3D plots

In order to create a graph of a surface in 3-space (or a contour plot of a surface), it is necessary to evaluate the function on a regular rectangular grid. This can be done using the meshgrid command. First, create 1D vectors describing the grids in the x- and y-directions:

>> x = (0:2*pi/20:2*pi)';
>> y = (0:4*pi/40:4*pi)';

Next, ``spread'' these grids into two dimensions using meshgrid:

>> [X,Y] = meshgrid(x,y);
>> whos
  Name      Size         Bytes  Class

  X        41x21          6888  double array
  Y        41x21          6888  double array
  x        21x1            168  double array
  y        41x1            328  double array

Grand total is 1784 elements using 14272 bytes

The effect of meshgrid is to create a vector X with the x-grid along each row, and a vector Y with the y-grid along each column. Then, using vectorized functions and/or operators, it is easy to evaluate a function z = f(x,y) of two variables on the rectangular grid:

>> z = cos(X).*cos(2*Y);

Having created the matrix containing the samples of the function, the surface can be graphed using either the mesh or the surf commands (see Figures 8 and 9, respectively):

>> mesh(x,y,z)
>> surf(x,y,z)

  
Figure 8: Using the mesh command

  
Figure 9: Using the surf command

(The difference is that surf shades the surface, while mesh does not.) In addition, a contour plot can be created (see Figure 10):

>> contour(x,y,z)

  
Figure 10: Using the contour command

Use the help command to learn the additional options. These commands can be very time-consuming if the grid is fine.