(Source code, png, pdf)
"""
Demonstrates high-resolution tricontouring of a random set of points ;
a matplotlib.tri.TriAnalyzer is used to improve the plot quality.
The initial data points and triangular grid for this demo are:
- a set of random points is instantiated, inside [-1, 1] x [-1, 1] square
- A Delaunay triangulation of these points is then computed, of which a
random subset of triangles is masked out by the user (based on
*init_mask_frac* parameter). This simulates invalidated data.
The proposed generic procedure to obtain a high resolution contouring of such
a data set is the following:
1) Compute an extended mask with a matplotlib.tri.TriAnalyzer, which will
exclude badly shaped (flat) triangles from the border of the
triangulation. Apply the mask to the triangulation (using set_mask).
2) Refine and interpolate the data using a
matplotlib.tri.UniformTriRefiner.
3) Plot the refined data with tricontour.
"""
from matplotlib.tri import Triangulation, TriAnalyzer, UniformTriRefiner
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import numpy as np
#-----------------------------------------------------------------------------
# Analytical test function
#-----------------------------------------------------------------------------
def experiment_res(x, y):
""" An analytic function representing experiment results """
x = 2.*x
r1 = np.sqrt((0.5 - x)**2 + (0.5 - y)**2)
theta1 = np.arctan2(0.5 - x, 0.5 - y)
r2 = np.sqrt((-x - 0.2)**2 + (-y - 0.2)**2)
theta2 = np.arctan2(-x - 0.2, -y - 0.2)
z = (4*(np.exp((r1/10)**2) - 1)*30. * np.cos(3*theta1) +
(np.exp((r2/10)**2) - 1)*30. * np.cos(5*theta2) +
2*(x**2 + y**2))
return (np.max(z) - z)/(np.max(z) - np.min(z))
#-----------------------------------------------------------------------------
# Generating the initial data test points and triangulation for the demo
#-----------------------------------------------------------------------------
# User parameters for data test points
n_test = 200 # Number of test data points, tested from 3 to 5000 for subdiv=3
subdiv = 3 # Number of recursive subdivisions of the initial mesh for smooth
# plots. Values >3 might result in a very high number of triangles
# for the refine mesh: new triangles numbering = (4**subdiv)*ntri
init_mask_frac = 0.0 # Float > 0. adjusting the proportion of
# (invalid) initial triangles which will be masked
# out. Enter 0 for no mask.
min_circle_ratio = .01 # Minimum circle ratio - border triangles with circle
# ratio below this will be masked if they touch a
# border. Suggested value 0.01 ; Use -1 to keep
# all triangles.
# Random points
random_gen = np.random.mtrand.RandomState(seed=127260)
x_test = random_gen.uniform(-1., 1., size=n_test)
y_test = random_gen.uniform(-1., 1., size=n_test)
z_test = experiment_res(x_test, y_test)
# meshing with Delaunay triangulation
tri = Triangulation(x_test, y_test)
ntri = tri.triangles.shape[0]
# Some invalid data are masked out
mask_init = np.zeros(ntri, dtype=np.bool)
masked_tri = random_gen.randint(0, ntri, int(ntri*init_mask_frac))
mask_init[masked_tri] = True
tri.set_mask(mask_init)
#-----------------------------------------------------------------------------
# Improving the triangulation before high-res plots: removing flat triangles
#-----------------------------------------------------------------------------
# masking badly shaped triangles at the border of the triangular mesh.
mask = TriAnalyzer(tri).get_flat_tri_mask(min_circle_ratio)
tri.set_mask(mask)
# refining the data
refiner = UniformTriRefiner(tri)
tri_refi, z_test_refi = refiner.refine_field(z_test, subdiv=subdiv)
# analytical 'results' for comparison
z_expected = experiment_res(tri_refi.x, tri_refi.y)
# for the demo: loading the 'flat' triangles for plot
flat_tri = Triangulation(x_test, y_test)
flat_tri.set_mask(~mask)
#-----------------------------------------------------------------------------
# Now the plots
#-----------------------------------------------------------------------------
# User options for plots
plot_tri = True # plot of base triangulation
plot_masked_tri = True # plot of excessively flat excluded triangles
plot_refi_tri = False # plot of refined triangulation
plot_expected = False # plot of analytical function values for comparison
# Graphical options for tricontouring
levels = np.arange(0., 1., 0.025)
cmap = cm.get_cmap(name='Blues', lut=None)
plt.figure()
plt.gca().set_aspect('equal')
plt.title("Filtering a Delaunay mesh\n" +
"(application to high-resolution tricontouring)")
# 1) plot of the refined (computed) data countours:
plt.tricontour(tri_refi, z_test_refi, levels=levels, cmap=cmap,
linewidths=[2.0, 0.5, 1.0, 0.5])
# 2) plot of the expected (analytical) data countours (dashed):
if plot_expected:
plt.tricontour(tri_refi, z_expected, levels=levels, cmap=cmap,
linestyles='--')
# 3) plot of the fine mesh on which interpolation was done:
if plot_refi_tri:
plt.triplot(tri_refi, color='0.97')
# 4) plot of the initial 'coarse' mesh:
if plot_tri:
plt.triplot(tri, color='0.7')
# 4) plot of the unvalidated triangles from naive Delaunay Triangulation:
if plot_masked_tri:
plt.triplot(flat_tri, color='red')
plt.show()
Keywords: python, matplotlib, pylab, example, codex (see Search examples)