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<section id="module-spatialmath.base.transforms2d">
<span id="transforms-in-2d"></span><h1>Transforms in 2D<a class="headerlink" href="#module-spatialmath.base.transforms2d" title="Permalink to this headline"></a></h1>
<p>These functions create and manipulate 2D rotation matrices and rigid-body
transformations as 2x2 SO(2) matrices and 3x3 SE(2) matrices respectively.
These matrices are represented as 2D NumPy arrays.</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.transforms2d.ICP2d">
<span class="sig-name descname"><span class="pre">ICP2d</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">reference</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">source</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">T</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_iter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_delta_err</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0001</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#ICP2d"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.ICP2d" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.adjoint2">
<span class="sig-name descname"><span class="pre">adjoint2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">T</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#adjoint2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.adjoint2" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.ishom2">
<span class="sig-name descname"><span class="pre">ishom2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">T</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">check</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#ishom2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.ishom2" title="Permalink to this definition"></a></dt>
<dd><p>Test if matrix belongs to SE(2)</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>T</strong> (<em>ndarray</em><em>(</em><em>3</em><em>,</em><em>3</em><em>)</em>) – SE(2) matrix to test</p></li>
<li><p><strong>check</strong> (<em>bool</em>) – check validity of rotation submatrix</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>whether matrix is an SE(2) homogeneous transformation matrix</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">ishom2(T)</span></code> is True if the argument <code class="docutils literal notranslate"><span class="pre">T</span></code> is of dimension 3x3</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">ishom2(T,</span> <span class="pre">check=True)</span></code> as above, but also checks orthogonality of the
rotation sub-matrix and validitity of the bottom row.</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="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="n">T</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</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">3</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">4</span><span class="p">],</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">1</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">ishom2</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">T</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</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">4</span><span class="p">],</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">1</span><span class="p">]])</span> <span class="c1"># invalid SE(2)</span>
<span class="gp">>>> </span><span class="n">ishom2</span><span class="p">(</span><span class="n">T</span><span class="p">)</span> <span class="c1"># a quick check says it is an SE(2)</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">ishom2</span><span class="p">(</span><span class="n">T</span><span class="p">,</span> <span class="n">check</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> <span class="c1"># but if we check more carefully...</span>
<span class="go">False</span>
<span class="gp">>>> </span><span class="n">R</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</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="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">ishom2</span><span class="p">(</span><span class="n">R</span><span class="p">)</span>
<span class="go">False</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p>isR, isrot2, ishom, isvec</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.isrot2">
<span class="sig-name descname"><span class="pre">isrot2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">R</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">check</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#isrot2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.isrot2" title="Permalink to this definition"></a></dt>
<dd><p>Test if matrix belongs to SO(2)</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>R</strong> (<em>ndarray</em><em>(</em><em>3</em><em>,</em><em>3</em><em>)</em>) – SO(2) matrix to test</p></li>
<li><p><strong>check</strong> (<em>bool</em>) – check validity of rotation submatrix</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>whether matrix is an SO(2) rotation matrix</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">isrot2(R)</span></code> is True if the argument <code class="docutils literal notranslate"><span class="pre">R</span></code> is of dimension 2x2</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">isrot2(R,</span> <span class="pre">check=True)</span></code> as above, but also checks orthogonality of the rotation matrix.</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="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="n">T</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</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">3</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">4</span><span class="p">],</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">1</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">isrot2</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
<span class="go">False</span>
<span class="gp">>>> </span><span class="n">R</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</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="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">isrot2</span><span class="p">(</span><span class="n">R</span><span class="p">)</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">R</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</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="c1"># invalid SO(2)</span>
<span class="gp">>>> </span><span class="n">isrot2</span><span class="p">(</span><span class="n">R</span><span class="p">)</span> <span class="c1"># a quick check says it is an SO(2)</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">isrot2</span><span class="p">(</span><span class="n">R</span><span class="p">,</span> <span class="n">check</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> <span class="c1"># but if we check more carefully...</span>
<span class="go">False</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p>isR, ishom2, isrot</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.points2tr2">
<span class="sig-name descname"><span class="pre">points2tr2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#points2tr2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.points2tr2" title="Permalink to this definition"></a></dt>
<dd><p>SE(2) transform from corresponding points</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>p1</strong> (<em>array_like</em><em>(</em><em>2</em><em>,</em><em>N</em><em>)</em>) – first set of points</p></li>
<li><p><strong>p2</strong> (<em>array_like</em><em>(</em><em>2</em><em>,</em><em>N</em><em>)</em>) – second set of points</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>transform from <code class="docutils literal notranslate"><span class="pre">p1</span></code> to <code class="docutils literal notranslate"><span class="pre">p2</span></code></p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3,3)</p>
</dd>
</dl>
<p>Compute an SE(2) matrix that transforms the point set <code class="docutils literal notranslate"><span class="pre">p1</span></code> to <code class="docutils literal notranslate"><span class="pre">p2</span></code>.
p1 and p2 must have the same number of columns, and columns correspond
to the same point.</p>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.rot2">
<span class="sig-name descname"><span class="pre">rot2</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">unit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'rad'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#rot2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.rot2" title="Permalink to this definition"></a></dt>
<dd><p>Create SO(2) rotation</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>theta</strong> (<em>float</em>) – rotation angle</p></li>
<li><p><strong>unit</strong> (<em>str</em>) – angular units: ‘rad’ [default], or ‘deg’</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>SO(2) rotation matrix</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(2,2)</p>
</dd>
</dl>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">rot2(θ)</span></code> is an SO(2) rotation matrix (2x2) representing a rotation of θ radians.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">rot2(θ,</span> <span class="pre">'deg')</span></code> as above but θ is in degrees.</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="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">rot2</span><span class="p">(</span><span class="mf">0.3</span><span class="p">)</span>
<span class="go">array([[ 0.9553, -0.2955],</span>
<span class="go"> [ 0.2955, 0.9553]])</span>
<span class="gp">>>> </span><span class="n">rot2</span><span class="p">(</span><span class="mi">45</span><span class="p">,</span> <span class="s1">'deg'</span><span class="p">)</span>
<span class="go">array([[ 0.7071, -0.7071],</span>
<span class="go"> [ 0.7071, 0.7071]])</span>
</pre></div>
</div>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.tr2jac2">
<span class="sig-name descname"><span class="pre">tr2jac2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">T</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#tr2jac2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.tr2jac2" title="Permalink to this definition"></a></dt>
<dd><p>SE(2) Jacobian matrix</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>T</strong> (<em>ndarray</em><em>(</em><em>3</em><em>,</em><em>3</em><em>)</em>) – SE(2) matrix</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Jacobian matrix</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3,3)</p>
</dd>
</dl>
<p>Computes an Jacobian matrix that maps spatial velocity between two frames defined by
an SE(2) matrix.</p>
<p><code class="docutils literal notranslate"><span class="pre">tr2jac2(T)</span></code> is a Jacobian matrix (3x3) that maps spatial velocity or
differential motion from frame {B} to frame {A} where the pose of {B}
elative to {A} is represented by the homogeneous transform T = <span class="math notranslate nohighlight">\({}^A {\bf T}_B\)</span>.</p>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">T</span> <span class="o">=</span> <span class="n">trot2</span><span class="p">(</span><span class="mf">0.3</span><span class="p">,</span> <span class="n">t</span><span class="o">=</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">tr2jac2</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
<span class="go">array([[ 0.9553, -0.2955, 0. ],</span>
<span class="go"> [ 0.2955, 0.9553, 0. ],</span>
<span class="go"> [ 0. , 0. , 1. ]])</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Reference</dt>
<dd class="field-odd"><p>Robotics, Vision & Control: Second Edition, P. Corke, Springer 2016; p65.</p>
</dd>
<dt class="field-even">SymPy</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.transforms2d.tr2xyt">
<span class="sig-name descname"><span class="pre">tr2xyt</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">T</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">unit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'rad'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#tr2xyt"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.tr2xyt" title="Permalink to this definition"></a></dt>
<dd><p>Convert SE(2) to x, y, theta</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>T</strong> (<em>ndarray</em><em>(</em><em>3</em><em>,</em><em>3</em><em>)</em>) – SE(2) matrix</p></li>
<li><p><strong>unit</strong> (<em>str</em>) – angular units: ‘rad’ [default], or ‘deg’</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>[x, y, θ]</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3)</p>
</dd>
</dl>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">tr2xyt(T)</span></code> is a vector giving the equivalent 2D translation and
rotation for this SO(2) matrix.</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="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">T</span> <span class="o">=</span> <span class="n">xyt2tr</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="mf">0.3</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">T</span>
<span class="go">array([[ 0.9553, -0.2955, 1. ],</span>
<span class="go"> [ 0.2955, 0.9553, 2. ],</span>
<span class="go"> [ 0. , 0. , 1. ]])</span>
<span class="gp">>>> </span><span class="n">tr2xyt</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
<span class="go">array([1. , 2. , 0.3])</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p>trot2</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.tranimate2">
<span class="sig-name descname"><span class="pre">tranimate2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">T</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#tranimate2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.tranimate2" title="Permalink to this definition"></a></dt>
<dd><p>Animate a 2D coordinate frame</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>T</strong> – an SE(2) or SO(2) pose to be displayed as coordinate frame</p></li>
<li><p><strong>nframes</strong> (<em>int</em>) – number of steps in the animation [defaault 100]</p></li>
<li><p><strong>repeat</strong> (<em>bool</em>) – animate in endless loop [default False]</p></li>
<li><p><strong>interval</strong> (<em>int</em>) – number of milliseconds between frames [default 50]</p></li>
<li><p><strong>movie</strong> (<em>str</em>) – name of file to write MP4 movie into</p></li>
</ul>
</dd>
<dt class="field-even">Type</dt>
<dd class="field-even"><p>ndarray(3,3) or ndarray(2,2)</p>
</dd>
</dl>
<p>Animates a 2D coordinate frame moving from the world frame to a frame represented by the SO(2) or SE(2) matrix to the current axes.</p>
<ul class="simple">
<li><p>If no current figure, one is created</p></li>
<li><p>If current figure, but no axes, a 3d Axes is created</p></li>
</ul>
<p>Examples:</p>
<blockquote>
<div><p>tranimate2(transl(1,2)@trot2(1), frame=’A’, arrow=False, dims=[0, 5])
tranimate2(transl(1,2)@trot2(1), frame=’A’, arrow=False, dims=[0, 5], movie=’spin.mp4’)</p>
</div></blockquote>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.transl2">
<span class="sig-name descname"><span class="pre">transl2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</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/transforms2d.html#transl2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.transl2" title="Permalink to this definition"></a></dt>
<dd><p>Create SE(2) pure translation, or extract translation from SE(2) matrix</p>
<p><strong>Create a translational SE(2) matrix</strong></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x</strong> (<em>float</em>) – translation along X-axis</p></li>
<li><p><strong>y</strong> (<em>float</em>) – translation along Y-axis</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>SE(2) matrix</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3,3)</p>
</dd>
</dl>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">T</span> <span class="pre">=</span> <span class="pre">transl2([X,</span> <span class="pre">Y])</span></code> is an SE(2) homogeneous transform (3x3)
representing a pure translation.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">T</span> <span class="pre">=</span> <span class="pre">transl2(</span> <span class="pre">V</span> <span class="pre">)</span></code> as above but the translation is given by a 2-element
list, dict, or a numpy array, row or column vector.</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="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="n">transl2</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([[1., 0., 3.],</span>
<span class="go"> [0., 1., 4.],</span>
<span class="go"> [0., 0., 1.]])</span>
<span class="gp">>>> </span><span class="n">transl2</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([[1., 0., 3.],</span>
<span class="go"> [0., 1., 4.],</span>
<span class="go"> [0., 0., 1.]])</span>
<span class="gp">>>> </span><span class="n">transl2</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</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([[1., 0., 3.],</span>
<span class="go"> [0., 1., 4.],</span>
<span class="go"> [0., 0., 1.]])</span>
</pre></div>
</div>
<p><strong>Extract the translational part of an SE(2) matrix</strong></p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>x</strong> (<em>ndarray</em><em>(</em><em>3</em><em>,</em><em>3</em><em>)</em>) – SE(2) transform matrix</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>translation elements of SE(2) matrix</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(2)</p>
</dd>
</dl>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">t</span> <span class="pre">=</span> <span class="pre">transl2(T)</span></code> is the translational part of the SE(3) matrix <code class="docutils literal notranslate"><span class="pre">T</span></code> as a
2-element NumPy array.</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="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="n">T</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</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">3</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">4</span><span class="p">],</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">1</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">transl2</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
<span class="go">array([3, 4])</span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This function is compatible with the MATLAB version of the Toolbox. It
is unusual/weird in doing two completely different things inside the one
function.</p>
</div>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.trexp2">
<span class="sig-name descname"><span class="pre">trexp2</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">theta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">check</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/transforms2d.html#trexp2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.trexp2" title="Permalink to this definition"></a></dt>
<dd><p>Exponential of so(2) or se(2) matrix</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>S</strong> – se(2), so(2) matrix or equivalent velctor</p></li>
<li><p><strong>theta</strong> (<em>float</em>) – motion</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>matrix exponential in SE(2) or SO(2)</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3,3) or ndarray(2,2)</p>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>ValueError</strong> – bad argument</p>
</dd>
</dl>
<p>An efficient closed-form solution of the matrix exponential for arguments
that are se(2) or so(2).</p>
<p>For se(2) the results is an SE(2) homogeneous transformation matrix:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">trexp2(Σ)</span></code> is the matrix exponential of the se(2) element <code class="docutils literal notranslate"><span class="pre">Σ</span></code> which is
a 3x3 augmented skew-symmetric matrix.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">trexp2(Σ,</span> <span class="pre">θ)</span></code> as above but for an se(3) motion of Σθ, where <code class="docutils literal notranslate"><span class="pre">Σ</span></code>
must represent a unit-twist, ie. the rotational component is a unit-norm skew-symmetric
matrix.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">trexp2(S)</span></code> is the matrix exponential of the se(3) element <code class="docutils literal notranslate"><span class="pre">S</span></code> represented as
a 3-vector which can be considered a screw motion.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">trexp2(S,</span> <span class="pre">θ)</span></code> as above but for an se(2) motion of Sθ, where <code class="docutils literal notranslate"><span class="pre">S</span></code>
must represent a unit-twist, ie. the rotational component is a unit-norm skew-symmetric
matrix.</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="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">trexp2</span><span class="p">(</span><span class="n">skew</span><span class="p">(</span><span class="mi">1</span><span class="p">))</span>
<span class="go">array([[ 0.5403, -0.8415],</span>
<span class="go"> [ 0.8415, 0.5403]])</span>
<span class="gp">>>> </span><span class="n">trexp2</span><span class="p">(</span><span class="n">skew</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="c1"># revolute unit twist</span>
<span class="go">array([[-0.4161, -0.9093],</span>
<span class="go"> [ 0.9093, -0.4161]])</span>
<span class="gp">>>> </span><span class="n">trexp2</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="go">array([[ 0.5403, -0.8415],</span>
<span class="go"> [ 0.8415, 0.5403]])</span>
<span class="gp">>>> </span><span class="n">trexp2</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="c1"># revolute unit twist</span>
<span class="go">array([[-0.4161, -0.9093],</span>
<span class="go"> [ 0.9093, -0.4161]])</span>
</pre></div>
</div>
<p>For so(2) the results is an SO(2) rotation matrix:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">trexp2(Ω)</span></code> is the matrix exponential of the so(3) element <code class="docutils literal notranslate"><span class="pre">Ω</span></code> which is a 2x2
skew-symmetric matrix.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">trexp2(Ω,</span> <span class="pre">θ)</span></code> as above but for an so(3) motion of Ωθ, where <code class="docutils literal notranslate"><span class="pre">Ω</span></code> is
unit-norm skew-symmetric matrix representing a rotation axis and a rotation magnitude
given by <code class="docutils literal notranslate"><span class="pre">θ</span></code>.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">trexp2(ω)</span></code> is the matrix exponential of the so(2) element <code class="docutils literal notranslate"><span class="pre">ω</span></code> expressed as
a 1-vector.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">trexp2(ω,</span> <span class="pre">θ)</span></code> as above but for an so(3) motion of ωθ where <code class="docutils literal notranslate"><span class="pre">ω</span></code> is a
unit-norm vector representing a rotation axis and a rotation magnitude
given by <code class="docutils literal notranslate"><span class="pre">θ</span></code>. <code class="docutils literal notranslate"><span class="pre">ω</span></code> is expressed as a 1-vector.</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="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">trexp2</span><span class="p">(</span><span class="n">skewa</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([[-0.99 , -0.1411, -1.2796],</span>
<span class="go"> [ 0.1411, -0.99 , 0.7574],</span>
<span class="go"> [ 0. , 0. , 1. ]])</span>
<span class="gp">>>> </span><span class="n">trexp2</span><span class="p">(</span><span class="n">skewa</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="mi">2</span><span class="p">)</span> <span class="c1"># prismatic unit twist</span>
<span class="go">array([[1., 0., 2.],</span>
<span class="go"> [0., 1., 0.],</span>
<span class="go"> [0., 0., 1.]])</span>
<span class="gp">>>> </span><span class="n">trexp2</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([[-0.99 , -0.1411, -1.2796],</span>
<span class="go"> [ 0.1411, -0.99 , 0.7574],</span>
<span class="go"> [ 0. , 0. , 1. ]])</span>
<span class="gp">>>> </span><span class="n">trexp2</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="mi">2</span><span class="p">)</span>
<span class="go">array([[1., 0., 2.],</span>
<span class="go"> [0., 1., 0.],</span>
<span class="go"> [0., 0., 1.]])</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p>trlog, trexp2</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.trinterp2">
<span class="sig-name descname"><span class="pre">trinterp2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">start</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">end</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">s</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/transforms2d.html#trinterp2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.trinterp2" title="Permalink to this definition"></a></dt>
<dd><p>Interpolate SE(2) or SO(2) matrices</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>start</strong> (<em>ndarray</em><em>(</em><em>3</em><em>,</em><em>3</em><em>) or </em><em>ndarray</em><em>(</em><em>2</em><em>,</em><em>2</em><em>) or </em><em>None</em>) – initial SE(2) or SO(2) matrix value when s=0, if None then identity is used</p></li>
<li><p><strong>end</strong> (<em>ndarray</em><em>(</em><em>3</em><em>,</em><em>3</em><em>) or </em><em>ndarray</em><em>(</em><em>2</em><em>,</em><em>2</em><em>)</em>) – final SE(2) or SO(2) matrix, value when s=1</p></li>
<li><p><strong>s</strong> (<em>float</em>) – interpolation coefficient, range 0 to 1</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>interpolated SE(2) or SO(2) matrix value</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3,3) or ndarray(2,2)</p>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>ValueError</strong> – bad arguments</p>
</dd>
</dl>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">trinterp2(None,</span> <span class="pre">T,</span> <span class="pre">S)</span></code> is an SE(2) matrix interpolated
between identity when <cite>S`=0 and `T</cite> when <a href="#id1"><span class="problematic" id="id2">`</span></a>S`=1.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">trinterp2(T0,</span> <span class="pre">T1,</span> <span class="pre">S)</span></code> as above but interpolated
between <cite>T0</cite> when <cite>S`=0 and `T1</cite> when <a href="#id3"><span class="problematic" id="id4">`</span></a>S`=1.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">trinterp2(None,</span> <span class="pre">R,</span> <span class="pre">S)</span></code> is an SO(2) matrix interpolated
between identity when <cite>S`=0 and `R</cite> when <a href="#id5"><span class="problematic" id="id6">`</span></a>S`=1.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">trinterp2(R0,</span> <span class="pre">R1,</span> <span class="pre">S)</span></code> as above but interpolated
between <cite>R0</cite> when <cite>S`=0 and `R1</cite> when <a href="#id7"><span class="problematic" id="id8">`</span></a>S`=1.</p></li>
</ul>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Rotation angle is linearly interpolated.</p>
</div>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">T1</span> <span class="o">=</span> <span class="n">transl2</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="gp">>>> </span><span class="n">T2</span> <span class="o">=</span> <span class="n">transl2</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="gp">>>> </span><span class="n">trinterp2</span><span class="p">(</span><span class="n">T1</span><span class="p">,</span> <span class="n">T2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="go">array([[ 1., -0., 1.],</span>
<span class="go"> [ 0., 1., 2.],</span>
<span class="go"> [ 0., 0., 1.]])</span>
<span class="gp">>>> </span><span class="n">trinterp2</span><span class="p">(</span><span class="n">T1</span><span class="p">,</span> <span class="n">T2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="go">array([[ 1., -0., 3.],</span>
<span class="go"> [ 0., 1., 4.],</span>
<span class="go"> [ 0., 0., 1.]])</span>
<span class="gp">>>> </span><span class="n">trinterp2</span><span class="p">(</span><span class="n">T1</span><span class="p">,</span> <span class="n">T2</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">)</span>
<span class="go">array([[ 1., -0., 2.],</span>
<span class="go"> [ 0., 1., 3.],</span>
<span class="go"> [ 0., 0., 1.]])</span>
<span class="gp">>>> </span><span class="n">trinterp2</span><span class="p">(</span><span class="kc">None</span><span class="p">,</span> <span class="n">T2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="go">array([[ 1., -0., 0.],</span>
<span class="go"> [ 0., 1., 0.],</span>
<span class="go"> [ 0., 0., 1.]])</span>
<span class="gp">>>> </span><span class="n">trinterp2</span><span class="p">(</span><span class="kc">None</span><span class="p">,</span> <span class="n">T2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="go">array([[ 1., -0., 3.],</span>
<span class="go"> [ 0., 1., 4.],</span>
<span class="go"> [ 0., 0., 1.]])</span>
<span class="gp">>>> </span><span class="n">trinterp2</span><span class="p">(</span><span class="kc">None</span><span class="p">,</span> <span class="n">T2</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">)</span>
<span class="go">array([[ 1. , -0. , 1.5],</span>
<span class="go"> [ 0. , 1. , 2. ],</span>
<span class="go"> [ 0. , 0. , 1. ]])</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="func_3d.html#spatialmath.base.transforms3d.trinterp" title="spatialmath.base.transforms3d.trinterp"><code class="xref py py-func docutils literal notranslate"><span class="pre">trinterp()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.trinv2">
<span class="sig-name descname"><span class="pre">trinv2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">T</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#trinv2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.trinv2" title="Permalink to this definition"></a></dt>
<dd><p>Invert an SE(2) matrix</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>T</strong> (<em>ndarray</em><em>(</em><em>3</em><em>,</em><em>3</em><em>)</em>) – SE(2) matrix</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>inverse of SE(2) matrix</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3,3)</p>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>ValueError</strong> – bad arguments</p>
</dd>
</dl>
<p>Computes an efficient inverse of an SE(2) matrix:</p>
<p><span class="math notranslate nohighlight">\(\begin{pmatrix} {\bf R} & t \\ 0\,0 & 1 \end{pmatrix}^{-1} = \begin{pmatrix} {\bf R}^T & -{\bf R}^T t \\ 0\, 0 & 1 \end{pmatrix}\)</span></p>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">T</span> <span class="o">=</span> <span class="n">trot2</span><span class="p">(</span><span class="mf">0.3</span><span class="p">,</span> <span class="n">t</span><span class="o">=</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">])</span>
<span class="gp">>>> </span><span class="n">trinv2</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
<span class="go">array([[ 0.9553, 0.2955, -5.2989],</span>
<span class="go"> [-0.2955, 0.9553, -3.5946],</span>
<span class="go"> [ 0. , 0. , 1. ]])</span>
<span class="gp">>>> </span><span class="n">T</span> <span class="o">@</span> <span class="n">trinv2</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
<span class="go">array([[ 1., -0., 0.],</span>
<span class="go"> [-0., 1., 0.],</span>
<span class="go"> [ 0., 0., 1.]])</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">SymPy</dt>
<dd class="field-odd"><p>supported</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.trlog2">
<span class="sig-name descname"><span class="pre">trlog2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">T</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">check</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">twist</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#trlog2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.trlog2" title="Permalink to this definition"></a></dt>
<dd><p>Logarithm of SO(2) or SE(2) matrix</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>T</strong> (<em>ndarray</em><em>(</em><em>3</em><em>,</em><em>3</em><em>) or </em><em>ndarray</em><em>(</em><em>2</em><em>,</em><em>2</em><em>)</em>) – SE(2) or SO(2) matrix</p></li>
<li><p><strong>check</strong> (<em>bool</em>) – check that matrix is valid</p></li>
<li><p><strong>twist</strong> (<em>bool</em>) – return a twist vector instead of matrix [default]</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>logarithm</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3,3) or ndarray(3); or ndarray(2,2) or ndarray(1)</p>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>ValueError</strong> – bad argument</p>
</dd>
</dl>
<p>An efficient closed-form solution of the matrix logarithm for arguments that
are SO(2) or SE(2).</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">trlog2(R)</span></code> is the logarithm of the passed rotation matrix <code class="docutils literal notranslate"><span class="pre">R</span></code> which
will be 2x2 skew-symmetric matrix. The equivalent vector from <code class="docutils literal notranslate"><span class="pre">vex()</span></code>
is parallel to rotation axis and its norm is the amount of rotation about
that axis.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">trlog(T)</span></code> is the logarithm of the passed homogeneous transformation
matrix <code class="docutils literal notranslate"><span class="pre">T</span></code> which will be 3x3 augumented skew-symmetric matrix. The
equivalent vector from <code class="docutils literal notranslate"><span class="pre">vexa()</span></code> is the twist vector (6x1) comprising [v
w].</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="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">trlog2</span><span class="p">(</span><span class="n">trot2</span><span class="p">(</span><span class="mf">0.3</span><span class="p">))</span>
<span class="go">array([[-0. , -0.3, 0. ],</span>
<span class="go"> [ 0.3, 0. , 0. ],</span>
<span class="go"> [ 0. , 0. , 0. ]])</span>
<span class="gp">>>> </span><span class="n">trlog2</span><span class="p">(</span><span class="n">trot2</span><span class="p">(</span><span class="mf">0.3</span><span class="p">),</span> <span class="n">twist</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="go">array([0. , 0. , 0.3])</span>
<span class="gp">>>> </span><span class="n">trlog2</span><span class="p">(</span><span class="n">rot2</span><span class="p">(</span><span class="mf">0.3</span><span class="p">))</span>
<span class="go">array([[-0. , -0.3],</span>
<span class="go"> [ 0.3, 0. ]])</span>
<span class="gp">>>> </span><span class="n">trlog2</span><span class="p">(</span><span class="n">rot2</span><span class="p">(</span><span class="mf">0.3</span><span class="p">),</span> <span class="n">twist</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="go">array([0.3])</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">trexp()</span></code>, <a class="reference internal" href="func_nd.html#spatialmath.base.transformsNd.vex" title="spatialmath.base.transformsNd.vex"><code class="xref py py-func docutils literal notranslate"><span class="pre">vex()</span></code></a>,
<a class="reference internal" href="func_nd.html#spatialmath.base.transformsNd.vexa" title="spatialmath.base.transformsNd.vexa"><code class="xref py py-func docutils literal notranslate"><span class="pre">vexa()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.trot2">
<span class="sig-name descname"><span class="pre">trot2</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">unit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'rad'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">t</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/transforms2d.html#trot2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.trot2" title="Permalink to this definition"></a></dt>
<dd><p>Create SE(2) pure rotation</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>theta</strong> – rotation angle about X-axis</p></li>
<li><p><strong>unit</strong> (<em>str</em>) – angular units: ‘rad’ [default], or ‘deg’</p></li>
<li><p><strong>t</strong> (<em>array_like</em><em>(</em><em>2</em><em>)</em>) – 2D translation vector, defaults to [0,0]</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>3x3 homogeneous transformation matrix</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3,3)</p>
</dd>
</dl>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">trot2(θ)</span></code> is a homogeneous transformation (3x3) representing a rotation of
θ radians.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">trot2(θ,</span> <span class="pre">'deg')</span></code> as above but θ is in degrees.</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="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">trot2</span><span class="p">(</span><span class="mf">0.3</span><span class="p">)</span>
<span class="go">array([[ 0.9553, -0.2955, 0. ],</span>
<span class="go"> [ 0.2955, 0.9553, 0. ],</span>
<span class="go"> [ 0. , 0. , 1. ]])</span>
<span class="gp">>>> </span><span class="n">trot2</span><span class="p">(</span><span class="mi">45</span><span class="p">,</span> <span class="s1">'deg'</span><span class="p">,</span> <span class="n">t</span><span class="o">=</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">array([[ 0.7071, -0.7071, 1. ],</span>
<span class="go"> [ 0.7071, 0.7071, 2. ],</span>
<span class="go"> [ 0. , 0. , 1. ]])</span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>By default, the translational component is zero but it can be
set to a non-zero value.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p>xyt2tr</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.trplot2">
<span class="sig-name descname"><span class="pre">trplot2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">T</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">color</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'blue'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">frame</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">axislabel</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">axissubscript</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">textcolor</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">labels</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">('X',</span> <span class="pre">'Y')</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">length</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">arrow</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rviz</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ax</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">block</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dims</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wtl</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">width</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">d1</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">d2</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.15</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#trplot2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.trplot2" title="Permalink to this definition"></a></dt>
<dd><p>Plot a 2D coordinate frame</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>T</strong> – an SE(3) or SO(3) pose to be displayed as coordinate frame</p></li>
<li><p><strong>color</strong> (<em>str</em>) – color of the lines defining the frame</p></li>
<li><p><strong>textcolor</strong> (<em>str</em>) – color of text labels for the frame, default color of lines above</p></li>
<li><p><strong>frame</strong> (<em>str</em>) – label the frame, name is shown below the frame and as subscripts on the frame axis labels</p></li>
<li><p><strong>axislabel</strong> (<em>bool</em>) – display labels on axes, default True</p></li>
<li><p><strong>axissubscript</strong> (<em>bool</em>) – display subscripts on axis labels, default True</p></li>
<li><p><strong>labels</strong> (<em>2-tuple of strings</em>) – labels for the axes, defaults to X and Y</p></li>
<li><p><strong>length</strong> (<em>float</em>) – length of coordinate frame axes, default 1</p></li>
<li><p><strong>arrow</strong> (<em>bool</em>) – show arrow heads, default True</p></li>
<li><p><strong>ax</strong> (<em>Axes3D reference</em>) – the axes to plot into, defaults to current axes</p></li>
<li><p><strong>block</strong> (<em>bool</em>) – run the GUI main loop until all windows are closed, default True</p></li>
<li><p><strong>dims</strong> (<em>array_like</em><em>(</em><em>4</em><em>)</em>) – dimension of plot volume as [xmin, xmax, ymin, ymax]</p></li>
<li><p><strong>wtl</strong> (<em>float</em>) – width-to-length ratio for arrows, default 0.2</p></li>
<li><p><strong>rviz</strong> (<em>bool</em>) – show Rviz style arrows, default False</p></li>
<li><p><strong>projection</strong> (<em>str</em>) – 3D projection: ortho [default] or persp</p></li>
<li><p><strong>width</strong> (<em>float</em>) – width of lines, default 1</p></li>
<li><p><strong>d1</strong> (<em>float</em>) – distance of frame axis label text from origin, default 0.05</p></li>
<li><p><strong>d2</strong> (<em>float</em>) – distance of frame label text from origin, default 1.15</p></li>
</ul>
</dd>
<dt class="field-even">Type</dt>
<dd class="field-even"><p>ndarray(3,3) or ndarray(2,2)</p>
</dd>
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>axes containing the frame</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>AxesSubplot</p>
</dd>
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><p><strong>ValueError</strong> – bad argument</p>
</dd>
</dl>
<p>Adds a 2D coordinate frame represented by the SO(2) or SE(2) matrix to the current axes.</p>
<p>The appearance of the coordinate frame depends on many parameters:</p>
<ul class="simple">
<li><dl class="simple">
<dt>coordinate axes depend on:</dt><dd><ul>
<li><p><code class="docutils literal notranslate"><span class="pre">color</span></code> of axes</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">width</span></code> of line</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">length</span></code> of line</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">arrow</span></code> if True [default] draw the axis with an arrow head</p></li>
</ul>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>coordinate axis labels depend on:</dt><dd><ul>
<li><p><code class="docutils literal notranslate"><span class="pre">axislabel</span></code> if True [default] label the axis, default labels are X, Y, Z</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">labels</span></code> 2-list of alternative axis labels</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">textcolor</span></code> which defaults to <code class="docutils literal notranslate"><span class="pre">color</span></code></p></li>
<li><dl class="simple">
<dt><code class="docutils literal notranslate"><span class="pre">axissubscript</span></code> if True [default] add the frame label <code class="docutils literal notranslate"><span class="pre">frame</span></code> as a subscript</dt><dd><p>for each axis label</p>
</dd>
</dl>
</li>
</ul>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>coordinate frame label depends on:</dt><dd><ul>
<li><p><cite>frame</cite> the label placed inside {} near the origin of the frame</p></li>
</ul>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>a dot at the origin</dt><dd><ul>
<li><p><code class="docutils literal notranslate"><span class="pre">originsize</span></code> size of the dot, if zero no dot</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">origincolor</span></code> color of the dot, defaults to <code class="docutils literal notranslate"><span class="pre">color</span></code></p></li>
<li><p>If no current figure, one is created</p></li>
<li><p>If current figure, but no axes, a 3d Axes is created</p></li>
</ul>
</dd>
</dl>
</li>
</ul>
<p>Examples:</p>
<blockquote>
<div><p>trplot2(T, frame=’A’)
trplot2(T, frame=’A’, color=’green’)
trplot2(T1, ‘labels’, ‘AB’);</p>
</div></blockquote>
<dl class="field-list simple">
<dt class="field-odd">SymPy</dt>
<dd class="field-odd"><p>not supported</p>
</dd>
<dt class="field-even">Seealso</dt>
<dd class="field-even"><p><a class="reference internal" href="#spatialmath.base.transforms2d.tranimate2" title="spatialmath.base.transforms2d.tranimate2"><code class="xref py py-func docutils literal notranslate"><span class="pre">tranimate2()</span></code></a> <code class="xref py py-func docutils literal notranslate"><span class="pre">plotvol2()</span></code> <code class="xref py py-func docutils literal notranslate"><span class="pre">axes_logic()</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.trprint2">
<span class="sig-name descname"><span class="pre">trprint2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">T</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">label=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">file=<_io.TextIOWrapper</span> <span class="pre">name='<stdout>'</span> <span class="pre">mode='w'</span> <span class="pre">encoding='UTF-8'></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fmt='{:.3g}'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">unit='deg'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#trprint2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.trprint2" title="Permalink to this definition"></a></dt>
<dd><p>Compact display of SE(2) or SO(2) matrices</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>T</strong> (<em>ndarray</em><em>(</em><em>3</em><em>,</em><em>3</em><em>) or </em><em>ndarray</em><em>(</em><em>2</em><em>,</em><em>2</em><em>)</em>) – matrix to format</p></li>
<li><p><strong>label</strong> (<em>str</em>) – text label to put at start of line</p></li>
<li><p><strong>file</strong> (<em>file object</em>) – file to write formatted string to</p></li>
<li><p><strong>fmt</strong> (<em>str</em>) – conversion format for each number</p></li>
<li><p><strong>unit</strong> (<em>str</em>) – angular units: ‘rad’ [default], or ‘deg’</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>formatted string</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>str</p>
</dd>
</dl>
<p>The matrix is formatted and written to <code class="docutils literal notranslate"><span class="pre">file</span></code> and the
string is returned. To suppress writing to a file, set <code class="docutils literal notranslate"><span class="pre">file=None</span></code>.</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">trprint2(R)</span></code> displays the SO(2) rotation matrix in a compact
single-line format and returns the string:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">LABEL</span><span class="p">:]</span> <span class="n">θ</span> <span class="n">UNIT</span>
</pre></div>
</div>
</li>
<li><p><code class="docutils literal notranslate"><span class="pre">trprint2(T)</span></code> displays the SE(2) homogoneous transform in a compact
single-line format and returns the string:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">LABEL</span><span class="p">:]</span> <span class="p">[</span><span class="n">t</span><span class="o">=</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">;]</span> <span class="n">θ</span> <span class="n">UNIT</span>
</pre></div>
</div>
</li>
</ul>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">T</span> <span class="o">=</span> <span class="n">transl2</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="o">@</span> <span class="n">trot2</span><span class="p">(</span><span class="mf">0.3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">trprint2</span><span class="p">(</span><span class="n">T</span><span class="p">,</span> <span class="n">file</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'T'</span><span class="p">)</span>
<span class="go">'T: t = 1, 2; 17.2°'</span>
<span class="gp">>>> </span><span class="n">trprint2</span><span class="p">(</span><span class="n">T</span><span class="p">,</span> <span class="n">file</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'T'</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">'</span><span class="si">{:8.4g}</span><span class="s1">'</span><span class="p">)</span>
<span class="go">'T: t = 1, 2; 17.19°'</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p>trprint</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.transforms2d.xyt2tr">
<span class="sig-name descname"><span class="pre">xyt2tr</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">xyt</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">unit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'rad'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/transforms2d.html#xyt2tr"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.transforms2d.xyt2tr" title="Permalink to this definition"></a></dt>
<dd><p>Create SE(2) pure rotation</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>xyt</strong> (<em>array_like</em><em>(</em><em>3</em><em>)</em>) – 2d translation and rotation</p></li>
<li><p><strong>unit</strong> (<em>str</em>) – angular units: ‘rad’ [default], or ‘deg’</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>SE(2) matrix</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3,3)</p>
</dd>
</dl>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">xyt2tr([x,y,θ])</span></code> is a homogeneous transformation (3x3) representing a rotation of
θ radians and a translation of (x,y).</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="nn">spatialmath.base</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">xyt2tr</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="mf">0.3</span><span class="p">])</span>
<span class="go">array([[ 0.9553, -0.2955, 1. ],</span>
<span class="go"> [ 0.2955, 0.9553, 2. ],</span>
<span class="go"> [ 0. , 0. , 1. ]])</span>
<span class="gp">>>> </span><span class="n">xyt2tr</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">45</span><span class="p">],</span> <span class="s1">'deg'</span><span class="p">)</span>
<span class="go">array([[ 0.7071, -0.7071, 1. ],</span>
<span class="go"> [ 0.7071, 0.7071, 2. ],</span>
<span class="go"> [ 0. , 0. , 1. ]])</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p>tr2xyt</p>
</dd>
</dl>
</dd></dl>
</section>
</div>
</div>
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<span class="lastupdated">Last updated on 01-Mar-2022.
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