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<li class="toctree-l3"><a class="reference internal" href="#spatialmath.base.vectors.angdiff"><code class="docutils literal notranslate"><span class="pre">angdiff()</span></code></a></li>
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<section id="module-spatialmath.base.vectors">
<span id="vectors"></span><h1>Vectors<a class="headerlink" href="#module-spatialmath.base.vectors" title="Permalink to this heading"></a></h1>
<p>Functions to manipulate vectors</p>
<p>Vector arguments are what numpy refers to as <code class="docutils literal notranslate"><span class="pre">array_like</span></code> and can be a list,
tuple, numpy array, numpy row vector or numpy column vector.</p>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.angdiff">
<span class="sig-name descname"><span class="pre">angdiff</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#angdiff"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.angdiff" title="Permalink to this definition"></a></dt>
<dd><p>Angular difference</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>a</strong> (<em>scalar</em><em> or </em><em>array_like</em>) – angle in radians</p></li>
<li><p><strong>b</strong> (<em>scalar</em><em> or </em><em>array_like</em>) – angle in radians</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>angular difference a-b</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>scalar or array_like</p>
</dd>
</dl>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">angdiff(a,</span> <span class="pre">b)</span></code> is the difference <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">-</span> <span class="pre">b</span></code> wrapped to the range
<span class="math notranslate nohighlight">\([-\pi, \pi)\)</span>. This is the operator <span class="math notranslate nohighlight">\(a \circleddash b\)</span> used
in the RVC book</p>
<blockquote>
<div><ul class="simple">
<li><p>If <code class="docutils literal notranslate"><span class="pre">a</span></code> and <code class="docutils literal notranslate"><span class="pre">b</span></code> are both scalars, the result is scalar</p></li>
<li><p>If <code class="docutils literal notranslate"><span class="pre">a</span></code> is array_like, the result is a NumPy array <code class="docutils literal notranslate"><span class="pre">a[i]-b</span></code></p></li>
<li><p>If <code class="docutils literal notranslate"><span class="pre">a</span></code> is array_like, the result is a NumPy array <code class="docutils literal notranslate"><span class="pre">a-b[i]</span></code></p></li>
<li><p>If <code class="docutils literal notranslate"><span class="pre">a</span></code> and <code class="docutils literal notranslate"><span class="pre">b</span></code> are both vectors of the same length, the result is
a NumPy array <code class="docutils literal notranslate"><span class="pre">a[i]-b[i]</span></code></p></li>
</ul>
</div></blockquote>
</li>
<li><p><code class="docutils literal notranslate"><span class="pre">angdiff(a)</span></code> is the angle or vector of angles <code class="docutils literal notranslate"><span class="pre">a</span></code> wrapped to the range
<span class="math notranslate nohighlight">\([-\pi, \pi)\)</span>.</p>
<blockquote>
<div><ul class="simple">
<li><p>If <code class="docutils literal notranslate"><span class="pre">a</span></code> is a scalar, the result is scalar</p></li>
<li><p>If <code class="docutils literal notranslate"><span class="pre">a</span></code> is array_like, the result is a NumPy array</p></li>
</ul>
</div></blockquote>
</li>
</ul>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">math</span><span class="w"> </span><span class="kn">import</span> <span class="n">pi</span>
<span class="gp">>>> </span><span class="n">angdiff</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">pi</span><span class="p">)</span>
<span class="go">0.0</span>
<span class="gp">>>> </span><span class="n">angdiff</span><span class="p">(</span><span class="mf">0.9</span> <span class="o">*</span> <span class="n">pi</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.9</span> <span class="o">*</span> <span class="n">pi</span><span class="p">)</span> <span class="o">/</span> <span class="n">pi</span>
<span class="go">-0.2</span>
<span class="gp">>>> </span><span class="n">angdiff</span><span class="p">(</span><span class="mi">3</span> <span class="o">*</span> <span class="n">pi</span><span class="p">)</span>
<span class="go">-3.141592653589793</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference internal" href="#spatialmath.base.vectors.vector_diff" title="spatialmath.base.vectors.vector_diff"><code class="xref py py-func docutils literal notranslate"><span class="pre">vector_diff()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_mpi_pi" title="spatialmath.base.vectors.wrap_mpi_pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_mpi_pi()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.angle_mean">
<span class="sig-name descname"><span class="pre">angle_mean</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">theta</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#angle_mean"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.angle_mean" title="Permalink to this definition"></a></dt>
<dd><p>Mean of angular values</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>theta</strong> (<span class="sphinx_autodoc_typehints-type"><code class="xref py py-data docutils literal notranslate"><span class="pre">Union</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">List</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code>], <code class="xref py py-data docutils literal notranslate"><span class="pre">Tuple</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code>, <code class="xref py py-data docutils literal notranslate"><span class="pre">...</span></code>], <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v2.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></a>[<code class="xref py py-data docutils literal notranslate"><span class="pre">Any</span></code>, <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v2.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dtype</span></code></a>[<code class="xref py py-class docutils literal notranslate"><span class="pre">TypeVar</span></code>(<code class="docutils literal notranslate"><span class="pre">ScalarType</span></code>, bound= <a class="reference external" href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.generic" title="(in NumPy v2.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">generic</span></code></a>, covariant=True)]]]</span>) – angular values</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>circular mean</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>float</p>
</dd>
</dl>
<p>The circular mean is given by</p>
<div class="math notranslate nohighlight">
\[\bar{\theta} = \tan^{-1} \frac{\sum \sin \theta_i}{\sum \cos \theta_i} \in [-\pi, \pi)]\]</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference internal" href="#spatialmath.base.vectors.angle_std" title="spatialmath.base.vectors.angle_std"><code class="xref py py-func docutils literal notranslate"><span class="pre">angle_std()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.angle_std">
<span class="sig-name descname"><span class="pre">angle_std</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">theta</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#angle_std"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.angle_std" title="Permalink to this definition"></a></dt>
<dd><p>Standard deviation of angular values</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>theta</strong> (<em>array_like</em>) – angular values</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>circular standard deviation</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>float</p>
</dd>
</dl>
<div class="math notranslate nohighlight">
\[\sigma_{\theta} = \sqrt{-2 \log \| \left[ \frac{\sum \sin \theta_i}{N}, \frac{\sum \sin \theta_i}{N} \right] \|} \in [0, \infty)\]</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference internal" href="#spatialmath.base.vectors.angle_mean" title="spatialmath.base.vectors.angle_mean"><code class="xref py py-func docutils literal notranslate"><span class="pre">angle_mean()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.angle_wrap">
<span class="sig-name descname"><span class="pre">angle_wrap</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">theta</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'-pi:pi'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#angle_wrap"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.angle_wrap" title="Permalink to this definition"></a></dt>
<dd><p>Generalized angle-wrapping</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v</strong> (<em>array_like</em>) – angles to wrap</p></li>
<li><p><strong>mode</strong> (<em>str</em><em>, </em><em>optional</em>) – wrapping mode, one of: <code class="docutils literal notranslate"><span class="pre">"0:2pi"</span></code>, <code class="docutils literal notranslate"><span class="pre">"0:pi"</span></code>, <code class="docutils literal notranslate"><span class="pre">"-pi/2:pi/2"</span></code> or <code class="docutils literal notranslate"><span class="pre">"-pi:pi"</span></code> [default]</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>wrapped angles</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray</p>
</dd>
</dl>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The modes <code class="docutils literal notranslate"><span class="pre">"0:pi"</span></code> and <code class="docutils literal notranslate"><span class="pre">"-pi/2:pi/2"</span></code> are used to wrap angles of
colatitude and latitude respectively.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference internal" href="#spatialmath.base.vectors.wrap_0_2pi" title="spatialmath.base.vectors.wrap_0_2pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_0_2pi()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_mpi_pi" title="spatialmath.base.vectors.wrap_mpi_pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_mpi_pi()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_0_pi" title="spatialmath.base.vectors.wrap_0_pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_0_pi()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_mpi2_pi2" title="spatialmath.base.vectors.wrap_mpi2_pi2"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_mpi2_pi2()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.colvec">
<span class="sig-name descname"><span class="pre">colvec</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#colvec"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.colvec" title="Permalink to this definition"></a></dt>
<dd><p>Create a column vector</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>v</strong> (<em>array_like</em><em>(</em><em>n</em><em>)</em>) – any vector</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>a column vector</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray(n,1)</p>
</dd>
</dl>
<p>Convert input to a column vector.</p>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">colvec</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
<span class="go">array([[1.],</span>
<span class="go"> [2.],</span>
<span class="go"> [3.]])</span>
</pre></div>
</div>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.cross">
<span class="sig-name descname"><span class="pre">cross</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">u</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">v</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#cross"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.cross" title="Permalink to this definition"></a></dt>
<dd><p>Cross product of vectors</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>u</strong> (<em>array_like</em><em>(</em><em>3</em><em>)</em>) – any vector</p></li>
<li><p><strong>v</strong> (<em>array_like</em><em>(</em><em>3</em><em>)</em>) – any vector</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>cross product</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>nd.array(3)</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">cross(u,</span> <span class="pre">v)</span></code> is the cross product of the vectors <code class="docutils literal notranslate"><span class="pre">u</span></code> and <code class="docutils literal notranslate"><span class="pre">v</span></code>.</p>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">cross</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="go">array([0, 0, 1])</span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This function does not use NumPy, it is ~1.5x faster than
<cite>numpy.cross()</cite></p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">unit()</span></code></p>
</dd>
<dt class="field-even">SymPy<span class="colon">:</span></dt>
<dd class="field-even"><p>supported</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.isunittwist">
<span class="sig-name descname"><span class="pre">isunittwist</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#isunittwist"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.isunittwist" title="Permalink to this definition"></a></dt>
<dd><p>Test if vector represents a unit twist in SE(2) or SE(3)</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v</strong> (<em>array_like</em><em>(</em><em>6</em><em>)</em>) – twist vector to test</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance in units of eps, defaults to 20</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>whether twist has unit length</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
<dt class="field-even">Raises<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>ValueError</strong> – for incorrect vector length</p>
</dd>
</dl>
<p>Vector is is intepretted as <span class="math notranslate nohighlight">\([v, \omega]\)</span> where <span class="math notranslate nohighlight">\(v \in \mathbb{R}^n\)</span> and
<span class="math notranslate nohighlight">\(\omega \in \mathbb{R}^1\)</span> for SE(2) and <span class="math notranslate nohighlight">\(\omega \in \mathbb{R}^3\)</span> for SE(3).</p>
<p>A unit twist can be a:</p>
<ul class="simple">
<li><p>unit rotational twist where <span class="math notranslate nohighlight">\(|| \omega || = 1\)</span>, or</p></li>
<li><p>unit translational twist where <span class="math notranslate nohighlight">\(|| \omega || = 0\)</span> and <span class="math notranslate nohighlight">\(|| v || = 1\)</span>.</p></li>
</ul>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">isunittwist</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">isunittwist</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="go">False</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p>unit, isunitvec</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.isunittwist2">
<span class="sig-name descname"><span class="pre">isunittwist2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#isunittwist2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.isunittwist2" title="Permalink to this definition"></a></dt>
<dd><p>Test if vector represents a unit twist in SE(2) or SE(3)</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v</strong> (<em>array_like</em><em>(</em><em>3</em><em>)</em>) – twist vector to test</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance in units of eps, defaults to 20</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>whether vector has unit length</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
<dt class="field-even">Raises<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>ValueError</strong> – for incorrect vector length</p>
</dd>
</dl>
<p>Vector is is intepretted as <span class="math notranslate nohighlight">\([v, \omega]\)</span> where <span class="math notranslate nohighlight">\(v \in \mathbb{R}^n\)</span> and
<span class="math notranslate nohighlight">\(\omega \in \mathbb{R}^1\)</span> for SE(2) and <span class="math notranslate nohighlight">\(\omega \in \mathbb{R}^3\)</span> for SE(3).</p>
<p>A unit twist can be a:</p>
<ul class="simple">
<li><p>unit rotational twist where <span class="math notranslate nohighlight">\(|| \omega || = 1\)</span>, or</p></li>
<li><p>unit translational twist where <span class="math notranslate nohighlight">\(|| \omega || = 0\)</span> and <span class="math notranslate nohighlight">\(|| v || = 1\)</span>.</p></li>
</ul>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">isunittwist2</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">isunittwist2</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="go">False</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p>unit, isunitvec</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.isunitvec">
<span class="sig-name descname"><span class="pre">isunitvec</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#isunitvec"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.isunitvec" title="Permalink to this definition"></a></dt>
<dd><p>Test if vector has unit length</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v</strong> (<em>ndarray</em><em>(</em><em>n</em><em>)</em>) – vector to test</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance in units of eps, defaults to 20</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>whether vector has unit length</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">isunitvec</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">isunitvec</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="go">False</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p>unit, iszerovec, isunittwist</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.iszero">
<span class="sig-name descname"><span class="pre">iszero</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#iszero"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.iszero" title="Permalink to this definition"></a></dt>
<dd><p>Test if scalar is zero</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v</strong> (<em>float</em>) – value to test</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance in units of eps, defaults to 20</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>whether value is zero</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">iszero</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">iszero</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="go">False</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p>unit, iszerovec, isunittwist</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.iszerovec">
<span class="sig-name descname"><span class="pre">iszerovec</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#iszerovec"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.iszerovec" title="Permalink to this definition"></a></dt>
<dd><p>Test if vector has zero length</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v</strong> (<em>ndarray</em><em>(</em><em>n</em><em>)</em>) – vector to test</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance in units of eps, defaults to 20</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>whether vector has zero length</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">iszerovec</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">iszerovec</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="go">False</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p>unit, isunitvec, isunittwist</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.norm">
<span class="sig-name descname"><span class="pre">norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.norm" title="Permalink to this definition"></a></dt>
<dd><p>Norm of vector</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>v</strong> (<em>array_like</em><em>(</em><em>n</em><em>)</em>) – any vector</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>norm of vector</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>float</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">norm(v)</span></code> is the 2-norm (length or magnitude) of the vector <code class="docutils literal notranslate"><span class="pre">v</span></code>.</p>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">norm</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
<span class="go">5.0</span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This function does not use NumPy, it is ~2x faster than
<cite>numpy.linalg.norm()</cite> for a 3-vector</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">unit()</span></code></p>
</dd>
<dt class="field-even">SymPy<span class="colon">:</span></dt>
<dd class="field-even"><p>supported</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.normsq">
<span class="sig-name descname"><span class="pre">normsq</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#normsq"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.normsq" title="Permalink to this definition"></a></dt>
<dd><p>Squared norm of vector</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>v</strong> (<em>array_like</em><em>(</em><em>n</em><em>)</em>) – any vector</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>norm of vector</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>float</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">norm(sq)</span></code> is the sum of squared elements of the vector <code class="docutils literal notranslate"><span class="pre">v</span></code>
or <span class="math notranslate nohighlight">\(|v|^2\)</span>.</p>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">normsq</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
<span class="go">13</span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This function does not use NumPy, it is ~2x faster than
<cite>numpy.linalg.norm() ** 2</cite> for a 3-vector</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">unit()</span></code></p>
</dd>
<dt class="field-even">SymPy<span class="colon">:</span></dt>
<dd class="field-even"><p>supported</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.orthogonalize">
<span class="sig-name descname"><span class="pre">orthogonalize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">v2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">normalize</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#orthogonalize"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.orthogonalize" title="Permalink to this definition"></a></dt>
<dd><p>Orthoginalizes vector v1 with respect to v2 with minimum rotation.
Returns a the nearest vector to v1 that is orthoginal to v2.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v1</strong> (<em>array_like</em><em>(</em><em>n</em><em>)</em>) – vector to be orthoginalized</p></li>
<li><p><strong>v2</strong> (<em>array_like</em><em>(</em><em>n</em><em>)</em>) – vector that returned vector will be orthoginal to</p></li>
<li><p><strong>normalize</strong> (<em>bool</em>) – whether to normalize the output vector</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>nearest vector to v1 that is orthoginal to v2</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray(n)</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.project">
<span class="sig-name descname"><span class="pre">project</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">v2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#project"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.project" title="Permalink to this definition"></a></dt>
<dd><p>Projects vector v1 onto v2. Returns a vector parallel to v2.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v1</strong> (<em>array_like</em><em>(</em><em>n</em><em>)</em>) – vector to be projected</p></li>
<li><p><strong>v2</strong> (<em>array_like</em><em>(</em><em>n</em><em>)</em>) – vector to be projected onto</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>vector projection of v1 onto v2 (parrallel to v2)</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray(n)</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.removesmall">
<span class="sig-name descname"><span class="pre">removesmall</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#removesmall"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.removesmall" title="Permalink to this definition"></a></dt>
<dd><p>Set small values to zero</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v</strong> (<em>array_like</em><em>(</em><em>n</em><em>) or </em><em>ndarray</em><em>(</em><em>n</em><em>,</em><em>m</em><em>)</em>) – any vector</p></li>
<li><p><strong>tol</strong> (<em>int</em><em>, </em><em>optional</em>) – Tolerance in units of eps, defaults to 20</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>vector with small values set to zero</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray(n) or ndarray(n,m)</p>
</dd>
</dl>
<p>Values with absolute value less than <code class="docutils literal notranslate"><span class="pre">tol</span></code> will be set to zero.</p>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mf">1e-16</span><span class="p">]</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="go">[1. 2. 3. 0.]</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">removesmall</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="go">[1. 2. 3. 0.]</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">3</span><span class="p">])</span>
<span class="go">0.0</span>
</pre></div>
</div>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.unittwist">
<span class="sig-name descname"><span class="pre">unittwist</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">S</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#unittwist"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.unittwist" title="Permalink to this definition"></a></dt>
<dd><p>Convert twist to unit twist</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>S</strong> (<em>array_like</em><em>(</em><em>6</em><em>)</em>) – twist vector</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance in units of eps, defaults to 20</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>unit twist</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray(6)</p>
</dd>
</dl>
<p>A unit twist is a twist where:</p>
<ul class="simple">
<li><p>the rotation part has unit magnitude</p></li>
<li><p>if the rotational part is zero, then the translational part has unit magnitude</p></li>
</ul>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">unittwist</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="go">array([1., 2., 3., 1., 0., 0.])</span>
<span class="gp">>>> </span><span class="n">unittwist</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="go">array([1., 0., 0., 0., 0., 0.])</span>
</pre></div>
</div>
<p>Returns None if the twist has zero magnitude</p>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.unittwist2">
<span class="sig-name descname"><span class="pre">unittwist2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">S</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#unittwist2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.unittwist2" title="Permalink to this definition"></a></dt>
<dd><p>Convert twist to unit twist</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>S</strong> (<em>array_like</em><em>(</em><em>3</em><em>)</em>) – twist vector</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance in units of eps, defaults to 20</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>unit twist</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray(3)</p>
</dd>
</dl>
<p>A unit twist is a twist where:</p>
<ul class="simple">
<li><p>the rotation part has unit magnitude</p></li>
<li><p>if the rotational part is zero, then the translational part has unit magnitude</p></li>
</ul>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Returns None if the twist has zero magnitude</p>
</div>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.unittwist2_norm">
<span class="sig-name descname"><span class="pre">unittwist2_norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">S</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#unittwist2_norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.unittwist2_norm" title="Permalink to this definition"></a></dt>
<dd><p>Convert twist to unit twist</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>S</strong> (<em>array_like</em><em>(</em><em>3</em><em>)</em>) – twist vector</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance in units of eps, defaults to 20</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>unit twist and scalar motion</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>tuple (ndarray(3), float)</p>
</dd>
</dl>
<p>A unit twist is a twist where:</p>
<ul class="simple">
<li><p>the rotation part has unit magnitude</p></li>
<li><p>if the rotational part is zero, then the translational part has unit magnitude</p></li>
</ul>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Returns (None, None) if the twist has zero magnitude</p>
</div>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.unittwist_norm">
<span class="sig-name descname"><span class="pre">unittwist_norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">S</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#unittwist_norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.unittwist_norm" title="Permalink to this definition"></a></dt>
<dd><p>Convert twist to unit twist and norm</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>S</strong> (<em>array_like</em><em>(</em><em>6</em><em>)</em>) – twist vector</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance in units of eps, defaults to 20</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>unit twist and scalar motion</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>tuple (ndarray(6), float)</p>
</dd>
</dl>
<p>A unit twist is a twist where:</p>
<ul class="simple">
<li><p>the rotation part has unit magnitude</p></li>
<li><p>if the rotational part is zero, then the translational part has unit magnitude</p></li>
</ul>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">S</span><span class="p">,</span> <span class="n">n</span> <span class="o">=</span> <span class="n">unittwist_norm</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">S</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
<span class="go">[1. 2. 3. 1. 0. 0.] 1.0</span>
<span class="gp">>>> </span><span class="n">S</span><span class="p">,</span> <span class="n">n</span> <span class="o">=</span> <span class="n">unittwist_norm</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">S</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
<span class="go">[0. 0. 0. 1. 0. 0.] 2.0</span>
<span class="gp">>>> </span><span class="n">S</span><span class="p">,</span> <span class="n">n</span> <span class="o">=</span> <span class="n">unittwist_norm</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">S</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
<span class="go">None None</span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Returns (None,None) if the twist has zero magnitude</p>
</div>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.unitvec">
<span class="sig-name descname"><span class="pre">unitvec</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#unitvec"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.unitvec" title="Permalink to this definition"></a></dt>
<dd><p>Create a unit vector</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v</strong> (<em>array_like</em><em>(</em><em>n</em><em>)</em>) – any vector</p></li>
<li><p><strong>tol</strong> (<span class="sphinx_autodoc_typehints-type"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></span>) – Tolerance in units of eps for zero-norm case, defaults to 20</p></li>
</ul>
</dd>
<dt class="field-even">Type<span class="colon">:</span></dt>
<dd class="field-even"><p>float</p>
</dd>
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>a unit-vector parallel to <code class="docutils literal notranslate"><span class="pre">v</span></code>.</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>ndarray(n)</p>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>ValueError</strong> – for zero length vector</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">unitvec(v)</span></code> is a vector parallel to <cite>v</cite> of unit length.</p>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">unitvec</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
<span class="go">array([0.6, 0.8])</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html#numpy.linalg.norm" title="(in NumPy v2.2)"><code class="xref py py-func docutils literal notranslate"><span class="pre">norm()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.unitvec_norm">
<span class="sig-name descname"><span class="pre">unitvec_norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#unitvec_norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.unitvec_norm" title="Permalink to this definition"></a></dt>
<dd><p>Create a unit vector</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v</strong> (<em>array_like</em><em>(</em><em>n</em><em>)</em>) – any vector</p></li>
<li><p><strong>tol</strong> (<span class="sphinx_autodoc_typehints-type"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></span>) – Tolerance in units of eps for zero-norm case, defaults to 20</p></li>
</ul>
</dd>
<dt class="field-even">Type<span class="colon">:</span></dt>
<dd class="field-even"><p>float</p>
</dd>
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>a unit-vector parallel to <code class="docutils literal notranslate"><span class="pre">v</span></code> and the norm</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>(ndarray(n), float)</p>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>ValueError</strong> – for zero length vector</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">unitvec(v)</span></code> is a vector parallel to <cite>v</cite> of unit length.</p>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">unitvec</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
<span class="go">array([0.6, 0.8])</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html#numpy.linalg.norm" title="(in NumPy v2.2)"><code class="xref py py-func docutils literal notranslate"><span class="pre">norm()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.vector_diff">
<span class="sig-name descname"><span class="pre">vector_diff</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">v2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#vector_diff"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.vector_diff" title="Permalink to this definition"></a></dt>
<dd><p>Generalized vector differnce</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v1</strong> (<em>array_like</em><em>(</em><em>n</em><em>)</em>) – first vector</p></li>
<li><p><strong>v2</strong> (<em>array_like</em><em>(</em><em>n</em><em>)</em>) – second vector</p></li>
<li><p><strong>mode</strong> (<em>str</em><em> of </em><em>length n</em>) – subtraction mode</p></li>
</ul>
</dd>
</dl>
<table class="docutils align-default">
<thead>
<tr class="row-odd"><th class="head"><p>mode character</p></th>
<th class="head"><p>purpose</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>r</p></td>
<td><p>real number, don’t wrap</p></td>
</tr>
<tr class="row-odd"><td><p>c</p></td>
<td><p>angle on circle, wrap to [-π, π)</p></td>
</tr>
<tr class="row-even"><td><p>C</p></td>
<td><p>angle on circle, wrap to [0, 2π)</p></td>
</tr>
<tr class="row-odd"><td><p>l</p></td>
<td><p>latitude angle, wrap to [-π/2, π/2]</p></td>
</tr>
<tr class="row-even"><td><p>L</p></td>
<td><p>colatitude angle, wrap to [0, π]</p></td>
</tr>
</tbody>
</table>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference internal" href="#spatialmath.base.vectors.angdiff" title="spatialmath.base.vectors.angdiff"><code class="xref py py-func docutils literal notranslate"><span class="pre">angdiff()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_0_2pi" title="spatialmath.base.vectors.wrap_0_2pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_0_2pi()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_mpi_pi" title="spatialmath.base.vectors.wrap_mpi_pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_mpi_pi()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_0_pi" title="spatialmath.base.vectors.wrap_0_pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_0_pi()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_mpi2_pi2" title="spatialmath.base.vectors.wrap_mpi2_pi2"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_mpi2_pi2()</span></code></a></p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p><span class="sphinx_autodoc_typehints-type"><a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v2.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></a>[<code class="xref py py-data docutils literal notranslate"><span class="pre">Any</span></code>, <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v2.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dtype</span></code></a>[<code class="xref py py-class docutils literal notranslate"><span class="pre">TypeVar</span></code>(<code class="docutils literal notranslate"><span class="pre">ScalarType</span></code>, bound= <a class="reference external" href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.generic" title="(in NumPy v2.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">generic</span></code></a>, covariant=True)]]</span></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.wrap_0_2pi">
<span class="sig-name descname"><span class="pre">wrap_0_2pi</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">theta</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#wrap_0_2pi"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.wrap_0_2pi" title="Permalink to this definition"></a></dt>
<dd><p>Wrap angle to range <span class="math notranslate nohighlight">\([0, 2\pi)\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>theta</strong> (<em>scalar</em><em> or </em><em>ndarray</em>) – input angle</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>angle wrapped into range <span class="math notranslate nohighlight">\([0, 2\pi)\)</span></p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>scalar or ndarray</p>
</dd>
<dt class="field-even">Seealso<span class="colon">:</span></dt>
<dd class="field-even"><p><a class="reference internal" href="#spatialmath.base.vectors.wrap_mpi_pi" title="spatialmath.base.vectors.wrap_mpi_pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_mpi_pi()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_0_pi" title="spatialmath.base.vectors.wrap_0_pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_0_pi()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_mpi2_pi2" title="spatialmath.base.vectors.wrap_mpi2_pi2"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_mpi2_pi2()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.angle_wrap" title="spatialmath.base.vectors.angle_wrap"><code class="xref py py-func docutils literal notranslate"><span class="pre">angle_wrap()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.wrap_0_pi">
<span class="sig-name descname"><span class="pre">wrap_0_pi</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">theta</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#wrap_0_pi"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.wrap_0_pi" title="Permalink to this definition"></a></dt>
<dd><p>Wrap angle to range <span class="math notranslate nohighlight">\([0, \pi]\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>theta</strong> (<em>scalar</em><em> or </em><em>ndarray</em>) – input angle</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>angle wrapped into range <span class="math notranslate nohighlight">\([0, \pi)\)</span></p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>scalar or ndarray</p>
</dd>
</dl>
<p>This is used to fold angles of colatitude. If zero is the angle of the
north pole, colatitude increases to <span class="math notranslate nohighlight">\(\pi\)</span> at the south pole then
decreases to <span class="math notranslate nohighlight">\(0\)</span> as we head back to the north pole.</p>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference internal" href="#spatialmath.base.vectors.wrap_mpi2_pi2" title="spatialmath.base.vectors.wrap_mpi2_pi2"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_mpi2_pi2()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_0_2pi" title="spatialmath.base.vectors.wrap_0_2pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_0_2pi()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_mpi_pi" title="spatialmath.base.vectors.wrap_mpi_pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_mpi_pi()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.angle_wrap" title="spatialmath.base.vectors.angle_wrap"><code class="xref py py-func docutils literal notranslate"><span class="pre">angle_wrap()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.wrap_mpi2_pi2">
<span class="sig-name descname"><span class="pre">wrap_mpi2_pi2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">theta</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#wrap_mpi2_pi2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.wrap_mpi2_pi2" title="Permalink to this definition"></a></dt>
<dd><p>Wrap angle to range <span class="math notranslate nohighlight">\([-\pi/2, \pi/2]\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>theta</strong> (<em>scalar</em><em> or </em><em>ndarray</em>) – input angle</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>angle wrapped into range <span class="math notranslate nohighlight">\([-\pi/2, \pi/2]\)</span></p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>scalar or ndarray</p>
</dd>
</dl>
<p>This is used to fold angles of latitude.</p>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference internal" href="#spatialmath.base.vectors.wrap_0_pi" title="spatialmath.base.vectors.wrap_0_pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_0_pi()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_0_2pi" title="spatialmath.base.vectors.wrap_0_2pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_0_2pi()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.wrap_mpi_pi" title="spatialmath.base.vectors.wrap_mpi_pi"><code class="xref py py-func docutils literal notranslate"><span class="pre">wrap_mpi_pi()</span></code></a> <a class="reference internal" href="#spatialmath.base.vectors.angle_wrap" title="spatialmath.base.vectors.angle_wrap"><code class="xref py py-func docutils literal notranslate"><span class="pre">angle_wrap()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.vectors.wrap_mpi_pi">
<span class="sig-name descname"><span class="pre">wrap_mpi_pi</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">theta</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/vectors.html#wrap_mpi_pi"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.vectors.wrap_mpi_pi" title="Permalink to this definition"></a></dt>
<dd><p>Wrap angle to range <span class="math notranslate nohighlight">\([-\pi, \pi)\)</span></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>theta</strong> (<em>scalar</em><em> or </em><em>ndarray</em>) – input angle</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>angle wrapped into range <span class="math notranslate nohighlight">\([-\pi, \pi)\)</span></p>
</dd>