I am drawing a map using basemap from matplotlib. The data are spreaded all over the world, but I just want to retain all the data on the continent and drop those on the ocean. Is there a way that I can filter the data, or is there a way to draw the ocean again to cover the data?
There's method in matplotlib.basemap: is_land(xpt, ypt)
It returns True if the given x,y point (in projection coordinates) is over land, False otherwise. The definition of land is based upon the GSHHS coastline polygons associated with the class instance. Points over lakes inside land regions are not counted as land points.
For more information, see here.
is_land() will loop all the polygons to check whether it's land or not. For large data size, it's very slow. You can use points_inside_poly() from matplotlib to check an array of points quickly. Here is the code. It doesn't check lakepolygons, if you want remove points in lakes, you can add your self.
It took 2.7 seconds to check 100000 points on my PC. If you want more speed, you can convert the polygons into a bitmap, but it's a little difficult to do this. Please tell me if the following code is not fast enought for your dataset.
from mpl_toolkits.basemap import Basemap
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.nxutils as nx
def points_in_polys(points, polys):
result = []
for poly in polys:
mask = nx.points_inside_poly(points, poly)
result.extend(points[mask])
points = points[~mask]
return np.array(result)
points = np.random.randint(0, 90, size=(100000, 2))
m = Basemap(projection='moll',lon_0=0,resolution='c')
m.drawcoastlines()
m.fillcontinents(color='coral',lake_color='aqua')
x, y = m(points[:,0], points[:,1])
loc = np.c_[x, y]
polys = [p.boundary for p in m.landpolygons]
land_loc = points_in_polys(loc, polys)
m.plot(land_loc[:, 0], land_loc[:, 1],'ro')
plt.show()
The HYRY's answer won't work on new versions of matplotlib (nxutils is deprecated). I've made a new version that works:
from mpl_toolkits.basemap import Basemap
import matplotlib.pyplot as plt
from matplotlib.path import Path
import numpy as np
map = Basemap(projection='cyl', resolution='c')
lons = [0., 0., 16., 76.]
lats = [0., 41., 19., 51.]
x, y = map(lons, lats)
locations = np.c_[x, y]
polygons = [Path(p.boundary) for p in map.landpolygons]
result = np.zeros(len(locations), dtype=bool)
for polygon in polygons:
result += np.array(polygon.contains_points(locations))
print result
The simplest way is to use basemap's maskoceans.
If for each lat, lon you have a data and you want to
use contours:
After meshgrid and interpolation:
from scipy.interpolate import griddata as gd
from mpl_toolkits.basemap import Basemap, cm, maskoceans
xi, yi = np.meshgrid(xi, yi)
zi = gd((mlon, mlat),
scores,
(xi, yi),
method=grid_interpolation_method)
#mask points on ocean
data = maskoceans(xi, yi, zi)
con = m.contourf(xi, yi, data, cmap=cm.GMT_red2green)
#note instead of zi we have data now.
Update (much faster than in_land or in_polygon solutions):
If for each lat, lon you don't have any data, and you just want to scatter the points only over land:
x, y = m(lons, lats)
samples = len(lons)
ocean = maskoceans(lons, lats, datain=np.arange(samples),
resolution='i')
ocean_samples = np.ma.count_masked(ocean)
print('{0} of {1} points in ocean'.format(ocean_samples, samples))
m.scatter(x[~ocean.mask], y[~ocean.mask], marker='.', color=colors[~ocean.mask], s=1)
m.drawcountries()
m.drawcoastlines(linewidth=0.7)
plt.savefig('a.png')
I was answering this question, when I was told that it would be better to post my answer over here. Basically, my solution extracts the polygons that are used to draw the coastlines of the Basemap instance and combines these polygons with the outline of the map to produce a matplotlib.PathPatch that overlays the ocean areas of the map.
This especially useful if the data is coarse and interpolation of the data is not wanted. In this case using maskoceans produces a very grainy outline of the coastlines, which does not look very good.
Here is the same example I posted as answer for the other question:
from matplotlib import pyplot as plt
from mpl_toolkits import basemap as bm
from matplotlib import colors
import numpy as np
import numpy.ma as ma
from matplotlib.patches import Path, PathPatch
fig, ax = plt.subplots()
lon_0 = 319
lat_0 = 72
##some fake data
lons = np.linspace(lon_0-60,lon_0+60,10)
lats = np.linspace(lat_0-15,lat_0+15,5)
lon, lat = np.meshgrid(lons,lats)
TOPO = np.sin(np.pi*lon/180)*np.exp(lat/90)
m = bm.Basemap(resolution='i',projection='laea', width=1500000, height=2900000, lat_ts=60, lat_0=lat_0, lon_0=lon_0, ax = ax)
m.drawcoastlines(linewidth=0.5)
x,y = m(lon,lat)
pcol = ax.pcolormesh(x,y,TOPO)
##getting the limits of the map:
x0,x1 = ax.get_xlim()
y0,y1 = ax.get_ylim()
map_edges = np.array([[x0,y0],[x1,y0],[x1,y1],[x0,y1]])
##getting all polygons used to draw the coastlines of the map
polys = [p.boundary for p in m.landpolygons]
##combining with map edges
polys = [map_edges]+polys[:]
##creating a PathPatch
codes = [
[Path.MOVETO] + [Path.LINETO for p in p[1:]]
for p in polys
]
polys_lin = [v for p in polys for v in p]
codes_lin = [c for cs in codes for c in cs]
path = Path(polys_lin, codes_lin)
patch = PathPatch(path,facecolor='white', lw=0)
##masking the data:
ax.add_patch(patch)
plt.show()
This produces the following plot:
Hope this is helpful to someone :)
Related
I've started working with Basemap, which seems potentially very useful.
If I plot some global data on a latitude/longitude grid as filled contours, it works great: Iff I leave the lat_0 and lon_0 as zero. Once I change the center location, the map moves but the data doesn't. I would be grateful for advice.
I've created a simple version of the code I'm using, with some simple sample data that illustrates the problem. The values should be (are) large at the equator but small at the poles. If you run the code with lat_0 and lon_0 = 0, it works fine. But if you change the center location to a different coordinate, the same pattern/data is presented even though the map has moved.
from mpl_toolkits.basemap import Basemap, cm
import matplotlib.pyplot as plt
import numpy as np
# create data
lat = np.linspace(-90,90,num=180)
lon = np.linspace(-180,180,num=361)
h2o_north = np.linspace(1,65,num=90)
h2o_south = np.flipud(h2o_north)
h2o = np.append(h2o_north,h2o_south)
data = np.transpose(np.tile(h2o,(len(lon),1)))
# create figure and axes instances
fig = plt.figure(figsize=(10,10))
ax = fig.add_axes([0.1,0.1,0.8,0.8])
# create map
m = Basemap(projection='ortho',lon_0=-50,lat_0=50,resolution='l')
# draw coastlines and country boundaries
m.drawcoastlines()
m.drawcountries()
# draw parallels
parallels = np.arange(-90.,90,10.)
m.drawparallels(parallels)
# draw meridians
meridians = np.arange(180.,360.,10.)
m.drawmeridians(meridians)
ny = data.shape[0]
nx = data.shape[1]
lons, lats = m.makegrid(nx, ny) # get lat/lons of ny by nx evenly space grid
x, y = m(lons, lats) # compute map projection coordinates
# draw filled contours.
clevs = np.linspace(0,70,num=281)
cs = m.contourf(x,y,data,clevs,cmap=plt.cm.jet)
# colorbar
cbar = m.colorbar(cs,location='bottom',pad="5%",ticks=np.linspace(0,70,15))
cbar.set_label('Scale of the data')
plt.title('Some global data', fontsize=14)
Use np.meshgrid() to create the meshgrid of lon-lat, then, convert it to projection coordinates, and the data are ready to generate contours and plot.
Here is the working code:
from mpl_toolkits.basemap import Basemap
import matplotlib.pyplot as plt
import numpy as np
# data for z (2D array)
h2o_north = np.linspace(1, 65, num=90)
h2o_south = np.flipud(h2o_north)
h2o = np.append(h2o_north, h2o_south)
data = np.transpose(np.tile(h2o, (len(h2o_north), 1)))
# create figure and axes instances
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot()
# create basemap instance
m = Basemap(projection='ortho', lon_0=-50, lat_0=50, resolution='c', ax=ax)
# create meshgrid covering the whole globe with ...
# conforming dimensions of the `data`
lat = np.linspace(-90, 90, data.shape[0])
lon = np.linspace(-180, 180, data.shape[1])
xs, ys = np.meshgrid(lon, lat) # basic mesh in lon, lat (degrees)
x, y = m(xs, ys) # convert (lon,lat) to map (x,y)
# draw filled contours
clevs = np.linspace(0, np.max(data), 60)
cs = m.contourf(x, y, data, clevs, cmap=plt.cm.jet)
m.drawcoastlines()
m.drawcountries()
m.drawmeridians(range(-180, 180, 30))
m.drawparallels(range(-90, 90, 30))
# draw colorbar
cbar = m.colorbar(cs, location='bottom', pad="5%", ticks=np.linspace(0, np.max(data), 5))
cbar.set_label('Scale of the data')
plt.show()
The resulting plot:
I would like to plot the surface of my data which is given by 3D vectors in cartesian coordinates x,y,z. The data can not be represented by a smooth function.
So first we generate some dummy data with the function eq_points(N_count, r) which returns an array points with the x,y,z coordinates of each point on the surface of our object. The quantity omega is the solid angle, and not of interest right now.
#credit to Markus Deserno from MPI
#https://www.cmu.edu/biolphys/deserno/pdf/sphere_equi.pdf
def eq_points(N_count, r):
points = []
a = 4*np.pi*r**2/N_count
d = np.sqrt(a)
M_theta = int(np.pi/d)
d_theta = np.pi/M_theta
d_phi = a/d_theta
for m in range(M_theta):
theta = np.pi*(m+0.5)/M_theta
M_phi = int(2*np.pi*np.sin(theta)/d_phi)
for n in range(M_phi):
phi = 2*np.pi*n/M_phi
points.append(np.array([r*np.sin(theta)*np.cos(phi),
r*np.sin(theta)*np.sin(phi),
r*np.cos(theta)]))
omega = 4*np.pi/N_count
return np.array(points), omega
#starting plotting sequence
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
points, omega = eq_points(400, 1.)
ax.scatter(points[:,0], points[:,1], points[:,2])
ax.scatter(0., 0., 0., c="r")
ax.set_xlabel(r'$x$ axis')
ax.set_ylabel(r'$y$ axis')
ax.set_zlabel(r'$Z$ axis')
plt.savefig("./sphere.png", format="png", dpi=300)
plt.clf()
The result is a sphere shown in the following figure. The blue points mark the data from the points array, while the red point is the origin.
I would like to get something like this
taken from here. However the data in the mplot3d tutorial is always a result of a smooth function. Except to the ax.scatter() function which I used for my sphere plot.
So in the end my goal would be to plot some data showing only its surface. This data is produced by changing the radial distance to the origin of each blue point. Further more it would be necessary to make sure each point is in contact with the surface. How are the surfaces which are plotted here e.g. in plot_surface() constructed in detail? Some actual live data looks like this:
I would suggest finding the hull, and then plotting the simplices (i.e. the triangles forming the hull). Make sure to update the x,y,z-limits appropriately.
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
from scipy.spatial import ConvexHull
N = 1000
pts = np.random.randn(N, 3)
# exclude outliers
# obviously, this is data dependent
cutoff = 3.
is_outlier = np.any(np.abs(pts) > cutoff, axis=1)
pts = pts[~is_outlier]
# plot points
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(pts[:,0], pts[:,1], pts[:,2])
ax.set_xlim(-(cutoff +1), cutoff+1)
ax.set_ylim(-(cutoff +1), cutoff+1)
ax.set_zlim(-(cutoff +1), cutoff+1)
# get and plot hull
hull = ConvexHull(pts)
fig = plt.figure()
ax = Axes3D(fig)
vertices = [pts[s] for s in hull.simplices]
triangles = Poly3DCollection(vertices, edgecolor='k')
ax.add_collection3d(triangles)
ax.set_xlim(-(cutoff +1), cutoff+1)
ax.set_ylim(-(cutoff +1), cutoff+1)
ax.set_zlim(-(cutoff +1), cutoff+1)
plt.show()
Solution to the question with the new specification that all points are touching the surface. Assuming that the angles are set by the user as shown in the example, it is easy to precompute the indices of the points forming the simplices making up the surface by computing the simplices of the hull formed by points on the unit sphere with the same angles as in the data set of interest. We can then use these indices to get the surface of interest.
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
from scipy.spatial import ConvexHull
def eq_points(N_count, r):
points = []
a = 4*np.pi*r**2/N_count
d = np.sqrt(a)
M_theta = int(np.pi/d)
d_theta = np.pi/M_theta
d_phi = a/d_theta
for m in range(M_theta):
theta = np.pi*(m+0.5)/M_theta
M_phi = int(2*np.pi*np.sin(theta)/d_phi)
for n in range(M_phi):
phi = 2*np.pi*n/M_phi
points.append(np.array([r*np.sin(theta)*np.cos(phi),
r*np.sin(theta)*np.sin(phi),
r*np.cos(theta)]))
omega = 4*np.pi/N_count
return np.array(points), omega
def eq_points_with_random_radius(N_count, r):
points = []
a = 4*np.pi*r**2/N_count
d = np.sqrt(a)
M_theta = int(np.pi/d)
d_theta = np.pi/M_theta
d_phi = a/d_theta
for m in range(M_theta):
theta = np.pi*(m+0.5)/M_theta
M_phi = int(2*np.pi*np.sin(theta)/d_phi)
for n in range(M_phi):
phi = 2*np.pi*n/M_phi
rr = r * np.random.rand()
points.append(np.array([rr*np.sin(theta)*np.cos(phi),
rr*np.sin(theta)*np.sin(phi),
rr*np.cos(theta)]))
omega = 4*np.pi/N_count
return np.array(points), omega
N = 400
pts, _ = eq_points(N, 1.)
pts_rescaled, _ = eq_points_with_random_radius(N, 1.)
extremum = 2.
# plot points
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(pts_rescaled[:,0], pts_rescaled[:,1], pts_rescaled[:,2])
ax.set_xlim(-extremum, extremum)
ax.set_ylim(-extremum, extremum)
ax.set_zlim(-extremum, extremum)
# get indices of simplices making up the surface using points on unit sphere;
# index into rescaled points
hull = ConvexHull(pts)
vertices = [pts_rescaled[s] for s in hull.simplices]
fig = plt.figure()
ax = Axes3D(fig)
triangles = Poly3DCollection(vertices, edgecolor='k')
ax.add_collection3d(triangles)
ax.set_xlim(-extremum, extremum)
ax.set_ylim(-extremum, extremum)
ax.set_zlim(-extremum, extremum)
plt.show()
I'm trying to plot streamlines on a global map with the Robinson projection, but basemap doesn't seem to like the projected co-ordinates. Of course, it works fine for a plain old cylindrical projection, which is regular in the x direction.
Here is an example:
import matplotlib.pyplot as plt
from mpl_toolkits.basemap import Basemap
import numpy as np
u = np.ones((21,21))
v = np.ones((21,21))
lats = np.arange(-90,91,9)
lons = np.arange(-180,181,18)
x,y = np.meshgrid(lons,lats)
# It works for Cylindrical
mp = Basemap(projection='cyl')
xx,yy = mp(x,y)
mp.streamplot(xx,yy,u,v)
mp.drawcoastlines()
plt.show()
# But not Robinson
mp = Basemap(projection='robin',lon_0=0)
xx, yy = mp(x, y)
mp.streamplot(xx,yy,u,v)
mp.drawcoastlines()
plt.show()
It complains about the x co-ordinates, raising:
ValueError: The rows of 'x' must be equal
So is it possible to plot streamlines on Robinson projections?
With the command xx,yy = mp(x,y) a coordinate transformation according to the particular projection is applied to your lon and lats. For most projections this will result in a distorsion of the gird point such that rows of x are no longer equal, hence the error: ValueError: The rows of 'x' must be equal. To fix this you need to re-grid your data, e.g. like this:
import matplotlib.pyplot as plt
from mpl_toolkits.basemap import Basemap
import numpy as np
import matplotlib as plt
u = np.ones((21,21))
v = np.ones((21,21))
lats = np.arange(-90,91,9)
lons = np.arange(-180,181,18)
x,y = np.meshgrid(lons,lats)
mp = Basemap(projection='robin',lon_0=0)
xx, yy = mp(x, y)
# generate a grid that is equally spaced in a plot with the current pojection
lons, lats, xxnew, yynew = mp.makegrid(21,21, returnxy=True)
# project the data onto the new grid
unew = plt.mlab.griddata(xx.flatten(), yy.flatten(),u.flatten(), xxnew, yynew ,interp='linear')
vnew = plt.mlab.griddata(xx.flatten(), yy.flatten(),v.flatten(), xxnew, yynew ,interp='linear')
mp.streamplot(xxnew,yynew,unew,vnew)
mp.drawcoastlines()
plt.show()
I am making a ConvexHull in python, by a set of latitude and longitudinal positions. Then I want to plot the points, alongside the ConvexHull in a basemap. Everything works fine if I plot them in a normal plot without a map,as I follow the instructions from http://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.ConvexHull.html#scipy.spatial.ConvexHull. When I try to plot them with a basemap, I just get the regular plot. What do I do wrong?
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.basemap import Basemap
map = Basemap(projection='merc',
resolution = 'c', area_thresh = 40,
llcrnrlon=27.72, llcrnrlat=69.41,
urcrnrlon=28.416, urcrnrlat=70.95)
con = lite.connect(databasepath)
with con:
cur = con.execute("SELECT DISTINCT latitude, longitude FROM MessageType1 where latitude>= 70.55 and latitude<= 70.7 and longitude >= 27.72 and longitude <= 28.416 limit 100 ")
points = [[float(x[1]), float(x[0])] for x in cur]
points = np.array(points)
hull = ConvexHull(points)
x,y = map(points[:,0], points[:,1])
plt.plot(x, y, 'o')
for simplex in hull.simplices:
x,y = map(points[simplex,0], points[simplex,1])
plt.plot(x,y, 'k-')
plt.show()
You need to add some methods after setting up the Basemap to draw the map features. Eg:
map.drawcoastlines()
map.drawstates()
map.drawcountries()
map.drawmapboundary()
See the documentation: http://matplotlib.org/basemap/users/geography.html
I have a collection of 3D points. These points are sampled at constant levels (z=0,1,...,7). An image should make it clear:
These points are in a numpy ndarray of shape (N, 3) called X. The above plot is created using:
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
X = load('points.npy')
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_wireframe(X[:,0], X[:,1], X[:,2])
ax.scatter(X[:,0], X[:,1], X[:,2])
plt.draw()
I'd like to instead triangulate only the surface of this object, and plot the surface. I do not want the convex hull of this object, however, because this loses subtle shape information I'd like to be able to inspect.
I have tried ax.plot_trisurf(X[:,0], X[:,1], X[:,2]), but this results in the following mess:
Any help?
Example data
Here's a snippet to generate 3D data that is representative of the problem:
import numpy as np
X = []
for i in range(8):
t = np.linspace(0,2*np.pi,np.random.randint(30,50))
for j in range(t.shape[0]):
# random circular objects...
X.append([
(-0.05*(i-3.5)**2+1)*np.cos(t[j])+0.1*np.random.rand()-0.05,
(-0.05*(i-3.5)**2+1)*np.sin(t[j])+0.1*np.random.rand()-0.05,
i
])
X = np.array(X)
Example data from original image
Here's a pastebin to the original data:
http://pastebin.com/YBZhJcsV
Here are the slices along constant z:
update 3
Here's a concrete example of what I describe in update 2. If you don't have mayavi for visualization, I suggest installing it via edm using edm install mayavi pyqt matplotlib.
Toy 2D contours stacked in 3D
Contours -> 3D surface
Code to generate the figures
from matplotlib import path as mpath
from mayavi import mlab
import numpy as np
def make_star(amplitude=1.0, rotation=0.0):
""" Make a star shape
"""
t = np.linspace(0, 2*np.pi, 6) + rotation
star = np.zeros((12, 2))
star[::2] = np.c_[np.cos(t), np.sin(t)]
star[1::2] = 0.5*np.c_[np.cos(t + np.pi / 5), np.sin(t + np.pi / 5)]
return amplitude * star
def make_stars(n_stars=51, z_diff=0.05):
""" Make `2*n_stars-1` stars stacked in 3D
"""
amps = np.linspace(0.25, 1, n_stars)
amps = np.r_[amps, amps[:-1][::-1]]
rots = np.linspace(0, 2*np.pi, len(amps))
zamps = np.linspace
stars = []
for i, (amp, rot) in enumerate(zip(amps, rots)):
star = make_star(amplitude=amp, rotation=rot)
height = i*z_diff
z = np.full(len(star), height)
star3d = np.c_[star, z]
stars.append(star3d)
return stars
def polygon_to_boolean(points, xvals, yvals):
""" Convert `points` to a boolean indicator mask
over the specified domain
"""
x, y = np.meshgrid(xvals, yvals)
xy = np.c_[x.flatten(), y.flatten()]
mask = mpath.Path(points).contains_points(xy).reshape(x.shape)
return x, y, mask
def plot_contours(stars):
""" Plot a list of stars in 3D
"""
n = len(stars)
for i, star in enumerate(stars):
x, y, z = star.T
mlab.plot3d(*star.T)
#ax.plot3D(x, y, z, '-o', c=(0, 1-i/n, i/n))
#ax.set_xlim(-1, 1)
#ax.set_ylim(-1, 1)
mlab.show()
if __name__ == '__main__':
# Make and plot the 2D contours
stars3d = make_stars()
plot_contours(stars3d)
xvals = np.linspace(-1, 1, 101)
yvals = np.linspace(-1, 1, 101)
volume = np.dstack([
polygon_to_boolean(star[:,:2], xvals, yvals)[-1]
for star in stars3d
]).astype(float)
mlab.contour3d(volume, contours=[0.5])
mlab.show()
update 2
I now do this as follows:
I use the fact that the paths in each z-slice are closed and simple and use matplotlib.path to determine points inside and outside of the contour. Using this idea, I convert the contours in each slice to a boolean-valued image, which is combined into a boolean-valued volume.
Next, I use skimage's marching_cubes method to obtain a triangulation of the surface for visualization.
Here's an example of the method. I think the data is slightly different, but you can definitely see that the results are much cleaner, and can handle surfaces that are disconnected or have holes.
Original answer
Ok, here's the solution I came up with. It depends heavily on my data being roughly spherical and sampled at uniformly in z I think. Some of the other comments provide more information about more robust solutions. Since my data is roughly spherical I triangulate the azimuth and zenith angles from the spherical coordinate transform of my data points.
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.tri as mtri
X = np.load('./mydatars.npy')
# My data points are strictly positive. This doesn't work if I don't center about the origin.
X -= X.mean(axis=0)
rad = np.linalg.norm(X, axis=1)
zen = np.arccos(X[:,-1] / rad)
azi = np.arctan2(X[:,1], X[:,0])
tris = mtri.Triangulation(zen, azi)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_trisurf(X[:,0], X[:,1], X[:,2], triangles=tris.triangles, cmap=plt.cm.bone)
plt.show()
Using the sample data from the pastebin above, this yields:
I realise that you mentioned in your question that you didn't want to use the convex hull because you might lose some shape information. I have a simple solution that works pretty well for your 'jittered spherical' example data, although it does use scipy.spatial.ConvexHull. I thought I would share it here anyway, just in case it's useful for others:
from matplotlib.tri import triangulation
from scipy.spatial import ConvexHull
# compute the convex hull of the points
cvx = ConvexHull(X)
x, y, z = X.T
# cvx.simplices contains an (nfacets, 3) array specifying the indices of
# the vertices for each simplical facet
tri = Triangulation(x, y, triangles=cvx.simplices)
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.hold(True)
ax.plot_trisurf(tri, z)
ax.plot_wireframe(x, y, z, color='r')
ax.scatter(x, y, z, color='r')
plt.draw()
It does pretty well in this case, since your example data ends up lying on a more-or-less convex surface. Perhaps you could make some more challenging example data? A toroidal surface would be a good test case which the convex hull method would obviously fail.
Mapping an arbitrary 3D surface from a point cloud is a really tough problem. Here's a related question containing some links that might be helpful.