@@ -124,7 +124,7 @@ <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">
 
@@ -794,11 +794,11 @@ <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([-0.92498, -0.68392, 0.0879, -0.77596, -1.4685, -2.3913])</span>
+<span class="go">Twist3([-0.52802, -0.41278, 0.09182, -0.41924, 1.552, -0.2224])</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([0.92498, 0.68392, -0.0879, 0.77596, 1.4685, 2.3913])</span>
+<span class="go">Twist3([0.52802, 0.41278, -0.09182, 0.41924, -1.552, 0.2224])</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([-5.5511e-16, 0, 2.2204e-16, 0, 0, 0])</span>
+<span class="go">Twist3([-5.5511e-17, 5.5511e-17, -5.5511e-17, 0, 0, 0])</span>
 </pre></div>
 </div>
 </dd></dl>
 
@@ -491,9 +491,9 @@ <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([[-0.2377, -0.8481, -0.4735],</span>
-<span class="go">           [ 0.971 , -0.2203, -0.0928],</span>
-<span class="go">           [-0.0256, -0.4818,  0.8759]]))</span>
+<span class="go">SO3(array([[-0.0891,  0.726 ,  0.6819],</span>
+<span class="go">           [ 0.9003, -0.2341,  0.3669],</span>
+<span class="go">           [ 0.426 ,  0.6466, -0.6328]]))</span>
 </pre></div>
 </div>
 <dl class="field-list simple">
 
@@ -440,11 +440,11 @@ <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"> 0.1272 &lt;&lt;  0.4787,  0.8663, -0.0643 &gt;&gt;</span>
+<span class="go"> 0.4125 &lt;&lt;  0.7858, -0.1564,  0.4336 &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"> 0.0848 &lt;&lt; -0.2652,  0.6795,  0.6788 &gt;&gt;</span>
-<span class="go"> 0.4564 &lt;&lt; -0.0687, -0.8649,  0.1973 &gt;&gt;</span>
-<span class="go"> 0.6422 &lt;&lt;  0.3841, -0.6516,  0.1241 &gt;&gt;</span>
+<span class="go"> 0.1575 &lt;&lt;  0.2317, -0.4137, -0.8662 &gt;&gt;</span>
+<span class="go"> 0.5194 &lt;&lt; -0.1000, -0.6397,  0.5577 &gt;&gt;</span>
+<span class="go"> 0.8042 &lt;&lt; -0.1158, -0.5816,  0.0392 &gt;&gt;</span>
 </pre></div>
 </div>
 <dl class="field-list simple">
 
@@ -589,13 +589,13 @@ <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([[ 0.6456, -0.1818, -0.7417, -0.1105],</span>
-<span class="go">       [ 0.2258, -0.8824,  0.4128,  0.1434],</span>
-<span class="go">       [-0.7295, -0.434 , -0.5286, -0.779 ],</span>
+<span class="go">array([[ 0.969 , -0.054 , -0.241 ,  0.9376],</span>
+<span class="go">       [-0.1558, -0.8907, -0.427 ,  0.6754],</span>
+<span class="go">       [-0.1916,  0.4513, -0.8715, -0.8556],</span>
 <span class="go">       [ 0.    ,  0.    ,  0.    ,  1.    ]]),</span>
-<span class="go">array([[-0.2848, -0.6252, -0.7267, -0.3887],</span>
-<span class="go">       [ 0.9414, -0.0395, -0.335 , -0.1161],</span>
-<span class="go">       [ 0.1807, -0.7795,  0.5998, -0.228 ],</span>
+<span class="go">array([[ 0.1697,  0.5392,  0.8249, -0.9237],</span>
+<span class="go">       [ 0.0757,  0.8275, -0.5564, -0.0156],</span>
+<span class="go">       [-0.9826,  0.1568,  0.0996,  0.6652],</span>
 <span class="go">       [ 0.    ,  0.    ,  0.    ,  1.    ]]) ])</span>
 </pre></div>
 </div>
 
@@ -144,17 +144,17 @@ <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">  -0.7199    0.6769   -0.1537   -0.7748    </span>
-<span class="go">  -0.3964   -0.5827   -0.7095    0.2387    </span>
-<span class="go">  -0.5697   -0.4498    0.6878   -0.5691    </span>
+<span class="go">  -0.3331   -0.9278    0.1678   -0.01478   </span>
+<span class="go">  -0.8662    0.3714    0.3341    0.04974   </span>
+<span class="go">  -0.3724   -0.03408  -0.9275   -0.266     </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">-0.3103 &lt;&lt; -0.2092, -0.3352,  0.8646 &gt;&gt; + ε  0.2050 &lt;  0.1280,  0.3574,  0.2431 &gt;</span>
+<span class="go"> 0.1665 &lt;&lt; -0.5529,  0.8112,  0.0925 &gt;&gt; + ε -0.0120 &lt;  0.1090,  0.0784, -0.0144 &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">  -0.7199    0.6769   -0.1537   -0.7748    </span>
-<span class="go">  -0.3964   -0.5827   -0.7095    0.2387    </span>
-<span class="go">  -0.5697   -0.4498    0.6878   -0.5691    </span>
+<span class="go">  -0.3331   -0.9278    0.1678   -0.01478   </span>
+<span class="go">  -0.8662    0.3714    0.3341    0.04974   </span>
+<span class="go">  -0.3724   -0.03408  -0.9275   -0.266     </span>
 <span class="go">   0         0         0         1</span>
 </pre></div>
 </div>
@@ -201,13 +201,13 @@ <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">  -0.6032   -0.7851    0.1407   -0.4729    </span>
-<span class="go">   0.7954   -0.6051    0.03359   0.9386    </span>
-<span class="go">   0.05877   0.1322    0.9895   -0.1008    </span>
+<span class="go">  -0.3633    0.8671    0.3407    0.3972    </span>
+<span class="go">   0.931     0.3241    0.168    -0.2854    </span>
+<span class="go">   0.03526   0.3782   -0.925     0.1576    </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"> 0.4419 &lt;&lt;  0.0558,  0.0463,  0.8941 &gt;&gt; + ε  0.0365 &lt;  0.3175,  0.4160, -0.0594 &gt;</span>
+<span class="go"> 0.0945 &lt;&lt;  0.5562,  0.8082,  0.1690 &gt;&gt; + ε -0.0085 &lt; -0.0690, -0.0032,  0.2473 &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>
 
@@ -273,8 +273,8 @@ <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">  [-0.43145, -0.41212, 0.77944, -0.14007, 0.74899, 0.39317],</span>
-<span class="go">  [-0.31406, 0.4207, -0.89012, -0.84211, 0.34752, -2.2467]</span>
+<span class="go">  [0.26661, -0.20005, 0.80501, -0.37584, 0.098103, 0.46538],</span>
+<span class="go">  [0.45378, -0.056676, 0.968, -1.1622, 0.75567, -2.566]</span>
 <span class="go">])</span>
 </pre></div>
 </div>
@@ -1067,11 +1067,11 @@ <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([0.39886, -1.0052, 0.19362, -1.8641, 0.83507, 1.8891])</span>
+<span class="go">Twist3([-1.0652, 0.041275, -0.553, -1.7192, -0.41336, 0.11859])</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([-0.39886, 1.0052, -0.19362, 1.8641, -0.83507, -1.8891])</span>
+<span class="go">Twist3([1.0652, -0.041275, 0.553, 1.7192, 0.41336, -0.11859])</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([-1.1102e-16, 1.0408e-16, -1.1102e-16, 0, 0, 0])</span>
+<span class="go">Twist3([3.3307e-16, -5.5511e-17, -5.5511e-17, 1.3878e-17, -2.7756e-17, -2.7756e-17])</span>
 </pre></div>
 </div>
 </dd></dl>