PlottingΒΆ

We will plot a surface two ways. First we will use easyviz. Consider the following code:

import numpy
from scitools import easyviz
x = numpy.arange(-8,8,.2)
xx,yy = numpy.meshgrid(x,x)
r = numpy.sqrt(xx**2+yy**2) + 0.01
zz = numpy.sin(r)/r
easyviz.surfc(x,x,zz)

The function surfc takes a list of x coordinates, and y coordinates and a numpy array z. Its plots a surface that has height z[i,j] at the point (x[i],y[i]). Note the use of meshgrid, and vectorized numpy functions that let us evaluate \(\frac{\sin(\sqrt{x^2+y^2})+1}{\sqrt{x^2+y^2}+1}\) over the grid very easily. We discussed meshgrid at the beginning when we were talking about numpy. Note that you can drag the plot around with your mouse and look at it from different angles.

We can make this plot look a bit nicer by adding some shading and nicer coloring and some labels as follows.

import numpy
RealNumber=float
Integer =int
from scitools import easyviz
x = numpy.arange(-8,8,.2)
xx,yy = numpy.meshgrid(x,x)
r = numpy.sqrt(xx**2+yy**2) + 0.01
zz = numpy.sin(r)/r
l = easyviz.Light(lightpos=(-10,-10,5), lightcolor=(1,1,1))
easyviz.surfc(x,x,zz,shading='interp',colormap=easyviz.jet(),
          zmin=-0.5,zmax=1,clevels=10,
          title='r=sqrt(x**2+y**2)+eps\nsin(r)/r',
          light=l,
          legend='sin',
          )

Let us now try to plot some vector fields. Consider the following code

import numpy
from scitools import easyviz
RealNumber=float
Integer=int
j=numpy.complex(0,1)
w=numpy.zeros((5,5,5))
u=w+1.0
xx,yy,zz=numpy.mgrid[-1.0:1.0:5*j,-1:1:5*j,-1:1:5*j]
easyviz.quiver3(xx,yy,zz,w,w,u)

This should plot a vector field that points up everywhere. The arguments to quiver3 are 6, \(n\times n\times n\) arrays. The first three arrays are the location of the vectors, that is there will be a vector at \((xx[i,j,k],yy[i,j,k],zz[i,j,k])\) for \(0\le i,j,k < n\). The second three arrays are the directions, i.e., the vector at \((xx[i,j,k],yy[i,j,k],zz[i,j,k])\) points in the direction \((w[i,j,k],w[i,j,k],u[i,j,k])\).

Now let us give some examples with MayaVi. First lets see how to plot a function like we did with easyviz.

import numpy
from mayavi.tools import imv
x=numpy.arange(-8,8,.2)
def f(x,y):
    r=numpy.sqrt(x**2+y**2)+.01
    return numpy.sin(r)/r
imv.surf(x,x,f)

This will open mayavi, and display the plot of the function. The first two arguments to surf are arrays \(x\) and \(y\), s.t. the function will be evaluated at \((x[i],y[j])\). The last argument is the function to graph. It probably looks a bit different than the easyviz example. Lets try to make it look similar to the easyviz example. First note that on the left there is a list of filters and modules. Double-click the warpscalars button in the filters menu, and change the scale factor from \(1\) to say \(5\). This should redraw the graph similar to how easyviz drew it. There are quite a few other options you can play around with. For example, next click on the module surfacemap, and you will see you can make the graph transparent by changing the opacity. You can also change it to a wireframe or make it plot contours.

TODO: More examples

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