import matplotlib.pyplot as plt from matplotlib.patches import FancyArrowPatch from mpl_toolkits.mplot3d import proj3d import pylbm import numpy as np class Arrow3D(FancyArrowPatch): def __init__(self, xs, ys, zs, *args, **kwargs): FancyArrowPatch.__init__(self, (0, 0), (0, 0), *args, **kwargs) self._verts3d = xs, ys, zs def draw(self, renderer): xs3d, ys3d, zs3d = self._verts3d xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M) self.set_positions((xs[0], ys[0]), (xs[1], ys[1])) FancyArrowPatch.draw(self, renderer) def Velocities_1D(n): dim = 1 fig = plt.figure(dim, figsize=(8, 4), facecolor="white") fig.clf() xmin, xmax, ymin, ymax = 1000, -1000, -1, 1 e = 0.2 for k in range((2 * n + 1) ** dim): v = pylbm.stencil.Velocity(dim=dim, num=k) x = v.vx xmin = min(xmin, x) xmax = max(xmax, x) couleur_texte = 0.0 couleur_trait = 0.5 plt.text( x, 0.0, str(v.num), color=[couleur_texte] * 3, horizontalalignment="center", verticalalignment="center", fontsize=15, ) plt.plot([xmin, xmax], [0, 0], ":", color=[couleur_trait] * 3) plt.text( 0.0, ymax + 2 * e, "Velocities numbering {0:1d}D".format(dim), fontsize=20, verticalalignment="center", horizontalalignment="center", color="b", ) plt.arrow( xmin - e, ymin - e, 1, 0, head_width=0.05 * dim, head_length=0.1, fc="b", ec="b" ) plt.text( xmin - e + 0.5, ymin - 1.5 * e, "x", color="b", verticalalignment="center", horizontalalignment="center", ) plt.axis("off") plt.xlim(xmin - 2 * e, xmax + 2 * e) plt.ylim(ymin - 2 * e, ymax + 2 * e) plt.draw() def Velocities_2D(n): dim = 2 fig = plt.figure(dim, figsize=(8, 8), facecolor="white") fig.clf() xmin, xmax, ymin, ymax = 1000, -1000, 1000, -1000 e = 0.5 for k in range((2 * n + 1) ** dim): v = pylbm.stencil.Velocity(dim=dim, num=k) x = v.vx y = v.vy xmin = min(xmin, x) xmax = max(xmax, x) ymin = min(ymin, y) ymax = max(ymax, y) couleur_texte = 0.0 couleur_trait = 0.5 plt.text( x, y, str(v.num), color=[couleur_texte] * 3, horizontalalignment="center", verticalalignment="center", fontsize=15, ) for x in range(xmin, xmax + 1): plt.plot([x, x], [ymin, ymax], ":", color=[couleur_trait] * 3) for y in range(ymin, ymax + 1): plt.plot([xmin, xmax], [y, y], ":", color=[couleur_trait] * 3) plt.text( 0.0, ymax + 2 * e, "Velocities numbering {0:1d}D".format(dim), fontsize=20, verticalalignment="center", horizontalalignment="center", color="b", ) plt.arrow( xmin - e, ymin - e, 1, 0, head_width=0.05 * dim, head_length=0.1, fc="b", ec="b" ) plt.arrow( xmin - e, ymin - e, 0, 1, head_width=0.05 * dim, head_length=0.1, fc="b", ec="b" ) plt.text( xmin - e + 0.5, ymin - 1.5 * e, "x", color="b", verticalalignment="center", horizontalalignment="center", ) plt.text( xmin - 1.5 * e, ymin - e + 0.5, "y", color="b", verticalalignment="center", horizontalalignment="center", ) plt.axis("off") plt.xlim(xmin - 2 * e, xmax + 2 * e) plt.ylim(ymin - 2 * e, ymax + 2 * e) plt.draw() def Velocities_3D(n): dim = 3 couleur_tour = "k" fig = plt.figure(dim, figsize=(8, 8), facecolor="white") fig.clf() ax = fig.add_subplot(111, projection="3d") xmin, xmax, ymin, ymax, zmin, zmax = 1000, -1000, 1000, -1000, 1000, -1000 e = 0.5 for k in range((2 * n + 1) ** dim): v = pylbm.stencil.Velocity(dim=dim, num=k) x = v.vx y = v.vy z = v.vz xmin = min(xmin, x) xmax = max(xmax, x) ymin = min(ymin, y) ymax = max(ymax, y) zmin = min(zmin, z) zmax = max(zmax, z) couleur_texte = [0.5 + 0.5 * x, 0.0, 0.5 - 0.5 * x] couleur_trait = 0.5 ax.text( x, y, z, str(v.num), color=couleur_texte, horizontalalignment="center", verticalalignment="center", fontsize=15, ) for x in range(xmin, xmax + 1): for y in range(ymin, ymax + 1): ax.plot([x, x], [y, y], [zmin, zmax], ":", color=[couleur_trait] * 3) for x in range(xmin, xmax + 1): for z in range(zmin, zmax + 1): ax.plot([x, x], [ymin, ymax], [z, z], ":", color=[couleur_trait] * 3) for z in range(zmin, zmax + 1): for y in range(ymin, ymax + 1): ax.plot([xmin, xmax], [y, y], [z, z], ":", color=[couleur_trait] * 3) XS, YS = np.meshgrid([-1, 1], [-1, 1]) ZS = np.zeros(XS.shape) for x in [-1, 0, 1]: ax.plot_surface( ZS + x, XS, YS, rstride=1, cstride=1, color=[0.5 + 0.5 * x, 0.0, 0.5 - 0.5 * x], shade=False, alpha=0.2, antialiased=False, linewidth=0, ) ax.text( 0.0, 0.0, zmax + 2 * e, "Velocities numbering {0:1d}D".format(dim), fontsize=20, verticalalignment="center", horizontalalignment="center", color=couleur_tour, ) vx = Arrow3D( [xmax + e, xmax + e + 1], [ymin - e, ymin - e], [zmin - e, zmin - e], mutation_scale=20, lw=1, arrowstyle="-|>", color=couleur_tour, ) ax.add_artist(vx) vy = Arrow3D( [xmax + e, xmax + e], [ymin - e, ymin - e + 1], [zmin - e, zmin - e], mutation_scale=20, lw=1, arrowstyle="-|>", color=couleur_tour, ) ax.add_artist(vy) vz = Arrow3D( [xmax + e, xmax + e], [ymin - e, ymin - e], [zmin - e, zmin - e + 1], mutation_scale=20, lw=1, arrowstyle="-|>", color=couleur_tour, ) ax.add_artist(vz) ax.text( xmax + e + 0.8, ymin - 0.8 * e, zmin - e, "x", color=couleur_tour, verticalalignment="center", horizontalalignment="center", ) ax.text( xmax + e, ymin - e + 0.8, zmin - 1.2 * e, "y", color=couleur_tour, verticalalignment="center", horizontalalignment="center", ) ax.text( xmax + e, ymin - 1.2 * e, zmin - e + 0.8, "z", color=couleur_tour, verticalalignment="center", horizontalalignment="center", ) ax.set_xlim(xmin - e, xmax + e) ax.set_ylim(ymin - e, ymax + e) ax.set_zlim(zmin - e, zmax + e) ax.azim = 34 ax.elev = 20 plt.axis("off") plt.draw() def Velocities(dim, n): if dim == 1: Velocities_1D(n) elif dim == 2: Velocities_2D(n) elif dim == 3: Velocities_3D(n) else: print("error of dimension") plt.show() Velocities(1, 3) Velocities(2, 2) Velocities(3, 1)