stripy predefined meshesOne common use of stripy is in meshing x,y coordinates and, to this end, we provide pre-defined meshes for square and elliptical triangulations. A random mesh is included as a counterpoint to the regular meshes. Each of these meshes is also a Triangulation object.
The Cartesian mesh classes in stripy are:
stripy.cartesian_meshes.square_mesh(extent, spacingX, spacingY)
stripy.cartesian_meshes.elliptical_mesh(extent, spacingX, spacingY)
stripy.cartesian_meshes.random_mesh(extent, number_of_points=5000)
Any of the above meshes can be uniformly refined by specifying the refinement_levels parameter. The square and elliptical meshes come with a random_scale parameter that specifies the amount of random noise to be added to the mesh (random_scale=0 by default).
The next example is Ex3-Interpolation
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import stripy
## A bunch of meshes with roughly similar overall numbers of points / triangles
xmin = 0.0
xmax = 10.0
ymin = 0.0
ymax = 10.0
extent = [xmin, xmax, ymin, ymax]
spacingX = 1.0
spacingY = 1.0
nsamples = 5000
str_fmt = "{:25} {:3}\t{:6}"
square0 = stripy.cartesian_meshes.square_mesh(extent, spacingX, spacingY, refinement_levels=0)
square2 = stripy.cartesian_meshes.square_mesh(extent, spacingX, spacingY, refinement_levels=2)
squareR = stripy.cartesian_meshes.square_mesh(extent, spacingX, spacingY, refinement_levels=4)
print(str_fmt.format('Square mesh', square0.npoints, squareR.npoints))
ellip0 = stripy.cartesian_meshes.elliptical_mesh(extent, spacingX, spacingY, refinement_levels=0)
ellip2 = stripy.cartesian_meshes.elliptical_mesh(extent, spacingX, spacingY, refinement_levels=2)
ellipR = stripy.cartesian_meshes.elliptical_mesh(extent, spacingX, spacingY, refinement_levels=4)
print(str_fmt.format('Elliptical mesh', ellip0.npoints, ellipR.npoints))
randR = stripy.cartesian_meshes.random_mesh(extent, nsamples)
rand0 = stripy.Triangulation(randR.x[::50], randR.y[::50])
rand2 = stripy.Triangulation(randR.x[::25], randR.y[::25])
print(str_fmt.format('Random mesh', rand0.npoints, randR.npoints))
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print("Square: {}".format(square0.__doc__))
print("Elliptical: {}".format(ellip0.__doc__))
print("Random: {}".format(randR.__doc__))
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%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
def area_histo(mesh):
freq, area_bin = np.histogram(mesh.areas(), bins=20, normed=True)
area = 0.5 * (area_bin[1:] + area_bin[:-1])
norm_area = area / mesh.areas().mean()
return norm_area, 0.25 * freq*area / np.pi**2
def add_plot(axis, mesh, xlim, ylim):
u, v = area_histo(mesh)
width = (u.max() - u.min()) / 30.
axis.bar(u, v, width=width)
axis.set_ylim(ylim)
axis.plot([1.0,1.0], [0.0,1.5], linewidth=1.0, linestyle="-.", color="Black")
return
fig, ax = plt.subplots(1,3, figsize=(14,4))
xlim=(0.75,1.5)
ylim=(0.0,0.05)
# square
add_plot(ax[0], squareR, xlim, ylim)
# elliptical
add_plot(ax[1], ellipR, xlim, ylim)
# random (this one is very different from the others ... )
add_plot(ax[2], randR, xlim, ylim)
fig.savefig("AreaDistributionsByMesh.png", dpi=250, transparent=True)
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def mesh_fig(mesh, meshR, name):
fig = plt.figure(figsize=(10, 10), facecolor="none")
ax = plt.subplot(111)
ax.axis('off')
generator = mesh
refined = meshR
x0 = generator.x
y0 = generator.y
xR = refined.x
yR = refined.y
ax.scatter(x0, y0, color="Red", marker="o", s=150.0)
ax.scatter(xR, yR, color="DarkBlue", marker="o", s=50.0)
ax.triplot(xR, yR, refined.simplices, color="black", linewidth=0.5)
fig.savefig(name, dpi=250, transparent=True)
return
mesh_fig(square0, square2, "Square" )
mesh_fig(ellip0, ellip2, "Elliptical" )
mesh_fig(rand0, rand2, "Random" )
The next example is Ex3-Interpolation