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+  <h1>Source code for fastvpinns.FE.fe_transformation_2d</h1><div class="highlight"><pre>
+<span></span><span class="c1"># This class provides an interface for the transformation methods used in the</span>
+<span class="c1"># 2D finite element analysis. The transformation is essential for mapping</span>
+<span class="c1"># element geometry in the reference domain to the actual physical domain.</span>
+<span class="c1"># The primary functionalities encapsulated within this class include:</span>
+<span class="c1">#   1. set_cell() - To set the physical coordinates of the cell. These coordinates</span>
+<span class="c1">#                   are essential for subsequent computations involving Jacobians and transformations.</span>
+<span class="c1">#   2. get_original_from_ref(xi, eta) - Given reference coordinates (xi, eta), this</span>
+<span class="c1">#                   method returns the corresponding coordinates in the physical domain.</span>
+<span class="c1">#   3. get_jacobian(xi, eta) - For a given point in the reference domain, represented</span>
+<span class="c1">#                   by (xi, eta), this method calculates and returns the Jacobian of</span>
+<span class="c1">#                   the transformation, which provides information about the local stretching,</span>
+<span class="c1">#                   rotation, and skewing of the element.</span>
+<span class="c1">#</span>
+<span class="c1"># Further implementations of this class for specific element types (like quad and triangular elements)</span>
+<span class="c1"># can incorporate more detailed and element-specific transformation techniques.</span>
+<span class="c1">#</span>
+<span class="c1"># Author: Thivin Anandh D</span>
+<span class="c1"># Date:   20-Sep-2023</span>
+<span class="c1"># History: First version -  20-Sep-2023 - Thivin Anandh</span>
+
+
+<span class="kn">from</span> <span class="nn">abc</span> <span class="kn">import</span> <span class="n">abstractmethod</span>
+
+
+<div class="viewcode-block" id="FETransforamtion2D">
+<a class="viewcode-back" href="../../../_rst/library/fe2d/fe2d_transformation.html#fastvpinns.FE.fe_transformation_2d.FETransforamtion2D">[docs]</a>
+<span class="k">class</span> <span class="nc">FETransforamtion2D</span><span class="p">:</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    This class represents a 2D finite element transformation.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Constructor for the FETransforamtion2D class.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+<div class="viewcode-block" id="FETransforamtion2D.set_cell">
+<a class="viewcode-back" href="../../../_rst/library/fe2d/fe2d_transformation.html#fastvpinns.FE.fe_transformation_2d.FETransforamtion2D.set_cell">[docs]</a>
+    <span class="nd">@abstractmethod</span>
+    <span class="k">def</span> <span class="nf">set_cell</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Set the cell coordinates, which will be used to calculate the Jacobian and actual values.</span>
+
+<span class="sd">        :return: None</span>
+<span class="sd">        &quot;&quot;&quot;</span></div>
+
+
+    <span class="nd">@abstractmethod</span>
+    <span class="k">def</span> <span class="nf">get_original_from_ref</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">eta</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        This method returns the original coordinates from the reference coordinates.</span>
+
+<span class="sd">        :param xi: The xi coordinate in the reference space.</span>
+<span class="sd">        :type xi: float</span>
+<span class="sd">        :param eta: The eta coordinate in the reference space.</span>
+<span class="sd">        :type eta: float</span>
+<span class="sd">        :return: The original coordinates (x, y) corresponding to the given reference coordinates.</span>
+<span class="sd">        :rtype: tuple</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+<div class="viewcode-block" id="FETransforamtion2D.get_original_from_ref">
+<a class="viewcode-back" href="../../../_rst/library/fe2d/fe2d_transformation.html#fastvpinns.FE.fe_transformation_2d.FETransforamtion2D.get_original_from_ref">[docs]</a>
+    <span class="nd">@abstractmethod</span>
+    <span class="k">def</span> <span class="nf">get_original_from_ref</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">eta</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        This method returns the original coordinates from the reference coordinates.</span>
+
+<span class="sd">        :param xi: The xi value of the reference coordinates.</span>
+<span class="sd">        :type xi: float</span>
+<span class="sd">        :param eta: The eta value of the reference coordinates.</span>
+<span class="sd">        :type eta: float</span>
+<span class="sd">        :return: The original coordinates corresponding to the given reference coordinates.</span>
+<span class="sd">        :rtype: tuple</span>
+<span class="sd">        &quot;&quot;&quot;</span></div>
+
+
+<div class="viewcode-block" id="FETransforamtion2D.get_jacobian">
+<a class="viewcode-back" href="../../../_rst/library/fe2d/fe2d_transformation.html#fastvpinns.FE.fe_transformation_2d.FETransforamtion2D.get_jacobian">[docs]</a>
+    <span class="nd">@abstractmethod</span>
+    <span class="k">def</span> <span class="nf">get_jacobian</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">eta</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        This method returns the Jacobian of the transformation.</span>
+
+<span class="sd">        :param xi: The xi coordinate.</span>
+<span class="sd">        :type xi: float</span>
+<span class="sd">        :param eta: The eta coordinate.</span>
+<span class="sd">        :type eta: float</span>
+<span class="sd">        :return: The Jacobian matrix.</span>
+<span class="sd">        :rtype: numpy.ndarray</span>
+<span class="sd">        &quot;&quot;&quot;</span></div>
+</div>
+
+
+
+<span class="c1">## Mandatory, Import all the basis functions here (Quad element Transformations)</span>
+<span class="kn">from</span> <span class="nn">.quad_affine</span> <span class="kn">import</span> <span class="o">*</span>
+<span class="kn">from</span> <span class="nn">.quad_bilinear</span> <span class="kn">import</span> <span class="o">*</span>
+</pre></div>
+
+           </div>
+          </div>
+          <footer>
+
+  <hr/>
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+    <p>&#169; Copyright 2024, Thivin Anandh, Divij Ghose, Sashikumaar Ganesan.</p>
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