|
| 1 | +""" |
| 2 | +=================== |
| 3 | +Intersecting planes |
| 4 | +=================== |
| 5 | +
|
| 6 | +This examples demonstrates drawing intersecting planes in 3D. It is a generalization |
| 7 | +of :doc:`/gallery/mplot3d/imshow3d`. |
| 8 | +
|
| 9 | +Drawing intersecting planes in `.mplot3d` is complicated, because `.mplot3d` is not a |
| 10 | +real 3D renderer, but only projects the Artists into 3D and draws them in the right |
| 11 | +order. This does not work correctly if Artists overlap each other mutually. In this |
| 12 | +example, we lift the problem of mutual overlap by segmenting the planes at their |
| 13 | +intersections, making four parts out of each plane. |
| 14 | +
|
| 15 | +This examples only works correctly for planes that cut each other in haves. This |
| 16 | +limitation is intentional to keep the code more readable. Cutting at arbitrary |
| 17 | +positions would of course be possible but makes the code even more complex. |
| 18 | +Thus, this example is more a demonstration of the concept how to work around |
| 19 | +limitations of the 3D visualization, it's not a refined solution for drawing |
| 20 | +arbitrary intersecting planes, which you can copy-and-paste as is. |
| 21 | +""" |
| 22 | +import matplotlib.pyplot as plt |
| 23 | +import numpy as np |
| 24 | + |
| 25 | + |
| 26 | +def plot_quadrants(ax, array, fixed_coord, cmap): |
| 27 | + """For a given 3d *array* plot a plane with *fixed_coord*, using four quadrants.""" |
| 28 | + nx, ny, nz = array.shape |
| 29 | + index = { |
| 30 | + 'x': (nx // 2, slice(None), slice(None)), |
| 31 | + 'y': (slice(None), ny // 2, slice(None)), |
| 32 | + 'z': (slice(None), slice(None), nz // 2), |
| 33 | + }[fixed_coord] |
| 34 | + plane_data = array[index] |
| 35 | + |
| 36 | + n0, n1 = plane_data.shape |
| 37 | + quadrants = [ |
| 38 | + plane_data[:n0 // 2, :n1 // 2], |
| 39 | + plane_data[:n0 // 2, n1 // 2:], |
| 40 | + plane_data[n0 // 2:, :n1 // 2], |
| 41 | + plane_data[n0 // 2:, n1 // 2:] |
| 42 | + ] |
| 43 | + |
| 44 | + min_val = array.min() |
| 45 | + max_val = array.max() |
| 46 | + |
| 47 | + cmap = plt.get_cmap(cmap) |
| 48 | + |
| 49 | + for i, quadrant in enumerate(quadrants): |
| 50 | + facecolors = cmap((quadrant - min_val) / (max_val - min_val)) |
| 51 | + if fixed_coord == 'x': |
| 52 | + Y, Z = np.mgrid[0:ny // 2, 0:nz // 2] |
| 53 | + X = nx // 2 * np.ones_like(Y) |
| 54 | + Y_offset = (i // 2) * ny // 2 |
| 55 | + Z_offset = (i % 2) * nz // 2 |
| 56 | + ax.plot_surface(X, Y + Y_offset, Z + Z_offset, rstride=1, cstride=1, |
| 57 | + facecolors=facecolors, shade=False) |
| 58 | + elif fixed_coord == 'y': |
| 59 | + X, Z = np.mgrid[0:nx // 2, 0:nz // 2] |
| 60 | + Y = ny // 2 * np.ones_like(X) |
| 61 | + X_offset = (i // 2) * nx // 2 |
| 62 | + Z_offset = (i % 2) * nz // 2 |
| 63 | + ax.plot_surface(X + X_offset, Y, Z + Z_offset, rstride=1, cstride=1, |
| 64 | + facecolors=facecolors, shade=False) |
| 65 | + elif fixed_coord == 'z': |
| 66 | + X, Y = np.mgrid[0:nx // 2, 0:ny // 2] |
| 67 | + Z = nz // 2 * np.ones_like(X) |
| 68 | + X_offset = (i // 2) * nx // 2 |
| 69 | + Y_offset = (i % 2) * ny // 2 |
| 70 | + ax.plot_surface(X + X_offset, Y + Y_offset, Z, rstride=1, cstride=1, |
| 71 | + facecolors=facecolors, shade=False) |
| 72 | + |
| 73 | + |
| 74 | +def figure_3D_array_slices(array, cmap=None): |
| 75 | + """Plot a 3d array using three intersecting centered planes.""" |
| 76 | + fig = plt.figure() |
| 77 | + ax = fig.add_subplot(projection='3d') |
| 78 | + ax.set_box_aspect(array.shape) |
| 79 | + plot_quadrants(ax, array, 'x', cmap=cmap) |
| 80 | + plot_quadrants(ax, array, 'y', cmap=cmap) |
| 81 | + plot_quadrants(ax, array, 'z', cmap=cmap) |
| 82 | + return fig, ax |
| 83 | + |
| 84 | + |
| 85 | +nx, ny, nz = 70, 100, 50 |
| 86 | +r_square = (np.mgrid[-1:1:1j * nx, -1:1:1j * ny, -1:1:1j * nz] ** 2).sum(0) |
| 87 | + |
| 88 | +figure_3D_array_slices(r_square, cmap='viridis_r') |
| 89 | +plt.show() |
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