3003])</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([-5.0272e-34, -1.6653e-16, 1.1102e-16, -2.7756e-17, -3.8588e-17, 3.1763e-17])</span>
+<span class="go">Twist3([0, -1.1102e-16, 1.1102e-16, 0, 0, 0])</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([[ 0.1545,  0.5164,  0.8423],</span>
-<span class="go">           [ 0.6414,  0.596 , -0.4831],</span>
-<span class="go">           [-0.7515,  0.6149, -0.2391]]))</span>
+<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>
 </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"> 0.7643 &lt;&lt;  0.1733,  0.2853, -0.5517 &gt;&gt;</span>
+<span class="go"> 0.4414 &lt;&lt;  0.4585,  0.4210, -0.6463 &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"> 0.5196 &lt;&lt; -0.4510,  0.4508,  0.5687 &gt;&gt;</span>
-<span class="go"> 0.3698 &lt;&lt;  0.6637, -0.6111,  0.2220 &gt;&gt;</span>
-<span class="go"> 0.2163 &lt;&lt;  0.0001, -0.9037, -0.3695 &gt;&gt;</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>
 </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([[-0.5472,  0.4278,  0.7194, -0.8533],</span>
-<span class="go">       [ 0.107 , -0.8167,  0.5671,  0.5322],</span>
-<span class="go">       [ 0.8301,  0.3873,  0.4012, -0.0011],</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">       [ 0.    ,  0.    ,  0.    ,  1.    ]]),</span>
-<span class="go">array([[ 0.3794,  0.8176,  0.4331, -0.0265],</span>
-<span class="go">       [ 0.778 , -0.5352,  0.3289, -0.831 ],</span>
-<span class="go">       [ 0.5008,  0.2122, -0.8392, -0.6685],</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">       [ 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">  -0.03437   0.6646   -0.7464    0.03953   </span>
-<span class="go">   0.0431   -0.7452   -0.6655   -0.02257   </span>
-<span class="go">  -0.9985   -0.05504  -0.003037  0.7378    </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         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">-0.2331 &lt;&lt; -0.6546, -0.2703,  0.6664 &gt;&gt; + ε -0.2360 &lt;  0.0876, -0.2520, -0.0987 &gt;</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="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">  -0.03437   0.6646   -0.7464    0.03953   </span>
-<span class="go">   0.0431   -0.7452   -0.6655   -0.02257   </span>
-<span class="go">  -0.9985   -0.05504  -0.003037  0.7378    </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         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">  -0.2297    0.7092    0.6665    0.9958    </span>
-<span class="go">   0.4777   -0.5145    0.7121   -0.6368    </span>
-<span class="go">   0.8479    0.482    -0.2206    0.4491    </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         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">-0.0938 &lt;&lt;  0.6135,  0.4837,  0.6172 &gt;&gt; + ε -0.2900 &lt; -0.3518, -0.1397,  0.4151 &gt;</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="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">  [-1.2224, -0.5482, 0.76683, 0.28234, -2.2656, 0.17246],</span>
-<span class="go">  [0.51344, -0.28223, -1.1025, 2.1847, -0.98562, 0.92987]</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">])</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([-0.64184, 0.39067, 0.54801, -2.4192, -0.019844, -1.0778])</span>
+<span class="go">Twist3([0.38159, -0.87725, -0.68071, 0.9069, 2.7033, 0.6204])</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([0.64184, -0.39067, -0.54801, 2.4192, 0.019844, 1.0778])</span>
+<span class="go">Twist3([-0.38159, 0.87725, 0.68071, -0.9069, -2.7033, -0.6204])</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, -2.2204e-16, -1.6653e-16, 0, 0, 0])</span>
+<span class="go">Twist3([2.2204e-16, 0, 2.2204e-16, 0, 0, 0])</span>
 </pre></div>
 </div>
 </dd></dl>