Map an array of indexes to an array of coordinates - python

I'm playing a bit with scikit-image marching cubes algorithm. Here is a simplified version of the example given in the docs.
from matplotlib import pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
from skimage import measure
x = np.linspace(-1, 1, 11)
X, Y, Z = np.meshgrid(x, x, x, indexing = 'ij')
def f(x, y, z):
return x
verts, faces = measure.marching_cubes(f(X, Y, Z), 0.6)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
mesh = Poly3DCollection(verts[faces])
ax.add_collection3d(mesh)
ax.set_xlim(0, 10)
ax.set_ylim(0, 10)
ax.set_zlim(0, 10)
plt.show()
Here is the resulting surface:
It appears that coordinates of vertices are given in terms of array index rather than coordinates of the meshgrid. How can I transform the coordinates of vertices so that they map to the meshgrid, like in the image below?
I can do that by hand:
mesh = Poly3DCollection((verts[faces] / 5) - 1)
but there must be some numpy magic here.
Thanks.

IMHO, no magic here. There is no 'plug and play' transformations in mplot3d.
for automation, you can just make your 'by hand' job with a function :
from matplotlib import pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
from skimage import measure
x=y=z= np.linspace(-1, 1, 11)
grid=np.meshgrid(x,y,z)
def f(x, y, z):
return x*x+y*y+z*z # more fun ;)
def scale_marching(x,verts):
return x[0]+ (x[-1]-x[0])/len(x)*verts
verts, faces = measure.marching_cubes(f(*grid), 1.5)
verts=scale_marching(x,verts)
ax = plt.figure().add_subplot(111, projection='3d')
ax.add_collection3d(Poly3DCollection(verts[faces]))
ax.auto_scale_xyz(*grid)

Related

Changing the position of x-y plane [duplicate]

I am using mplot3d from the mpl_toolkits library. When displaying the 3D surface on the figure I'm realized the axis were not positioned as I wished they would.
Let me show, I have added to the following screenshot the position of each axis:
Is there a way to change the position of the axes in order to get this result:
Here's the working code:
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
ax = Axes3D(plt.figure())
def f(x,y) :
return -x**2 - y**2
X = np.arange(-1, 1, 0.02)
Y = np.arange(-1, 1, 0.02)
X, Y = np.meshgrid(X, Y)
Z = f(X, Y)
ax.plot_surface(X, Y, Z, alpha=0.5)
# Hide axes ticks
ax.set_xticks([-1,1])
ax.set_yticks([-1,1])
ax.set_zticks([-2,0])
ax.set_yticklabels([-1,1],rotation=-15, va='center', ha='right')
plt.show()
I have tried using xaxis.set_ticks_position('left') statement, but it doesn't work.
No documented methods, but with some hacking ideas from https://stackoverflow.com/a/15048653/1149007 you can.
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = ax = fig.add_subplot(111, projection='3d')
ax.view_init(30, 30)
def f(x,y) :
return -x**2 - y**2
X = np.arange(-1, 1, 0.02)
Y = np.arange(-1, 1, 0.02)
X, Y = np.meshgrid(X, Y)
Z = f(X, Y)
ax.plot_surface(X, Y, Z, alpha=0.5)
# Hide axes ticks
ax.set_xticks([-1,1])
ax.set_yticks([-1,1])
ax.set_zticks([-2,0])
ax.xaxis._axinfo['juggled'] = (0,0,0)
ax.yaxis._axinfo['juggled'] = (1,1,1)
ax.zaxis._axinfo['juggled'] = (2,2,2)
plt.show()
I can no idea of the meaning of the third number in triples. If set zeros nothing changes in the figure. So should look in the code for further tuning.
You can also look at related question Changing position of vertical (z) axis of 3D plot (Matplotlib)? with low level hacking of _PLANES property.
Something changed, code blow doesn't work, all axis hide...
ax.xaxis._axinfo['juggled'] = (0,0,0)
ax.yaxis._axinfo['juggled'] = (1,1,1)
ax.zaxis._axinfo['juggled'] = (2,2,2)
I suggest using the plot function to create a graph

Interpolation for 3D surface

I have my data in an ndarray of size 21 by 30; it contains velocity values at each point. I have made a 3D surface plot to visualize it but the data is not so smooth. In order to interpolate the data, so that I have smooth peaks, I tried the function griddata but it does not seem to work.
Here is my code:
import numpy as np
import matplotlib.pyplot as plt
vel = np.genfromtxt(r'velocity.txt')
x = np.arange(0, 21, 1)
y = np.arange(0, 30, 1)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
X,Y = np.meshgrid(x, y)
surf = ax.plot_surface(x, y, vel, cmap="RdBu")
fig.set_size_inches(10, 10)
plt.show()
From what I can understand from the question, what you need to do is grid interpolation. It is possible to do that using RegularGridInterpolator from scipy here. Just make a finer mesh, interpolate on that grid, and plot.
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import RegularGridInterpolator
vel=np.random.random((21,30))
#grid old
x=np.arange(0,21,1)
y=np.arange(0,30,1)
grid_old=(x,y)
#grid new
# the limits of the interpolated x and y val have to be less than the original grid
x_new=np.arange(0.1,19.9,0.1)
y_new=np.arange(0.1,28.9,0.1)
grid_new = np.meshgrid(x_new, y_new)
grid_flattened = np.transpose(np.array([k.flatten() for k in grid_new]))
#Interpolation onto a finer grid
grid_interpol = RegularGridInterpolator(grid_old,vel,method='linear')
vel_interpol = grid_interpol(grid_flattened)
#Unflatten the interpolated velocities and store into a new variable.
index=0
vel_new=np.zeros((len(x_new),len(y_new)))
for i in range(len(x_new)):
for j in range(len(y_new)):
vel_new[i,j] =vel_interpol[index]
index+=1
fig=plt.figure()
ax=fig.add_subplot(111,projection='3d')
surf=ax.plot_surface(grid_new[0],grid_new[1],vel_new.T, cmap="RdBu")
fig.set_size_inches(10,10)
plt.show()

how to plot in python f(x,y)=sqrt(2x-y)

I'm trying to plot the following multivariable f(x,y)=sqrt(2x-y)
but can't make it work with numpy and matplotlib.
I've been trying by defining function but still cant makee it work
from numpy import exp,arange
from pylab import meshgrid,cm,imshow,contour,clabel,colorbar,axis,title,show
from math import sqrt
# the function that I'm going to plot
def z_func(x,y):
return (sqrt(2*x - y))
X,Y = meshgrid(x, y) # grid of point
Z = z_func(X, Y) # evaluation of the function on the grid
im = imshow(Z,cmap=cm.RdBu) # drawing the function
# adding the Contour lines with labels
cset = contour(Z,arange(-1,1.5,0.2),linewidths=2,cmap=cm.Set2)
clabel(cset,inline=True,fmt='%1.1f',fontsize=10)
colorbar(im) # adding the colobar on the right
# latex fashion title
title('my plot')
show()
You need to have more data in order to plot the entire function.
Look at the following code as a reference
import numpy as np
import math
import matplotlib.pyplot as plt
def z_func(x,y):
return (math.sqrt(2*x - y))
x = [10,20,30,40,50]
y =[2,4,6,8,11]
Z = []
for i in range(len(x)):
Z.append(z_func(x[i],y[i]))
plt.plot(Z)
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
import numpy as np
# the function that I'm going to plot.
# Vectorize so we don't need to loop through
# grid points.
#np.vectorize
def z_func(x, y):
return (np.sqrt(2*x - y))
# define the range where you evaluate
# the function
extent = (0, 10, 0, 10)
x = np.arange(0, 10.1, .1)
y = np.arange(0, 10.1, .1)
# create grid
X, Y = np.meshgrid(x, y)
# evaluate over grid
Z = z_func(X, Y)
# plot contour image
fig = plt.figure()
im = plt.imshow(Z, origin='image', cmap=cm.RdBu, extent=extent)
cset = plt.contour(Z, np.arange(-1,1.5,0.2),linewidths=2,cmap=cm.Set2, extent=extent)
plt.clabel(cset,inline=True, fmt='%1.1f',fontsize=10)
plt.colorbar(im)
plt.show()

Plot stack of unit vectors in cylindrical coordinates - matplotlib

I have a python program that calculates angles for me and outputs them in a list.
What I would like to do is plot a stack of arrows that are unit vectors pointing in the direction of the angle. So I thought cylindrical coordinates would be best since they only have one angular coordinate.
I've tried pyplot.quiver but I don't think that can do anything in 3D, and a 3D line plot didn't work either.
Is there a way of doing this without laboriously converting each (length, height, angle) into a pair of vectors (a, b, c),(length*cos(angle), length*sin(angle), height)?
If you have a list of angles, you can easily calculate vectors associated with those angles using numpy.
import numpy as np
import matplotlib.pyplot as plt
angles = np.random.rand(100)
length = 1.
vectors_2d = np.vstack((length * np.cos(angles), length * np.sin(angles))).T
for x, y in vectors_2d:
plt.plot([0, x], [0, y])
plt.show()
If you really want it in cylindrical instead of polar coords, then
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
angles = np.random.rand(100)
length = 1.
heights = np.arange(len(angles))
vectors_3d = np.vstack((length * np.cos(angles),
length * np.sin(angles),
heights)).T
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
for x, y, z in vectors_3d:
ax.plot([0, x], [0, y], zs=[z, z])
plt.show()
Edit: I know how to put arrows on plots using pyplot.quiver. However, I don't think mplot3d plays nicely with quiver. Maybe someone like #tcaswell can help out with a work around. But in 2D, you can do
import numpy as np
import matplotlib.pyplot as plt
angles = np.random.rand(100)
# Define coords for arrow tails (the origin)
x0, y0 = np.zeros(100), np.zeros(100)
# Define coords for arrow tips (cos/sin)
x, y = np.cos(angles), np.sin(angles)
# in case you want colored arrows
colors = 'bgrcmyk'
colors *= colors * (len(x0) / len(colors) + 1)
plt.quiver(x0, y0, x, y, color=colors[:len(x0)], scale=1) #scale sets the length
plt.show()

Fixing jagged edges of 3D plot, selecting an appropriate mask

So I have some 3D data that I am able to plot just fine except the edges look jagged.
The relevant code:
import numpy as np
from matplotlib import cm
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
x = np.arange(-1, 1, 0.01)
y = np.arange(-1, 1, 0.01)
x, y = np.meshgrid(x, y)
rho = np.sqrt(x**2 + y**2)
# Attempts at masking shown here
# My Mask
row=0
while row<np.shape(x)[0]:
col=0
while col<np.shape(x)[1]:
if rho[row][col] > 1:
rho[row][col] = None
col=col+1
row=row+1
# Calculate & Plot
z = rho**2
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(x, y, z, rstride=8, cstride=8, cmap=cm.bone, alpha=0.15, linewidth=0.25)
plt.show()
Produces:
This is so close to what I want except the edges are jagged.
If I disable my mask in the code above & replace it with rho = np.ma.masked_where(rho > 1, rho) it gives:
It isn't jagged but not want I want in the corners.
Any suggestions on different masking or plotting methods to get rid of this jaggedness?
Did you consider using polar coordinates (like in this example) ?
Something like:
import numpy as np
from matplotlib import cm
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# create supporting points in polar coordinates
r = np.linspace(0,1.25,50)
p = np.linspace(0,2*np.pi,50)
R,P = np.meshgrid(r,p)
# transform them to cartesian system
x, y = R * np.cos(P), R * np.sin(P)
rho = np.sqrt(x**2 + y**2)
# Calculate & Plot
z = rho**2
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(x, y, z, rstride=1, cstride=1, cmap=cm.bone, alpha=0.15, linewidth=0.25)
plt.show()

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