@@ -129,7 +129,7 @@ <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><span class="n">Ellipse</span><span class="o">.</span><span class="n">FromPerimeter</span><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">
 
@@ -505,9 +505,9 @@ <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> <span class="n">SO3</span>
 <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>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">x</span>
-<span class="go">SO3(array([[ 0.7528027 , -0.59887622, -0.27319475],</span>
-<span class="go">           [ 0.23555874, -0.14245052,  0.96136358],</span>
-<span class="go">           [-0.61465452, -0.78807051,  0.03383339]]))</span>
+<span class="go">SO3(array([[-0.10700407, -0.81874594,  0.56409681],</span>
+<span class="go">           [-0.89958248,  0.32135229,  0.29577705],</span>
+<span class="go">           [-0.42344006, -0.47580227, -0.77091551]]))</span>
 </pre></div>
 </div>
 <dl class="field-list simple">
 
@@ -467,11 +467,11 @@ <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> <span class="n">UnitQuaternion</span> <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><span class="n">UQ</span><span class="o">.</span><span class="n">Rand</span><span class="p">())</span>
-<span class="go"> 0.1975 &lt;&lt;  0.1813,  0.9205, -0.2843 &gt;&gt;</span>
+<span class="go"> 0.1749 &lt;&lt; -0.2219,  0.7205, -0.6333 &gt;&gt;</span>
 <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>
-<span class="go"> 0.8216 &lt;&lt; -0.4796, -0.1604, -0.2630 &gt;&gt;</span>
-<span class="go"> 0.5958 &lt;&lt; -0.5805,  0.3888,  0.3961 &gt;&gt;</span>
-<span class="go"> 0.5051 &lt;&lt; -0.5357,  0.4044,  0.5426 &gt;&gt;</span>
+<span class="go"> 0.0213 &lt;&lt;  0.3621, -0.6221, -0.6939 &gt;&gt;</span>
+<span class="go"> 0.3613 &lt;&lt;  0.0444,  0.9270, -0.0908 &gt;&gt;</span>
+<span class="go"> 0.2562 &lt;&lt; -0.1184,  0.4185,  0.8632 &gt;&gt;</span>
 </pre></div>
 </div>
 <dl class="field-list simple">
@@ -1953,6 +1953,8 @@ <h1>Unit quaternion<a class="headerlink" href="#unit-quaternion" title="Link to
 <p><code class="docutils literal notranslate"><span class="pre">q.log()</span></code> is the logarithm of the quaternion <code class="docutils literal notranslate"><span class="pre">q</span></code>, ie.</p>
 <div class="math notranslate nohighlight">
 \[\ln \| q \|,  \langle \frac{\vec{v}}{\| \vec{v} \|} \cos^{-1} \frac{s}{\| q \|} \rangle\]</div>
+<p>The implementation uses the equivalent <span class="math notranslate nohighlight">\(\operatorname{atan2}(\|\vec{v}\|, s)\)</span>
+to avoid the loss of precision in <code class="docutils literal notranslate"><span class="pre">acos</span></code> for small rotation angles.</p>
 <p>For a <code class="docutils literal notranslate"><span class="pre">UnitQuaternion</span></code> the logarithm is a pure quaternion whose vector
 part <span class="math notranslate nohighlight">\(\vec{v}\)</span> and <span class="math notranslate nohighlight">\(\vec{v}/2\)</span> is a Euler vector: parallel
 to the axis of rotation and whose norm is the magnitude of rotation.</p>
 
@@ -606,13 +606,13 @@ <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> <span class="n">SE3</span>
 <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>
 <span class="go">SE3([</span>
-<span class="go">array([[-0.29716131,  0.36013091, -0.88430814, -0.44785191],</span>
-<span class="go">       [-0.23749314,  0.86916127,  0.43376918, -0.36300241],</span>
-<span class="go">       [ 0.92482007,  0.33891653, -0.17275248,  0.06994773],</span>
+<span class="go">array([[-0.26363769, -0.71894927,  0.64312294,  0.11196973],</span>
+<span class="go">       [ 0.96434083, -0.18034652,  0.19370571,  0.26535018],</span>
+<span class="go">       [-0.02327959,  0.67125783,  0.74085827, -0.42334514],</span>
 <span class="go">       [ 0.        ,  0.        ,  0.        ,  1.        ]]),</span>
-<span class="go">array([[ 0.27083834, -0.8507628 , -0.45038789,  0.21943805],</span>
-<span class="go">       [ 0.73406169, -0.12014378,  0.66837034,  0.87041772],</span>
-<span class="go">       [-0.62273592, -0.51163281,  0.59197284, -0.40218846],</span>
+<span class="go">array([[-0.08817415,  0.67945201, -0.72840256, -0.34937729],</span>
+<span class="go">       [ 0.93823432,  0.30226638,  0.16837871, -0.46053018],</span>
+<span class="go">       [ 0.33457686, -0.66856563, -0.66413727, -0.84614947],</span>
 <span class="go">       [ 0.        ,  0.        ,  0.        ,  1.        ]]) ])</span>
 </pre></div>
 </div>
 
@@ -197,14 +197,14 @@ <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> <span class="n">UnitDualQuaternion</span><span class="p">,</span> <span class="n">SE3</span>
 <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>
 <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>
-<span class="go">   0.5249    0.7013    0.4824   -0.3676    </span>
-<span class="go">  -0.569    -0.1324    0.8116    0.2074    </span>
-<span class="go">   0.633    -0.7005    0.3296    0.3649    </span>
+<span class="go">  -0.063    -0.9965   -0.05568  -0.9454    </span>
+<span class="go">   0.1606    0.04494  -0.986     0.2167    </span>
+<span class="go">   0.985    -0.07105   0.1572   -0.8178    </span>
 <span class="go">   0         0         0         1         </span>
 
 <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>
 <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>
-<span class="go"> 0.6561 &lt;&lt; -0.5761, -0.0574, -0.4840 &gt;&gt; + ε -0.0116 &lt; -0.1603, -0.1260,  0.1900 &gt;</span>
+<span class="go"> 0.5336 &lt;&lt;  0.4286, -0.4875,  0.5420 &gt;&gt; + ε  0.4771 &lt; -0.3929,  0.1388, -0.0342 &gt;</span>
 <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>
 <span class="go">&lt;class 'spatialmath.DualQuaternion.UnitDualQuaternion'&gt;</span>
 </pre></div>
 
@@ -281,8 +281,8 @@ <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> <span class="n">Twist3</span>
 <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>
 <span class="go">Twist3([</span>
-<span class="go">  [-0.46786, -0.89462, 0.096997, 1.3011, -2.1156, -1.8492],</span>
-<span class="go">  [-0.75761, 0.60357, -0.1593, -1.6765, -1.622, -1.5894]</span>
+<span class="go">  [-1.6368, -0.25704, -1.2338, 0.68355, 2.9561, -0.0017026],</span>
+<span class="go">  [0.73548, -0.86065, -0.73111, 0.46759, 0.413, 1.6905]</span>
 <span class="go">])</span>
 </pre></div>
 </div>
 
@@ -1044,6 +1044,8 @@ <h1>Quaternion<a class="headerlink" href="#quaternion" title="Link to this headi
 <p><code class="docutils literal notranslate"><span class="pre">q.log()</span></code> is the logarithm of the quaternion <code class="docutils literal notranslate"><span class="pre">q</span></code>, ie.</p>
 <div class="math notranslate nohighlight">
 \[\ln \| q \|,  \langle \frac{\vec{v}}{\| \vec{v} \|} \cos^{-1} \frac{s}{\| q \|} \rangle\]</div>
+<p>The implementation uses the equivalent <span class="math notranslate nohighlight">\(\operatorname{atan2}(\|\vec{v}\|, s)\)</span>
+to avoid the loss of precision in <code class="docutils literal notranslate"><span class="pre">acos</span></code> for small rotation angles.</p>
 <p>For a <code class="docutils literal notranslate"><span class="pre">UnitQuaternion</span></code> the logarithm is a pure quaternion whose vector
 part <span class="math notranslate nohighlight">\(\vec{v}\)</span> and <span class="math notranslate nohighlight">\(\vec{v}/2\)</span> is a Euler vector: parallel
 to the axis of rotation and whose norm is the magnitude of rotation.</p>