To get an overview of available graphics functions in Matlab, look at the help pages for the following topics:

This article illustrates the use of the easy to use graphics commands listed under the topic specgraph. At the end of the writeup two examples are given showing how one can set up the necessary data arrays to use the more primitive commands contour,  mesh,  and surf.

This brief document mainly consists of examples of Matlab code. It is suggested that you have Matlab running while reading so that you can verify the examples. Each of the examples includes an image of the expected result. Just click on the View Result   tag to the right of the Matlab code.

We begin with an example of 2-D graphics using ezplot to plot the graph y = x + 2sin(2x) on the interval 0  ≤  x  ≤  10. For simple functions that can be easily written in one line of code we pass the Matlab expression, enclosed in single quotation marks, as the first input argument to ezplot. The optional second argument specifies the plotting limits for the independent variable. These "easy-to-use" functions place the equation in the figure title and label the horizontal axes with the independent variables.

>> ezplot('x + 2*sin(2*x)', [0 10]);

For more complicated functions, first define the function through an m-file, then pass the name of the function to the plotting routine. Note that such a function must be written to operate on a vector of input values (in Matlab lingo, the function must be vectorized). For example, consider the following piecewise function defined in the file func1.m:

function y = func1(x,a)
for i = 1 : length(x)
  if ( x(i) < a )
    y(i) = a + (x(i) - a)^2;
  else
    y(i) = a - (x(i) - a)^2;
  end
end

Now plot y = f(x) for several choices of the parameter a, overlaying the plots on a single axis.

>> ezplot('func1(x,0)', [-1 5]);
>> hold on
>> ezplot('func1(x,1)', [-1 5]);
>> ezplot('func1(x,2)', [-1 5]);
>> ezplot('x', [-1 5]);
>> axis([-1 5 -4 6]);

Plot the parametric curve,  x(t) = t + 2sin(2t),   y(t) = t + 2cos(5t).

>> ezplot('t+2*sin(2*t)','t+2*cos(5*t)',[-10 10]);

In xyz-space, use ezplot3 to plot the parametric curve defined by,  {x(t) = cost,   y(t) = sint,  z(t) = sin(5t)}.

>> ezplot3('cos(t)','sin(t)','sin(5*t)',[-pi pi]);

Note :  When using the ez functions, there does not appear to be any simple way to control plot attributes such as line color or style. The input arguments for ezplot do not include a color/style specification as permitted in the case of the plot command. More importantly, these ez functions do not return a graphics handle. There are methods for retrieving the handle and manipulating the attributes through the set function, but these techniques are too advanced for this introductory document. If editing is needed, the most direct solution is to turn on Enable Plot Editing from the menu bar along the top of the Figure window and use the mouse to select the line to be edited. Holding down the right mouse button over the object brings up a menu of attributes to be edited.

The exact sequence for editing graphics windows is not the same across all operating systems and versions of Matlab. Some of these editing features first appeared in version 5 but underwent significant changes in version 6. Moreover, the Linux version appears to be different than the Windows version.

The function ezcontour plots level curves for functions of two variables z = f(x,y). The second and third arguments are the plotting limits for each of the independent variables x and y. One drawback to ezcontour is that it does identify the contour levels. Adding a colorbar to the graph will give you an approximate idea of the level associated with each curve.   [The function ezcontourf produces filled contour plots.]

>> ezcontour('y^2 - x^2', [-3 3],[-3 3]);
>> colorbar

To plot specific level curves, it is more effective to use ezplot. The command ezplot('g(x,y)',[..],[..]) plots the level curve g(x,y) = 0. To plot the level curve f(x,y) = k, define g(x,y) = f(x,y) - k in the previous command. In the following sequence, level curves for z = -4, -2, 0, 2, 4 are plotted on a single graph. The lines have been edited to make the negative levels (z < 0) dashed blue lines and the positive levels (z > 0) solid red lines. The labels are added by selecting Insert -> Text.

>> ezplot('y^2 - x^2 + 4', [-3 3],[-3 3]);
>> hold on
>> ezplot('y^2 - x^2 + 2', [-3 3],[-3 3]);
>> ezplot('y^2 - x^2',     [-3 3],[-3 3]);
>> ezplot('y^2 - x^2 - 2', [-3 3],[-3 3]);
>> ezplot('y^2 - x^2 - 4', [-3 3],[-3 3]);
>> grid on

To introduce three-dimensional viewing of surfaces, we first consider examples of surfaces that can be plotted as graphs,  z = f(x,y).

The mesh functions represent the surface with a mesh where the four edges of each mesh element are colored according to the height of the function, but the faces of the mesh elements are left uncolored.

>> ezmesh('y^2 - x^2', [-3 3],[-3 3]);

The function ezmeshc also includes the level contours of the function f(x,y) plotted on the "floor" of the 3-D plot. That is, if the plotting limits in the z-direction are z_min ≤  z  ≤  z_max, then the level curves are plotted in the plane z = z_min.

The hidden command controls whether or not to show hidden lines (this only applies to mesh plots). Use hidden off to make hidden lines visible.

The viewing angle for 3-D graphics can be changed by dragging the mouse inside the figure window if rotate3d has been turned on, either from the menu bar or by typing rotate3d on from the command line. From the command line, view(125,30) will set the viewing angle with horizontal rotation 125 degrees and vertical elevation 30 degrees. This is very similar to the viewing perspective typically used in Stewart's text.

>> ezplot3('cos(t)','sin(t)','sin(5*t)',[-pi pi]);
>> ezmeshc('y^2 - x^2', [-3 3],[-3 3]);
>> hidden off
>> view(125, 30);

The surf commands produce a colored surface with the faces of each mesh element colored according to the height of the surface z = f(x,y).

>> ezsurf('-10*x*y*exp(-(x^2 + y^2))',...
          [-2.5 2.5],[-2.5 2.5]);
>> view(125, 30)

The choice of colors for surface plots is determined by the current colormap. To see a list of available colormaps and a one-line description of each, run helpwin graph3d. The default colormap is jet.

The shading command controls the color shading of the mesh elements making up a surface. There are three choices:  flat uses a single color within each mesh element; faceted uses flat shading with superimposed black mesh lines (this is the default); interp uses linear interpolation to make the shading change smoothly across the surface.

>> ezsurf('-10*x*y*exp(-(x^2 + y^2))',...
          [-2.5 2.5],[-2.5 2.5]);
>> colormap(hot)
>> shading('flat')
>> view(110,-20)

The following example graphs the upper half of the sphere x² + y² + z² = 9 and overlays the tangent plane at (x, y, z) = (0.5, 0.5, 2.915).

>> ezsurf('sqrt(9 - x^2 - y^2)', [-4 4], [-4 4]);
>> view(110,30);
>> hold on
>> ezmesh('2.915 - 0.172*(x-0.5) - 0.172*(y-0.5)',...
          [-3 3],[-3 3]);
>> hidden off
>> hp = plot3(.5, .5, 2.915, 'r.');
>> set(hp, 'markersize', 20);
>> axis([-4 4 -4 4 0 4]);

In the previous example for the upper half-sphere, note the ragged edge where the sphere meets the xy-plane. Here is an example of a surface that is best represented in parametric form,

The functions ezmesh and ezsurf accept parametric representations; in this case the first three input arguments are the Matlab expressions for x(u,v), y(u,v), and z(u,v). In this first example, we graph the upper halves of two concentric spheres with a section removed from the outer sphere.

>> ezsurf('sin(u)*cos(v)', 'sin(u)*sin(v)',...
          'cos(u)', [0 pi/2 0 2*pi]);
>> hold on
>> ezsurf('2*sin(u)*cos(v)', '2*sin(u)*sin(v)',...
          '2*cos(u)', [0 pi/2 0 7*pi/4]);
>> axis([-2.1 2.1 -2.1 2.1 0 2.1]);
>> set(gca, 'DataAspectRatio', [1 1 1]);
>> view(45,25);

Surfaces of revolution are best represented in parametric form. In the following example, the curve x = sin²(πx) is rotated about the z-axis on the interval   -1  ≤  z  ≤  1.

>> ezsurf('sin(pi*u)*sin(pi*u)*cos(v)',...
          'sin(pi*u)*sin(pi*u)*sin(v)',...
          'u', [-1 1 0 2*pi]);
>> set(gca, 'DataAspectRatio', [1 1 1]);
>> view(135,15);

>> x = [-1 : 1/16 : 1];
>> y = [-1 : 1/16 : 1];
>> [x2,y2] = meshgrid(x,y);
>> z = sin(pi*x2) .* sin(pi*y2);
>> subplot(1,2,1);
>> [c,h] = contour(x, y, z, [-1 : 0.125 : 1]);
>> clabel(c, h, [-1 : .25 : 1]);
>> set(gca, 'DataAspectRatio', [1 1 1]);
>> title('sin(\pi x) sin(\pi y)');
>> subplot(1,2,2);
>> surfc(x, y, z);
>> view(125,30);
>> xlabel('x');  ylabel('y');  zlabel('z');
>> set(gca, 'DataAspectRatio', [1 1 1]);