def test_find_natural_neighbors(): r"""Test find natural neighbors function.""" x = list(range(0, 20, 4)) y = list(range(0, 20, 4)) gx, gy = np.meshgrid(x, y) pts = np.vstack([gx.ravel(), gy.ravel()]).T tri = Delaunay(pts) test_points = np.array([[2, 2], [5, 10], [12, 13.4], [12, 8], [20, 20]]) neighbors, tri_info = find_natural_neighbors(tri, test_points) # Need to check point indices rather than simplex indices neighbors_truth = [[(1, 5, 0), (5, 1, 6)], [(11, 17, 16), (17, 11, 12)], [(23, 19, 24), (19, 23, 18), (23, 17, 18), (17, 23, 22)], [(7, 13, 12), (13, 7, 8), (9, 13, 8), (13, 9, 14), (13, 19, 18), (19, 13, 14), (17, 13, 18), (13, 17, 12)], np.zeros((0, 3), dtype=np.int32)] centers_truth = [[(2.0, 2.0), (2.0, 2.0)], [(6.0, 10.0), (6.0, 10.0)], [(14.0, 14.0), (14.0, 14.0), (10.0, 14.0), (10.0, 14.0)], [(10.0, 6.0), (10.0, 6.0), (14.0, 6.0), (14.0, 6.0), (14.0, 10.0), (14.0, 10.0), (10.0, 10.0), (10.0, 10.0)], np.zeros((0, 2), dtype=np.int32)] for i, true_neighbor in enumerate(neighbors_truth): assert set(true_neighbor) == {tuple(v) for v in tri.simplices[neighbors[i]]} assert set(centers_truth[i]) == {tuple(c) for c in tri_info[neighbors[i]]}
def test_find_natural_neighbors(): r"""Test find natural neighbors function.""" x = list(range(0, 20, 4)) y = list(range(0, 20, 4)) gx, gy = np.meshgrid(x, y) pts = np.vstack([gx.ravel(), gy.ravel()]).T tri = Delaunay(pts) test_points = np.array([[2, 2], [5, 10], [12, 13.4], [12, 8], [20, 20]]) neighbors, tri_info = find_natural_neighbors(tri, test_points) neighbors_truth = [[0, 1], [24, 25], [16, 17, 30, 31], [18, 19, 20, 21, 22, 23, 26, 27], []] for i, true_neighbor in enumerate(neighbors_truth): assert_array_almost_equal(true_neighbor, neighbors[i]) cc_truth = np.array([(2.0, 2.0), (2.0, 2.0), (14.0, 2.0), (14.0, 2.0), (6.0, 2.0), (6.0, 2.0), (10.0, 2.0), (10.0, 2.0), (2.0, 14.0), (2.0, 14.0), (6.0, 6.0), (6.0, 6.0), (2.0, 6.0), (2.0, 6.0), (2.0, 10.0), (2.0, 10.0), (14.0, 14.0), (14.0, 14.0), (10.0, 6.0), (10.0, 6.0), (14.0, 6.0), (14.0, 6.0), (14.0, 10.0), (14.0, 10.0), (6.0, 10.0), (6.0, 10.0), (10.0, 10.0), (10.0, 10.0), (6.0, 14.0), (6.0, 14.0), (10.0, 14.0), (10.0, 14.0)]) r_truth = np.empty((32, )) r_truth.fill(2.8284271247461916) for key in tri_info: assert_almost_equal(cc_truth[key], tri_info[key]['cc']) assert_almost_equal(r_truth[key], tri_info[key]['r'])
def test_nn_point(test_data): r"""Test find natural neighbors for a point interpolation function.""" xp, yp, z = test_data tri = Delaunay(list(zip(xp, yp))) sim_gridx = [30] sim_gridy = [30] members, tri_info = find_natural_neighbors(tri, list(zip(sim_gridx, sim_gridy))) val = natural_neighbor_point(xp, yp, z, [sim_gridx[0], sim_gridy[0]], tri, members[0], tri_info) truth = 1.009 assert_almost_equal(truth, val, 3)
def test_nn_point(test_data): r"""Test find natural neighbors for a point interpolation function.""" xp, yp, z = test_data tri = Delaunay(list(zip(xp, yp))) sim_gridx = [30] sim_gridy = [30] members, tri_info = find_natural_neighbors(tri, list(zip(sim_gridx, sim_gridy))) val = natural_neighbor_point(xp, yp, z, [sim_gridx[0], sim_gridy[0]], tri, members[0], tri_info) truth = 1.009 assert_almost_equal(truth, val, 3)
def test_find_natural_neighbors(): r"""Test find natural neighbors function.""" x = list(range(0, 20, 4)) y = list(range(0, 20, 4)) gx, gy = np.meshgrid(x, y) pts = np.vstack([gx.ravel(), gy.ravel()]).T tri = Delaunay(pts) test_points = np.array([[2, 2], [5, 10], [12, 13.4], [12, 8], [20, 20]]) neighbors, tri_info = find_natural_neighbors(tri, test_points) neighbors_truth = [[0, 1], [24, 25], [16, 17, 30, 31], [18, 19, 20, 21, 22, 23, 26, 27], []] for i, true_neighbor in enumerate(neighbors_truth): assert_array_almost_equal(true_neighbor, neighbors[i]) cc_truth = np.array([(2.0, 2.0), (2.0, 2.0), (14.0, 2.0), (14.0, 2.0), (6.0, 2.0), (6.0, 2.0), (10.0, 2.0), (10.0, 2.0), (2.0, 14.0), (2.0, 14.0), (6.0, 6.0), (6.0, 6.0), (2.0, 6.0), (2.0, 6.0), (2.0, 10.0), (2.0, 10.0), (14.0, 14.0), (14.0, 14.0), (10.0, 6.0), (10.0, 6.0), (14.0, 6.0), (14.0, 6.0), (14.0, 10.0), (14.0, 10.0), (6.0, 10.0), (6.0, 10.0), (10.0, 10.0), (10.0, 10.0), (6.0, 14.0), (6.0, 14.0), (10.0, 14.0), (10.0, 14.0)]) r_truth = np.empty((32,)) r_truth.fill(2.8284271247461916) for key in tri_info: assert_almost_equal(cc_truth[key], tri_info[key]['cc']) assert_almost_equal(r_truth[key], tri_info[key]['r'])
test_points = np.array([[2, 2], [5, 10], [12, 13.4], [12, 8], [20, 20]]) for i, (x, y) in enumerate(test_points): ax.plot(x, y, 'k.', markersize=6) ax.annotate('test ' + str(i), xy=(x, y)) ########################################### # Since finding natural neighbors already calculates circumcenters, return # that information for later use. # # The key of the neighbors dictionary refers to the test point index, and the list of integers # are the triangles that are natural neighbors of that particular test point. # # Since point 4 is far away from the triangulation, it has no natural neighbors. # Point 3 is at the confluence of several triangles so it has many natural neighbors. neighbors, circumcenters = find_natural_neighbors(tri, test_points) print(neighbors) ########################################### # We can plot all of the triangles as well as the circles representing the circumcircles # fig, ax = plt.subplots(figsize=(15, 10)) for i, inds in enumerate(tri.simplices): pts = tri.points[inds] x, y = np.vstack((pts, pts[0])).T ax.plot(x, y) ax.annotate(i, xy=(np.mean(x), np.mean(y))) # Using circumcenters and calculated circumradii, plot the circumcircles for idx, cc in enumerate(circumcenters): ax.plot(cc[0], cc[1], 'k.', markersize=5)
fig, ax = plt.subplots(1, 1, figsize=(15, 10)) delaunay_plot_2d(tri, ax=ax) for i, zval in enumerate(zp): ax.annotate('{} F'.format(zval), xy=(pts[i, 0] + 2, pts[i, 1])) sim_gridx = [30., 60.] sim_gridy = [30., 60.] ax.plot(sim_gridx, sim_gridy, '+', markersize=10) ax.set_aspect('equal', 'datalim') ax.set_title('Triangulation of observations and test grid cell ' 'natural neighbor interpolation values') members, tri_info = geometry.find_natural_neighbors( tri, list(zip(sim_gridx, sim_gridy))) val = natural_neighbor_point(xp, yp, zp, (sim_gridx[0], sim_gridy[0]), tri, members[0], tri_info) ax.annotate('grid 0: {:.3f}'.format(val), xy=(sim_gridx[0] + 2, sim_gridy[0])) val = natural_neighbor_point(xp, yp, zp, (sim_gridx[1], sim_gridy[1]), tri, members[1], tri_info) ax.annotate('grid 1: {:.3f}'.format(val), xy=(sim_gridx[1] + 2, sim_gridy[1])) ########################################### # Using the circumcenter and circumcircle radius information from # :func:`metpy.interpolate.geometry.find_natural_neighbors`, we can visually # examine the results to see if they are correct. def draw_circle(ax, x, y, r, m, label):
fig, ax = plt.subplots(1, 1, figsize=(15, 10)) ax.ishold = lambda: True # Work-around for Matplotlib 3.0.0 incompatibility delaunay_plot_2d(tri, ax=ax) for i, zval in enumerate(zp): ax.annotate(f'{zval} F', xy=(pts[i, 0] + 2, pts[i, 1])) sim_gridx = [30., 60.] sim_gridy = [30., 60.] ax.plot(sim_gridx, sim_gridy, '+', markersize=10) ax.set_aspect('equal', 'datalim') ax.set_title('Triangulation of observations and test grid cell ' 'natural neighbor interpolation values') members, circumcenters = geometry.find_natural_neighbors( tri, list(zip(sim_gridx, sim_gridy))) val = natural_neighbor_point(xp, yp, zp, (sim_gridx[0], sim_gridy[0]), tri, members[0], circumcenters) ax.annotate(f'grid 0: {val:.3f}', xy=(sim_gridx[0] + 2, sim_gridy[0])) val = natural_neighbor_point(xp, yp, zp, (sim_gridx[1], sim_gridy[1]), tri, members[1], circumcenters) ax.annotate(f'grid 1: {val:.3f}', xy=(sim_gridx[1] + 2, sim_gridy[1])) ########################################### # Using the circumcenter and circumcircle radius information from # :func:`metpy.interpolate.geometry.find_natural_neighbors`, we can visually # examine the results to see if they are correct. def draw_circle(ax, x, y, r, m, label):
test_points = np.array([[2, 2], [5, 10], [12, 13.4], [12, 8], [20, 20]]) for i, (x, y) in enumerate(test_points): ax.plot(x, y, 'k.', markersize=6) ax.annotate('test ' + str(i), xy=(x, y)) ########################################### # Since finding natural neighbors already calculates circumcenters and circumradii, return # that information for later use. # # The key of the neighbors dictionary refers to the test point index, and the list of integers # are the triangles that are natural neighbors of that particular test point. # # Since point 4 is far away from the triangulation, it has no natural neighbors. # Point 3 is at the confluence of several triangles so it has many natural neighbors. neighbors, tri_info = find_natural_neighbors(tri, test_points) print(neighbors) ########################################### # We can then use the information in tri_info later. # # The dictionary key is the index of a particular triangle in the Delaunay triangulation data # structure. 'cc' is that triangle's circumcenter, and 'r' is the radius of the circumcircle # containing that triangle. fig, ax = plt.subplots(figsize=(15, 10)) for i, inds in enumerate(tri.simplices): pts = tri.points[inds] x, y = np.vstack((pts, pts[0])).T ax.plot(x, y) ax.annotate(i, xy=(np.mean(x), np.mean(y)))
fig, ax = plt.subplots(1, 1, figsize=(15, 10)) ax.ishold = lambda: True # Work-around for Matplotlib 3.0.0 incompatibility delaunay_plot_2d(tri, ax=ax) for i, zval in enumerate(zp): ax.annotate('{} F'.format(zval), xy=(pts[i, 0] + 2, pts[i, 1])) sim_gridx = [30., 60.] sim_gridy = [30., 60.] ax.plot(sim_gridx, sim_gridy, '+', markersize=10) ax.set_aspect('equal', 'datalim') ax.set_title('Triangulation of observations and test grid cell ' 'natural neighbor interpolation values') members, tri_info = geometry.find_natural_neighbors(tri, list(zip(sim_gridx, sim_gridy))) val = natural_neighbor_point(xp, yp, zp, (sim_gridx[0], sim_gridy[0]), tri, members[0], tri_info) ax.annotate('grid 0: {:.3f}'.format(val), xy=(sim_gridx[0] + 2, sim_gridy[0])) val = natural_neighbor_point(xp, yp, zp, (sim_gridx[1], sim_gridy[1]), tri, members[1], tri_info) ax.annotate('grid 1: {:.3f}'.format(val), xy=(sim_gridx[1] + 2, sim_gridy[1])) ########################################### # Using the circumcenter and circumcircle radius information from # :func:`metpy.interpolate.geometry.find_natural_neighbors`, we can visually # examine the results to see if they are correct. def draw_circle(ax, x, y, r, m, label):
test_points = np.array([[2, 2], [5, 10], [12, 13.4], [12, 8], [20, 20]]) for i, (x, y) in enumerate(test_points): ax.plot(x, y, 'k.', markersize=6) ax.annotate('test ' + str(i), xy=(x, y)) ########################################### # Since finding natural neighbors already calculates circumcenters and circumradii, return # that information for later use. # # The key of the neighbors dictionary refers to the test point index, and the list of integers # are the triangles that are natural neighbors of that particular test point. # # Since point 4 is far away from the triangulation, it has no natural neighbors. # Point 3 is at the confluence of several triangles so it has many natural neighbors. neighbors, tri_info = find_natural_neighbors(tri, test_points) print(neighbors) ########################################### # We can then use the information in tri_info later. # # The dictionary key is the index of a particular triangle in the Delaunay triangulation data # structure. 'cc' is that triangle's circumcenter, and 'r' is the radius of the circumcircle # containing that triangle. fig, ax = plt.subplots(figsize=(15, 10)) for i, inds in enumerate(tri.simplices): pts = tri.points[inds] x, y = np.vstack((pts, pts[0])).T ax.plot(x, y) ax.annotate(i, xy=(np.mean(x), np.mean(y)))