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<section id="spatial-vector">
<h1>Spatial vector<a class="headerlink" href="#spatial-vector" title="Permalink to this heading"></a></h1>
<dl class="py class">
<dt class="sig sig-object py" id="spatialmath.spatialvector.SpatialVector">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SpatialVector</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/spatialvector.html#SpatialVector"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.spatialvector.SpatialVector" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">BasePoseList</span></code></p>
<p>Spatial 6-vector abstract superclass</p>
<p>This class has two abstract subclasses, which each have concrete subclasses.
Key characteristics:</p>
<ul class="simple">
<li><p>6D vectors that represent velocity, acceleration, momentum and force of
bodies in 3D.</p></li>
<li><p>inherit list-like properties from <code class="docutils literal notranslate"><span class="pre">SMUserList</span></code> class</p></li>
<li><p>support operators:</p></li>
</ul>
<table class="docutils align-default">
<thead>
<tr class="row-odd"><th class="head"><p>Operator</p></th>
<th class="head"><p>Operation</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">+</span></code></p></td>
<td><p>addition of spatial vectors of the same subclass</p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">-</span></code></p></td>
<td><p>subtraction of spatial vectors of the same subclass</p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">-</span></code></p></td>
<td><p>unary minus</p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">*</span></code></p></td>
<td><p>see table below</p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">^</span></code></p></td>
<td><p>cross product x or x*</p></td>
</tr>
</tbody>
</table>
<p>Certain subtypes can be multiplied</p>
<table class="docutils align-default">
<thead>
<tr class="row-odd"><th class="head" colspan="2"><p>Multiplicands</p></th>
<th class="head" colspan="2"><p>Product</p></th>
</tr>
<tr class="row-even"><th class="head"><p>left</p></th>
<th class="head"><p>right</p></th>
<th class="head"><p>type</p></th>
<th class="head"><p>operation</p></th>
</tr>
</thead>
<tbody>
<tr class="row-odd"><td><p>SE3, Twist3</p></td>
<td><p>SpatialVelocity</p></td>
<td><p>SpatialVelocity</p></td>
<td><p>adjoint product</p></td>
</tr>
<tr class="row-even"><td><p>SE3, Twist3</p></td>
<td><p>SpatialAcceleration</p></td>
<td><p>SpatialAcceleration</p></td>
<td><p>adjoint product</p></td>
</tr>
<tr class="row-odd"><td><p>SE3, Twist3</p></td>
<td><p>SpatialMomentum</p></td>
<td><p>SpatialMomentum</p></td>
<td><p>adjoint transpose product</p></td>
</tr>
<tr class="row-even"><td><p>SE3, Twist3</p></td>
<td><p>SpatialForce</p></td>
<td><p>SpatialForce</p></td>
<td><p>adjoint transpose product</p></td>
</tr>
<tr class="row-odd"><td><p>SpatialAcceleration</p></td>
<td><p>SpatialInertia</p></td>
<td><p>SpatialForce</p></td>
<td><p>matrix-vector product**</p></td>
</tr>
<tr class="row-even"><td><p>SpatialVelocity</p></td>
<td><p>SpatialInertia</p></td>
<td><p>SpatialMomentum</p></td>
<td><p>matrix-vector product**</p></td>
</tr>
</tbody>
</table>
<p>** indicates commutative operator.</p>
<div class="graphviz"><img src="_images/inheritance-aa1fa65f5514c596ac49efe69597c6576c5241e9.png" alt="Inheritance diagram of spatialmath.spatialvector.SpatialVelocity, spatialmath.spatialvector.SpatialAcceleration, spatialmath.spatialvector.SpatialForce, spatialmath.spatialvector.SpatialMomentum" usemap="#inheritanceb7c59f0386" class="inheritance graphviz" /></div>
<map id="inheritanceb7c59f0386" name="inheritanceb7c59f0386">
<area shape="rect" id="node1" href="6d_acceleration.html#spatialmath.spatialvector.SpatialAcceleration" target="_top" title="Spatial acceleration class" alt="" coords="296,5,444,31"/>
<area shape="rect" id="node2" href="6d_m6.html#spatialmath.spatialvector.SpatialM6" target="_top" title="Spatial 6-vector abstract motion superclass" alt="" coords="161,55,248,80"/>
<area shape="rect" id="node7" href="6d_velocity.html#spatialmath.spatialvector.SpatialVelocity" target="_top" title="Spatial velocity class" alt="" coords="311,55,429,80"/>
<area shape="rect" id="node3" href="6d_f6.html#spatialmath.spatialvector.SpatialF6" target="_top" title="Spatial 6-vector abstract force superclass" alt="" coords="163,104,246,129"/>
<area shape="rect" id="node5" href="6d_force.html#spatialmath.spatialvector.SpatialForce" target="_top" title="Spatial force class" alt="" coords="319,104,421,129"/>
<area shape="rect" id="node6" href="6d_momentum.html#spatialmath.spatialvector.SpatialMomentum" target="_top" title="Spatial momentum class" alt="" coords="299,153,441,179"/>
<area shape="rect" id="node4" href="#spatialmath.spatialvector.SpatialVector" target="_top" title="Spatial 6-vector abstract superclass" alt="" coords="5,80,113,105"/>
</map><p><strong>References:</strong></p>
<ul class="simple">
<li><p>“Robot Dynamics Algorithms”, R. Featherstone, volume 22,
Springer International Series in Engineering and Computer Science,
Springer, 1987.</p></li>
<li><p>“A beginner’s guide to 6-d vectors (part 1)”, R. Featherstone,
IEEE Robotics Automation Magazine, 17(3):83-94, Sep. 2010.</p></li>
<li><p><a class="reference external" href="http://users.cecs.anu.edu.au/~roy/spatial">Online notes</a>
Methods:</p></li>
</ul>
<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="6d_m6.html#spatialmath.spatialvector.SpatialM6" title="spatialmath.spatialvector.SpatialM6"><code class="xref py py-func docutils literal notranslate"><span class="pre">SpatialM6()</span></code></a>, <a class="reference internal" href="6d_f6.html#spatialmath.spatialvector.SpatialF6" title="spatialmath.spatialvector.SpatialF6"><code class="xref py py-func docutils literal notranslate"><span class="pre">SpatialF6()</span></code></a>, <a class="reference internal" href="6d_velocity.html#spatialmath.spatialvector.SpatialVelocity" title="spatialmath.spatialvector.SpatialVelocity"><code class="xref py py-func docutils literal notranslate"><span class="pre">SpatialVelocity()</span></code></a>, <a class="reference internal" href="6d_acceleration.html#spatialmath.spatialvector.SpatialAcceleration" title="spatialmath.spatialvector.SpatialAcceleration"><code class="xref py py-func docutils literal notranslate"><span class="pre">SpatialAcceleration()</span></code></a>, <a class="reference internal" href="6d_force.html#spatialmath.spatialvector.SpatialForce" title="spatialmath.spatialvector.SpatialForce"><code class="xref py py-func docutils literal notranslate"><span class="pre">SpatialForce()</span></code></a>, <a class="reference internal" href="6d_momentum.html#spatialmath.spatialvector.SpatialMomentum" title="spatialmath.spatialvector.SpatialMomentum"><code class="xref py py-func docutils literal notranslate"><span class="pre">SpatialMomentum()</span></code></a>.</p>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.spatialvector.SpatialVector.__add__">
<span class="sig-name descname"><span class="pre">__add__</span></span><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/spatialvector.html#SpatialVector.__add__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.spatialvector.SpatialVector.__add__" title="Permalink to this definition"></a></dt>
<dd><p>Overloaded <code class="docutils literal notranslate"><span class="pre">*</span></code> operator (superclass method)</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>sum of spatial vectors</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>SpatialVector subclass instance</p>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>TypeError</strong> – attempting to add SpatialVectors of different subclass</p></li>
<li><p><strong>ValueErrror</strong> – attempting to add SpatialVectors with different numbers of values</p></li>
</ul>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">v1</span> <span class="pre">+</span> <span class="pre">v2</span></code> is a spatial vector of the same type as <code class="docutils literal notranslate"><span class="pre">v1</span></code> and <code class="docutils literal notranslate"><span class="pre">v2</span></code> whose value is
the element-wise sum of <code class="docutils literal notranslate"><span class="pre">v1</span></code> and <code class="docutils literal notranslate"><span class="pre">v2</span></code>. If both are arrays of spatial vectors V1 (1xN) and
V2 (1xN) the result is an array (1xN).</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.spatialvector.SpatialVector.__sub__" title="spatialmath.spatialvector.SpatialVector.__sub__"><code class="xref py py-func docutils literal notranslate"><span class="pre">__sub__()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.spatialvector.SpatialVector.__init__">
<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/spatialvector.html#SpatialVector.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.spatialvector.SpatialVector.__init__" title="Permalink to this definition"></a></dt>
<dd><p>Create a new spatial vector (abstract superclass)</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>value</strong> – Value of the</p>
</dd>
</dl>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">SpatialVector(vec)</span></code> is a spatial vector constructed from the 6-element array-like <code class="docutils literal notranslate"><span class="pre">vec</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">SpatialVector([V1,</span> <span class="pre">V2,</span> <span class="pre">...</span> <span class="pre">VN])</span></code> is a spatial vector array with N elements, constructed from the 6-element
array-like values <code class="docutils literal notranslate"><span class="pre">Vi</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">SpatialVector(A)</span></code> is a spatial vector array with N elements, constructed from the columns of the 6xN
array <code class="docutils literal notranslate"><span class="pre">A</span></code>.</p></li>
</ul>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.spatialvector.SpatialVector.__neg__">
<span class="sig-name descname"><span class="pre">__neg__</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/spatialvector.html#SpatialVector.__neg__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.spatialvector.SpatialVector.__neg__" title="Permalink to this definition"></a></dt>
<dd><p>Overloaded unary <code class="docutils literal notranslate"><span class="pre">-</span></code> operator (superclass method)</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>negative of spatial vector</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>SpatialVector subclass instance</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">-v</span></code> is a spatial vector of the same type as <code class="docutils literal notranslate"><span class="pre">v</span></code> whose value is
the element-wise negative of <code class="docutils literal notranslate"><span class="pre">v</span></code>.</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.spatialvector.SpatialVector.__sub__" title="spatialmath.spatialvector.SpatialVector.__sub__"><code class="xref py py-func docutils literal notranslate"><span class="pre">__sub__()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.spatialvector.SpatialVector.__sub__">
<span class="sig-name descname"><span class="pre">__sub__</span></span><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/spatialvector.html#SpatialVector.__sub__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.spatialvector.SpatialVector.__sub__" title="Permalink to this definition"></a></dt>
<dd><p>Overloaded <code class="docutils literal notranslate"><span class="pre">-</span></code> operator (superclass method)</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>difference of spatial vectors</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>SpatialVector subclass instance</p>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>TypeError</strong> – attempting to subtract SpatialVectors of different subclass</p></li>
<li><p><strong>ValueErrror</strong> – attempting to subtract SpatialVectors with different numbers of values</p></li>
</ul>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">v1</span> <span class="pre">-</span> <span class="pre">v2</span></code> is a spatial vector of the same type as <code class="docutils literal notranslate"><span class="pre">v1</span></code> and <code class="docutils literal notranslate"><span class="pre">v2</span></code>
whose value is the element-wise difference of <code class="docutils literal notranslate"><span class="pre">v1</span></code> and <code class="docutils literal notranslate"><span class="pre">v2</span></code>. If
both are arrays of spatial vectors V1 (1xN) and V2 (1xN) the result is
an array (1xN).</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.spatialvector.SpatialVector.__add__" title="spatialmath.spatialvector.SpatialVector.__add__"><code class="xref py py-func docutils literal notranslate"><span class="pre">__add__()</span></code></a>, <a class="reference internal" href="#spatialmath.spatialvector.SpatialVector.__neg__" title="spatialmath.spatialvector.SpatialVector.__neg__"><code class="xref py py-func docutils literal notranslate"><span class="pre">__neg__()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.spatialvector.SpatialVector.isvalid">
<span class="sig-name descname"><span class="pre">isvalid</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">check</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/spatialvector.html#SpatialVector.isvalid"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.spatialvector.SpatialVector.isvalid" title="Permalink to this definition"></a></dt>
<dd><p>Test if vector is valid spatial 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>x</strong> (<a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v2.2)"><em>numpy.ndarray</em></a>) – vector to test</p></li>
<li><p><strong>check</strong> (<em>bool</em>) – ignored</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>True if the matrix has shape (6,).</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="spatialmath.spatialvector.SpatialVector.shape">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">shape</span></span><a class="headerlink" href="#spatialmath.spatialvector.SpatialVector.shape" title="Permalink to this definition"></a></dt>
<dd><p>Shape of the object’s interal matrix representation</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>(6,)</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>tuple</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
</section>
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