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‎2d_orient_SO2.html

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‎2d_pose_SE2.html

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‎2d_pose_twist.html

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‎3d_dualquaternion.html

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<h1>Dual Quaternion<a class="headerlink" href="#dual-quaternion" title="Permalink to this headline"></a></h1>
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<dl class="py class">
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<dt id="spatialmath.DualQuaternion.DualQuaternion">
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<em class="property">class </em><code class="sig-name descname">DualQuaternion</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">real</span><span class="o">=</span><span class="default_value">None</span></em>, <em class="sig-param"><span class="n">dual</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion" title="Permalink to this definition"></a></dt>
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<em class="property"><span class="pre">class</span> </em><code class="sig-name descname"><span class="pre">DualQuaternion</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">real</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">dual</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/DualQuaternion.html#DualQuaternion"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion" title="Permalink to this definition"></a></dt>
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<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
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<p>A dual number is an ordered pair <span class="math notranslate nohighlight">\(\hat{a} = (a, b)\)</span> or written as
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<span class="math notranslate nohighlight">\(a + \epsilon b\)</span> where <span class="math notranslate nohighlight">\(\epsilon^2 = 0\)</span>.</p>
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</dl>
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<dl class="py method">
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<dt id="spatialmath.DualQuaternion.DualQuaternion.__init__">
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<code class="sig-name descname">__init__</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">real</span><span class="o">=</span><span class="default_value">None</span></em>, <em class="sig-param"><span class="n">dual</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.__init__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.__init__" title="Permalink to this definition"></a></dt>
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<code class="sig-name descname"><span class="pre">__init__</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">real</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">dual</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/DualQuaternion.html#DualQuaternion.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.__init__" title="Permalink to this definition"></a></dt>
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<dd><p>Construct a new dual quaternion</p>
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<dl class="field-list simple">
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<dt class="field-odd">Parameters</dt>
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<dl class="py method">
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<dt id="spatialmath.DualQuaternion.DualQuaternion.Pure">
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<em class="property">classmethod </em><code class="sig-name descname">Pure</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">x</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.Pure"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.Pure" title="Permalink to this definition"></a></dt>
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<em class="property"><span class="pre">classmethod</span> </em><code class="sig-name descname"><span class="pre">Pure</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.Pure"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.Pure" title="Permalink to this definition"></a></dt>
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<dd></dd></dl>
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<dl class="py method">
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<dt id="spatialmath.DualQuaternion.DualQuaternion.norm">
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<code class="sig-name descname">norm</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.norm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.norm" title="Permalink to this definition"></a></dt>
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<code class="sig-name descname"><span class="pre">norm</span></code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.norm" title="Permalink to this definition"></a></dt>
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<dd><p>Norm of a dual quaternion</p>
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<dl class="field-list simple">
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<dt class="field-odd">Returns</dt>
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<dt id="spatialmath.DualQuaternion.DualQuaternion.conj">
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<code class="sig-name descname">conj</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.conj"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.conj" title="Permalink to this definition"></a></dt>
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<code class="sig-name descname"><span class="pre">conj</span></code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.conj"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.conj" title="Permalink to this definition"></a></dt>
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<dd><p>Conjugate of dual quaternion</p>
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<dt class="field-odd">Returns</dt>
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<dt id="spatialmath.DualQuaternion.DualQuaternion.__add__">
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<code class="sig-name descname">__add__</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">right</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.__add__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.__add__" title="Permalink to this definition"></a></dt>
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<code class="sig-name descname"><span class="pre">__add__</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">right</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.__add__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.__add__" title="Permalink to this definition"></a></dt>
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<dd><p>Sum of two dual quaternions</p>
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<dt class="field-odd">Returns</dt>
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<dt id="spatialmath.DualQuaternion.DualQuaternion.__sub__">
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<code class="sig-name descname">__sub__</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">right</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.__sub__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.__sub__" title="Permalink to this definition"></a></dt>
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<code class="sig-name descname"><span class="pre">__sub__</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">right</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.__sub__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.__sub__" title="Permalink to this definition"></a></dt>
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<dd><p>Difference of two dual quaternions</p>
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<dl class="field-list simple">
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<dt class="field-odd">Returns</dt>
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<dl class="py method">
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<dt id="spatialmath.DualQuaternion.DualQuaternion.__mul__">
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<code class="sig-name descname">__mul__</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">right</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.__mul__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.__mul__" title="Permalink to this definition"></a></dt>
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<code class="sig-name descname"><span class="pre">__mul__</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">right</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.__mul__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.__mul__" title="Permalink to this definition"></a></dt>
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<dd><p>Product of dual quaternion</p>
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<ul class="simple">
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<li><p><code class="docutils literal notranslate"><span class="pre">dq1</span> <span class="pre">*</span> <span class="pre">dq2</span></code> is a dual quaternion representing the product of
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<dt id="spatialmath.DualQuaternion.DualQuaternion.matrix">
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<code class="sig-name descname">matrix</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.matrix"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.matrix" title="Permalink to this definition"></a></dt>
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<code class="sig-name descname"><span class="pre">matrix</span></code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/DualQuaternion.html#DualQuaternion.matrix"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.matrix" title="Permalink to this definition"></a></dt>
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<dd><p>Dual quaternion as a matrix</p>
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<dt class="field-odd">Returns</dt>
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<dt id="spatialmath.DualQuaternion.DualQuaternion.vec">
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<em class="property">property </em><code class="sig-name descname">vec</code><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.vec" title="Permalink to this definition"></a></dt>
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<em class="property"><span class="pre">property</span> </em><code class="sig-name descname"><span class="pre">vec</span></code><a class="headerlink" href="#spatialmath.DualQuaternion.DualQuaternion.vec" title="Permalink to this definition"></a></dt>
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<dd><p>Dual quaternion as a vector</p>
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<dt class="field-odd">Returns</dt>
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<p>
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&#169; Copyright 2020, Peter Corke.
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<span class="lastupdated">
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Last updated on 14-Feb-2021.
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Last updated on 15-Feb-2021.
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</span>
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</p>

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