.. _pylab_examples-trigradient_demo: pylab_examples example code: trigradient_demo.py ================================================ .. plot:: /home/tcaswell/source/p/matplotlib/doc/mpl_examples/pylab_examples/trigradient_demo.py :: """ Demonstrates computation of gradient with matplotlib.tri.CubicTriInterpolator. """ from matplotlib.tri import Triangulation, UniformTriRefiner,\ CubicTriInterpolator import matplotlib.pyplot as plt import matplotlib.cm as cm import numpy as np import math #----------------------------------------------------------------------------- # Electrical potential of a dipole #----------------------------------------------------------------------------- def dipole_potential(x, y): """ The electric dipole potential V """ 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*math.pi, n_angles, endpoint=False) angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1) angles[:, 1::2] += math.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. xmid = x[triang.triangles].mean(axis=1) ymid = y[triang.triangles].mean(axis=1) mask = np.where(xmid*xmid + ymid*ymid < min_radius*min_radius, 1, 0) triang.set_mask(mask) #----------------------------------------------------------------------------- # 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 #----------------------------------------------------------------------------- plt.figure() plt.gca().set_aspect('equal') plt.triplot(triang, color='0.8') levels = np.arange(0., 1., 0.01) cmap = cm.get_cmap(name='hot', lut=None) plt.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 plt.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.) plt.title('Gradient plot: an electrical dipole') plt.show() Keywords: python, matplotlib, pylab, example, codex (see :ref:`how-to-search-examples`)