MATLAB Language Drawing Pseudo 4D plot
Example
A (m x n) matrix can be representes by a surface by using surf;
The color of the surface is automatically set as function of the values in the (m x n) matrix.
If the colormap is not specified, the default one is applied.
A colorbar can be added to display the current colormap and indicate the mapping of data values into the colormap.
In the following example, the z (m x n) matrix is generated by the function:
z=x.*y.*sin(x).*cos(y);
over the interval [-pi,pi]. The x and y values can be generated using the meshgrid
function and the surface is rendered as follows:
% Create a Figure
figure
% Generate the `x` and `y` values in the interval `[-pi,pi]`
[x,y] = meshgrid([-pi:.2:pi],[-pi:.2:pi]);
% Evaluate the function over the selected interval
z=x.*y.*sin(x).*cos(y);
% Use surf to plot the surface
S=surf(x,y,z);
xlabel('X Axis');
ylabel('Y Axis');
zlabel('Z Axis');
grid minor
colormap('hot')
colorbar
Figure 1
Now it could be the case that additional information are linked to the values
of the z matrix and they are store in another (m x n) matrix
It is possible to add these additional information on the plot by modifying the way the surface is colored.
This will allows having kinda of 4D plot: to the 3D representation of the surface
generated by the first (m x n) matrix, the fourth dimension will be represented by the
data contained in the second (m x n) matrix.
It is possible to create such a plot by calling surf with 4 input:
surf(x,y,z,C)
where the C parameter is the second matrix (which has to be of the same size of z) and
is used to define the color of the surface.
In the following example, the C matrix is generated by the function:
C=10*sin(0.5*(x.^2.+y.^2))*33;
over the interval [-pi,pi]
The surface generated by C is
Figure 2
Now we can call surf with four input:
figure
surf(x,y,z,C)
% shading interp
xlabel('X Axis');
ylabel('Y Axis');
zlabel('Z Axis');
grid minor
colormap('hot')
colorbar
Figure 3
Comparing Figure 1 and Figure 3, we can notice that:
- the shape of the surface corresponds to the
zvalues (the first(m x n)matrix) - the colour of the surface (and its range, given by the colorbar) corresponds to the
Cvalues (the first(m x n)matrix)
Figure 4
Of course, it is possible to swap z and C in the plot to have the shape of the surface given by the C matrix and the color given by the z matrix:
figure
surf(x,y,C,z)
% shading interp
xlabel('X Axis');
ylabel('Y Axis');
zlabel('Z Axis');
grid minor
colormap('hot')
colorbar
and to compare Figure 2 with Figure 4
