operations/transformations/affine.html


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  <section id="affine-transformation">
<span id="affine"></span><h1>Affine transformation<a class="headerlink" href="#affine-transformation" title="Permalink to this headline">¶</a></h1>
<div class="versionadded">
<p><span class="versionmodified added">New in version 6.0.0.</span></p>
</div>
<p>The affine transformation applies translation and scaling/rotation terms on the
x,y,z coordinates, and translation and scaling on the temporal coordinate.</p>
<table class="docutils align-default">
<colgroup>
<col style="width: 27%" />
<col style="width: 73%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><strong>Alias</strong></p></td>
<td><p>affine</p></td>
</tr>
<tr class="row-even"><td><p><strong>Domain</strong></p></td>
<td><p>4D</p></td>
</tr>
<tr class="row-odd"><td><p><strong>Input type</strong></p></td>
<td><p>XYZT</p></td>
</tr>
<tr class="row-even"><td><p><strong>output type</strong></p></td>
<td><p>XYZT</p></td>
</tr>
</tbody>
</table>
<p>By default, the parameters are set for an identity transforms. The transformation
is reversible unless the determinant of the sji matrix is 0, or <cite>tscale</cite> is 0</p>
<section id="parameters">
<h2>Parameters<a class="headerlink" href="#parameters" title="Permalink to this headline">¶</a></h2>
<section id="optional">
<h3>Optional<a class="headerlink" href="#optional" title="Permalink to this headline">¶</a></h3>
<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-xoff">
<span class="sig-name descname"><span class="pre">+xoff</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-xoff" title="Permalink to this definition">¶</a></dt>
<dd><p>Offset in X. Default value: 0</p>
</dd></dl>

<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-yoff">
<span class="sig-name descname"><span class="pre">+yoff</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-yoff" title="Permalink to this definition">¶</a></dt>
<dd><p>Offset in Y. Default value: 0</p>
</dd></dl>

<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-zoff">
<span class="sig-name descname"><span class="pre">+zoff</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-zoff" title="Permalink to this definition">¶</a></dt>
<dd><p>Offset in Z. Default value: 0</p>
</dd></dl>

<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-toff">
<span class="sig-name descname"><span class="pre">+toff</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-toff" title="Permalink to this definition">¶</a></dt>
<dd><p>Offset in T. Default value: 0</p>
</dd></dl>

<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-s11">
<span class="sig-name descname"><span class="pre">+s11</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-s11" title="Permalink to this definition">¶</a></dt>
<dd><p>Rotation/scaling term. Default value: 1</p>
</dd></dl>

<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-s12">
<span class="sig-name descname"><span class="pre">+s12</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-s12" title="Permalink to this definition">¶</a></dt>
<dd><p>Rotation/scaling term. Default value: 0</p>
</dd></dl>

<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-s13">
<span class="sig-name descname"><span class="pre">+s13</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-s13" title="Permalink to this definition">¶</a></dt>
<dd><p>Rotation/scaling term. Default value: 0</p>
</dd></dl>

<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-s21">
<span class="sig-name descname"><span class="pre">+s21</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-s21" title="Permalink to this definition">¶</a></dt>
<dd><p>Rotation/scaling term. Default value: 0</p>
</dd></dl>

<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-s22">
<span class="sig-name descname"><span class="pre">+s22</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-s22" title="Permalink to this definition">¶</a></dt>
<dd><p>Rotation/scaling term. Default value: 1</p>
</dd></dl>

<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-s23">
<span class="sig-name descname"><span class="pre">+s23</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-s23" title="Permalink to this definition">¶</a></dt>
<dd><p>Rotation/scaling term. Default value: 0</p>
</dd></dl>

<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-s31">
<span class="sig-name descname"><span class="pre">+s31</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-s31" title="Permalink to this definition">¶</a></dt>
<dd><p>Rotation/scaling term. Default value: 0</p>
</dd></dl>

<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-s32">
<span class="sig-name descname"><span class="pre">+s32</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-s32" title="Permalink to this definition">¶</a></dt>
<dd><p>Rotation/scaling term. Default value: 0</p>
</dd></dl>

<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-s33">
<span class="sig-name descname"><span class="pre">+s33</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-s33" title="Permalink to this definition">¶</a></dt>
<dd><p>Rotation/scaling term. Default value: 1</p>
</dd></dl>

<dl class="std option">
<dt class="sig sig-object std" id="cmdoption-arg-tscale">
<span class="sig-name descname"><span class="pre">+tscale</span></span><span class="sig-prename descclassname"><span class="pre">=&lt;value&gt;</span></span><a class="headerlink" href="#cmdoption-arg-tscale" title="Permalink to this definition">¶</a></dt>
<dd><p>Time scaling term. Default value: 1</p>
</dd></dl>

<section id="mathematical-description">
<h4>Mathematical description<a class="headerlink" href="#mathematical-description" title="Permalink to this headline">¶</a></h4>
<div class="math notranslate nohighlight" id="equation-formula">
<span class="eqno">(1)<a class="headerlink" href="#equation-formula" title="Permalink to this equation">¶</a></span>\[\begin{split}\begin{align}
    \begin{bmatrix}
        X \\
        Y \\
        Z \\
        T \\
    \end{bmatrix}^{dest} =
    \begin{bmatrix}
        xoff \\
        yoff \\
        zoff \\
        toff \\
    \end{bmatrix} +
    \begin{bmatrix}
         s11 &amp; s12 &amp; s13 &amp; 0 \\
         s21 &amp; s22 &amp; s23 &amp; 0 \\
         s31 &amp; s32 &amp; s33 &amp; 0 \\
         0   &amp; 0   &amp; 0   &amp; tscale \\
    \end{bmatrix}
    \begin{bmatrix}
        X \\
        Y \\
        Z \\
        T \\
    \end{bmatrix}^{source}
\end{align}\end{split}\]</div>
</section>
</section>
</section>
</section>


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