Tutorial on `jInv.Vis`

This tutorial explores the plotting functionalities of jInv. We provide minimal examples for each viewer and explain the inputs and outputs. This document can also be used as a starting point to implement new viewers.

The general philosophy of our viewers is that we use a Cartesian coordinate system that is described by a mesh from jInv.Mesh. We aim at providing a consistent visualization across different mesh types. There are different types of objects that we commonly want to visualize:

Image data (2D / 3D) - is assumed to be discretized in the cell-centers of the mesh
Meshes (2D / 3D) - we have viewers for all mesh types in jInv.

Requirements: : Our visualization package is based on PyPlot.jl which must be installed.



In [1]:

    
using PyPlot
using jInv.Mesh
using jInvVis

2D Viewers

`viewImage2D` - Image Data

Example: Here we plot the functions $f(x,y) = x$ and $f(x,y) = y$ on a regular mesh. Our function, viewImage2D is based on PyPlot.pcolormesh and all keyword arguments are forward to that method.



In [2]:

    
domain = [-1 1.5 0 3]
n      = [12,23]

M    = getRegularMesh(domain,n)
xc   = getCellCenteredGrid(M)


subplot(2,2,1)
viewImage2D(xc[:,1],M,vmin=-1,vmax=3)
xlabel("x")
ylabel("y")
title("viewImage2D - f(x,y) = x")
subplot(2,2,2)
viewImage2D(xc[:,2],M,vmin=-1,vmax=3)
colorbar()
title("viewImage2D - f(x,y) = y")
xlabel("x")
ylabel("y")









    












    Out[2]:





PyObject <matplotlib.text.Text object at 0x32713f090>

Meshes

Using plotGrid we can visualize regular and deformed meshes. plotGrid is based on PyPlot.plot and PyPlot.plot3D and as two optional arguments.

spacing - defines the number of grid lines to skip in the visualization, default=[1,1,1]
color - color for grid lines, default="b"



In [9]:

    
domain = [0 1 0 1]
n      = [13 15]
M      = getRegularMesh(domain,n)

xc     = getNodalGrid(M)
yc     = [xc[:,1].^3-xc[:,2] xc[:,2]+xc[:,1]-1]

subplot(1,2,1)
plotGrid(M)
title("plotGrid - regular mesh")
xlabel("x"); ylabel("y")
subplot(1,2,2)
plotGrid(yc,M,color="r",linewidth=3)
title("plotGrid - deformed mesh")
xlabel("x");

3D Viewers

`viewOrthoSlice2D` - orthogonal projections of 3D image data

Example : Here we visualize the function $f(x,y,z)=x y z$ on a RegularMesh and TensorMesh3D.



In [4]:

    
domain = [0 1 0 1 0 1]
n  = [4 6 8]

f(XYZ) = XYZ[:,1].*XYZ[:,2].*XYZ[:,3]

# construct a regular mesh on domain and discretize function
Mreg = getRegularMesh(domain,n)
xr   = getCellCenteredGrid(Mreg)
fr   = f(xr)

# get a tensor mesh with random cell sizes on the same domain
x0 = Mreg.x0;
h1 = rand(n[1]); h1 = (domain[2]-domain[1])*h1./sum(h1)
h2 = rand(n[2]); h2 = (domain[4]-domain[3])*h2./sum(h2)
h3 = rand(n[3]); h3 = (domain[6]-domain[5])*h3./sum(h3)
Mten = getTensorMesh3D(h1,h2,h3,x0)
xt   = getCellCenteredGrid(Mten)
ft   = f(xt)

subplot(1,2,1)
viewOrthoSlices2D(fr,Mreg,axis=true,cmap="gray",vmin=0,vmax=.5*maximum(fr))
title("viewOrthoSlice2D - regular mesh")
subplot(1,2,2)
viewOrthoSlices2D(ft,Mten,axis=true)
title("viewOrthoSlice2D - tensor mesh")









    












    Out[4]:





PyObject <matplotlib.text.Text object at 0x32795d090>

`viewSlice2D` - visualize image slice

This viewer generates a 2D plot of a slice of a 3D image. The 3D data can be visualized along all three directions using the keyword argument view=:xz. Other keyword arguments are forwarded to PyPlot.pcolormesh



In [5]:

    
subplot(1,3,1)
viewSlice2D(fr,Mreg,round(Int,Mreg.n[3]/2),cmap="gray",addLabel=true,vmin=0,vmax=.5*maximum(fr))
title("viewSlice2D - view=:xy")

subplot(1,3,2)
viewSlice2D(fr,Mreg,round(Int,Mreg.n[2]/2),view=:xz,addLabel=true,cmap="gray",vmin=0,vmax=.5*maximum(fr))
title("viewSlice2D - view=:xz")

subplot(1,3,3)
viewSlice2D(fr,Mreg,round(Int,Mreg.n[1]/2),view=:yz,addLabel=true,cmap="gray",vmin=0,vmax=.5*maximum(fr))
title("viewSlice2D - view=:yz")









    












    Out[5]:





PyObject <matplotlib.text.Text object at 0x327d13550>

`plotGrid` for 3D Meshes

Thanks to multiple dispatch, the syntax of plotGrid is the same for 2D and 3D meshes. As before, we can control the spacing and the appearance through the keyword arguments of PyPlot.plot3D



In [6]:

    
plotGrid(Mreg,spacing=[2,2,2])
title("plotGrid - regular mesh")









    












    Out[6]:





PyObject <matplotlib.text.Text object at 0x327e04810>



In [7]:

    
xc = getNodalGrid(Mreg)
yn = [xc[:,1].^3-xc[:,2] xc[:,2]+xc[:,1]-1 xc[:,3]]

plotGrid(yn,Mreg)
title("plotGrid - deformed regular mesh")









    












    Out[7]:





PyObject <matplotlib.text.Text object at 0x32838ca90>



In [8]:

    
plotGrid(Mten,color="r")
title("plotGrid - tensor mesh")









    












    Out[8]:





PyObject <matplotlib.text.Text object at 0x327a818d0>



In [ ]:

Tutorial on jInv.Vis

2D Viewers

viewImage2D - Image Data