sim icon

Scalar Field Visualisation

The simulation below represents a generic scalar field in two dimensions. A number of preset fields are available in the simulation or a custom equation can be used. Use the simulation to investigate how a scalar field can be pictorially represented. There are several different representations in the simulation.

Now make use of the simulation below which shows an arbitrary field and its gradient (only the field is shown in the surface plot). Move the mouse in the field of view to see field and gradient values. Try the following

Field Value:
Position:
Show gradient:
Field Gradient:
Equation:

Code Samples

Matlab 
% Calculate a grid of points from -2-2 with 100 points in each direction
[x,y] = meshgrid(linspace(-2,2,100),linspace(-2,2,100));

% Calculate the scalar field
f = x.*x + y.*y;    % Bowl (.* means multiply element by element)

% False colour plot
figure(1)
pcolor(x,y,f);
colormap('Hot');    % Set colourmap
axis image;         % Makes the x and y axes have equal step size
shading interp;     % Interpolates

% Contour plot
figure(2)
limits = linspace(0, max(max(f)), 10);
contour(x,y,f,limits);
axis image

% Surface plot
figure(3)
surf(x,y,f);
Gnuplot 
# The function to plot
# Gnuplot can also plot a (scalar) datafile using `splot 'datafile' u 1:2:3`
f(x, y) = x*x + y*y

set multiplot layout 1,3 title "2-D Scalar Field Plotting" font ",14"
set zrange [0:9]; set xrange [-3:3]; set yrange [-3:3];
set samples 40; set isosamples 21

# Colour plot
set title "False Colour"
set pm3d map
splot f(x, y) notitle
unset pm3d; unset view

# Contour plot
set title "Contour"
set contour; set view map; unset surface
set cntrparam levels incr 0,1,9
splot f(x, y) notitle
unset contour; unset view; set surface

# Surface plot
set title "Surface"
splot f(x, y) notitle

unset multiplot
Python 
import numpy as np
from mpl_toolkits.mplot3d import Axes3D     # For surface plot
import matplotlib.pyplot as plt

# Calculate a grid of points from -2-2 with 100 points in each direction
x,y = np.meshgrid(np.linspace(-2,2,100),np.linspace(-2,2,100));

# Calculate the scalar field
f = x**2 + y**2;

# False colour plot
plt.figure();
plt.pcolor(x,y,f);
plt.colorbar();

# Contour plot
plt.figure();
limits = np.linspace(0, np.amax(f), 10);
plt.contour(x,y,f,limits);

# Surface plot
fig = plt.figure();
ax = fig.gca(projection='3d')
ax.plot_surface(x,y,f);

plt.show();