.. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_gallery_images_contours_and_fields_trigradient_demo.py: ================ Trigradient Demo ================ Demonstrates computation of gradient with `matplotlib.tri.CubicTriInterpolator`. .. code-block:: default from matplotlib.tri import ( Triangulation, UniformTriRefiner, CubicTriInterpolator) import matplotlib.pyplot as plt import matplotlib.cm as cm import numpy as np #----------------------------------------------------------------------------- # Electrical potential of a dipole #----------------------------------------------------------------------------- def dipole_potential(x, y): """The electric dipole potential V, at position *x*, *y*.""" r_sq = x**2 + y**2 theta = np.arctan2(y, x) z = np.cos(theta)/r_sq return (np.max(z) - z) / (np.max(z) - np.min(z)) #----------------------------------------------------------------------------- # Creating a Triangulation #----------------------------------------------------------------------------- # First create the x and y coordinates of the points. n_angles = 30 n_radii = 10 min_radius = 0.2 radii = np.linspace(min_radius, 0.95, n_radii) angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False) angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1) angles[:, 1::2] += np.pi / n_angles x = (radii*np.cos(angles)).flatten() y = (radii*np.sin(angles)).flatten() V = dipole_potential(x, y) # Create the Triangulation; no triangles specified so Delaunay triangulation # created. triang = Triangulation(x, y) # Mask off unwanted triangles. triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1), y[triang.triangles].mean(axis=1)) < min_radius) #----------------------------------------------------------------------------- # Refine data - interpolates the electrical potential V #----------------------------------------------------------------------------- refiner = UniformTriRefiner(triang) tri_refi, z_test_refi = refiner.refine_field(V, subdiv=3) #----------------------------------------------------------------------------- # Computes the electrical field (Ex, Ey) as gradient of electrical potential #----------------------------------------------------------------------------- tci = CubicTriInterpolator(triang, -V) # Gradient requested here at the mesh nodes but could be anywhere else: (Ex, Ey) = tci.gradient(triang.x, triang.y) E_norm = np.sqrt(Ex**2 + Ey**2) #----------------------------------------------------------------------------- # Plot the triangulation, the potential iso-contours and the vector field #----------------------------------------------------------------------------- fig, ax = plt.subplots() ax.set_aspect('equal') # Enforce the margins, and enlarge them to give room for the vectors. ax.use_sticky_edges = False ax.margins(0.07) ax.triplot(triang, color='0.8') levels = np.arange(0., 1., 0.01) cmap = cm.get_cmap(name='hot', lut=None) ax.tricontour(tri_refi, z_test_refi, levels=levels, cmap=cmap, linewidths=[2.0, 1.0, 1.0, 1.0]) # Plots direction of the electrical vector field ax.quiver(triang.x, triang.y, Ex/E_norm, Ey/E_norm, units='xy', scale=10., zorder=3, color='blue', width=0.007, headwidth=3., headlength=4.) ax.set_title('Gradient plot: an electrical dipole') plt.show() .. image:: /gallery/images_contours_and_fields/images/sphx_glr_trigradient_demo_001.png :alt: Gradient plot: an electrical dipole :class: sphx-glr-single-img ------------ References """""""""" The use of the following functions, methods, classes and modules is shown in this example: .. code-block:: default import matplotlib matplotlib.axes.Axes.tricontour matplotlib.pyplot.tricontour matplotlib.axes.Axes.triplot matplotlib.pyplot.triplot matplotlib.tri matplotlib.tri.Triangulation matplotlib.tri.CubicTriInterpolator matplotlib.tri.CubicTriInterpolator.gradient matplotlib.tri.UniformTriRefiner matplotlib.axes.Axes.quiver matplotlib.pyplot.quiver .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. _sphx_glr_download_gallery_images_contours_and_fields_trigradient_demo.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: trigradient_demo.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: trigradient_demo.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature Keywords: matplotlib code example, codex, python plot, pyplot `Gallery generated by Sphinx-Gallery `_