CHAPTER 5

Graphics Special Commands

5.1 Two Dimensional Graphics: FPLOT and EZPLOT

Commands fplot and ezplot graph curves using commands developed for a wide array of cases without having to specify all the details built in every time. Their syntax is as follows:

As a first example, perform the graph of the function over the range [0,10]. Figure 5-1 presents the results of the following syntax:

>> x = 0:0.05:10;
>> y = sin(x) .* exp(-0.4*x);
>> plot(x,y)

The representation of the previous curve (Figure 5-2) can also be done using the following syntax:

>> ezplot('sin(x) * exp(-0.4*x)', [0,10])

Note that ezplot automatically sets the title. You could also obtain the same graphical representation using the following command:

>> fplot('sin(x) * exp(-0.4*x)', [0,10])

Figure 5-3 shows the curve for in the range [-2π,2π] using the following syntax:

>> ezplot('x^2-y^4')

Then we graph the parametric curve– x(t) = 4cos(t) –cos(4t), y(t) = 4sin(t) –sin(4t) varying t between 0 and 2π (Figure 5-4). The syntax is as follows:

>> t = 0:0.1:2*pi;
>> x = 4 * cos(t) - cos(4*t);
>> y = 4 * sin(t) - sin(4*t);
>> plot(x,y)

The same graph (Figure 5-5) could have been obtained by using the following syntax:

>> ezplot('4*cos(t) - cos(4*t)', '4*sin(t) - sin(4*t)', [0, 2*pi])

Next, were present the curves Sine (x), Sine (2x) and Sine (3x) about the same axes as shown in Figure 5-6. The syntax is as follows:

>> fplot('[sin(x), sin(2*x), sin(3*x)]', [0, 2*pi])

We can try to represent every previous curve using different strokes (Figure 5-7) by using the following syntax:

>> fplot('[sin(x), sin(2*x), sin(3*x)]', [0, 2*pi],'*')

Below you will find the syntax used to represent the polar curve r = Sin (2a) Cos (2a) for t between 0 and 2π (Figure 5-8).

>> t = 0:0.1:2*pi;
>> r = sin(2*t).* cos(2*t);
>> polar(t,r)

This example  could also represent this polar curve with a dashed line of red color (Figure 5-9) using the following syntax:

>> t = 0:0.1:2*pi;
>> r = sin(2*t).*cos(2*t);
>> polar(t,r,'--r')

5.2 Three-Dimensional Graphics with EZ Command

In the same way that ez functions are used to represent two-dimensional graphics without specifying the field of existence of  an array form, three-dimensional graphics of warped curves, surfaces, contour lines, contour and other types of graphics can also be used, the commands to use are as follows:

Below is the contour graph (Figure 5-10) for the function:

>> f = ['3 *(1-x)^2*exp(-(x^2)-(y + 1)^2)',...
'-10*(x/5-x^3-y^5)*exp(-x^2-y^2)','-1/3*exp(-(x + 1)^2 - y^2)'];

>> ezcontour(f,[-3,3],49)
   colormap summer

Then fill in color in the previous contour (Figure 5-11).

>> ezcontourf(f,[-3,3],49)

In the following example we do a mixed mesh-contour (Figure 5-12) for the chart function:

>> ezmeshc('y /(1 + x^2 + y^2)', [- 5, 5, - 2*pi, 2*pi])

Later is a graphical surface and contour (Figure 5-13).

>> ezsurfc('y/(1 + x^2 + y^2)', [- 5, 5, - 2*pi, 2*pi], 35)

Then we graph a curve in parametric space.

>> ezplot3('sin(t)', 'cos(t)',', [0, 6 * pi])

5.3 Steps to Graphing Data

As we have seen, the Basic module of MATLAB offers a wide range of options when it comes to graphic representations. It allows graphs of planar curves and surfaces, enabling grouping and overlapping. It is also possible to work colors, grids, frames, etc., into the graphics. Representations of functions can be in implicit, explicit and parametric coordinates. MATLAB is therefore mathematical software with high graphics performance, distinguishing it from many other symbolic calculation packages. MATLAB also allows graphics of bars, lines, stars, histograms, polyhedra, geographical maps and animations. The creation of a graph is usually attached to the following steps:

5.4 Steps to Perform 3 –D Graphics

The Basic module of MATLAB allows graphics in three dimensions, both lines and nets and surfaces. You can also use explicit and parametric coordinates. The steps followed in general to carry out a three-dimensional graph are presented in the following table:

colormap hot
shading interp
set(h,'EdgeColor','k')

light('Position',[-2,2,20])
lighting phong
material([0.4,0.6,0.5,30])
set(h,'FaceColor',[0.7 0.7 0],...
      'BackFaceLighting','lit')

view([30,25])
set(gca,'CameraViewAngleMode','Manual')

axis([5 15 5 15 -8 8])
set(gca,'ZTickLabel','Negative||Positive')

set(gca, 'PlotBoxAspectRatio', [2.5 2.5 1])

xlabel('X Axis')
ylabel('Y Axis')
zlabel('Function Value')
title('Peaks')

set(gcf,'PaperPositionMode','auto')
print -dps2

You can use some or all of these steps to create your graphic. So let’s go through a few examples. As a first example we consider the surface z = x² - y² in [-2,2] x [- 2,2] and represent it with strong lighting, shading dense grayish colors (Figure 5-25).

>> [X, and] = meshgrid(-2:0.05:2);
Z = X .^ 2 – Y .^ 2;
surf(X,Y,Z),shading interp,brighten(0.75),colormap(gray(5))

Then we represent, on the same axes, the curve focused from four different points of view and with shading by default (Figure 5-26).

>> [X, Y] = meshgrid(-2:0.05:2);
Z = X .^ 2 – Y .^ 2;
subplot(2,2,1)
surf(X,Y,Z)
subplot(2,2,2)
surf(X,Y,Z),view(-90,0)
subplot(2,2,3)
surf(X,Y,Z),view(60,30)
subplot(2,2,4)
surf(X,Y,Z),view(-10,30)

Then MATLAB reads a file and appropriate properties are used to generate the colorful graph in Figure 5-27.

>> load clown
surface(peaks,flipud(X),...
'FaceColor','texturemap',...
'EdgeColor','none',...
'CDataMapping','direct')
colormap(map)
view(-35, 45)

Our clown could use a ball, so let’s create one for him. Different shaders are used for the sphere (Figure 5-28).

>> subplot(3,1,1)
sphere(16)
axis square
shading flat
title('Soft shading')

subplot(3,1,2)
sphere(16)
axis square
shading faceted
title(' Normal shading')

subplot(3,1,3)
sphere(16)
axis square
shading interp
title('Dense shading')

The following example changes the ratio of appearance for the sphere (Figure 5-29).

>> sphere
set(gca,'DataAspectRatio',[1 1 1],...
'PlotBoxAspectRatio',[1 1 1],'ZLim',[-0.6 0.6])

Now place the background color of the current figure in white (Figure 5-30).

>> set(gcf, 'Color', 'w')

In the following example (Figure 5-31), we represent a surface utilizing the function peaks predefined in MATLAB (similar to a two-dimensional Gaussian distribution) with change of origin and scale.

>> surf(peaks(20))

Then we rotate the figure above 180 degrees around the axis X (Figure 5-32).

>> h = surf(peaks(20));
rotate(h,[1 0 0],15)

Then we change the center and rotate the start surface 45° in the direction of the axis z (Figure 5-33).

>> h = surf(peaks(20));
zdir = [0 0 1];
center = [10 10 0];
rotate(h,zdir,45,center)

In the following example we define several axes in a simple window (Figure 5-34).

>> axes('position',[.1  .1  .8  .6])
mesh(peaks(20));
axes('position',[.1  .7  .8  .2])
pcolor([1:10;1:10]);

Then we equip special lighting, grey dense shading and variation of axes in [- 3, 3] x [- 3, 3] x [- 8, 8] to the peaks surface (Figure 5-35).

>> [x, y] = meshgrid(-3:1/8:3);
z = peaks(x,y);
surfl(x,y,z);
shading interp
colormap (gray);
axis([-3 3,-3 3,-8 8])

Then we change perspective, mesh and color to the previous illuminated surface (Figure 5-36).

>> view([10 10])
grid on
hold on
surfl(peaks)
shading interp
colormap copper
hold off

Below are two examples of triangle graphics (Figures 5-37 and 5-38).  Note that because  the rand function is used, your results will not be the same as these.

>> x = rand(1,50);
y = rand(1,50);
z = peaks(6*x-3,6*x-3);
tri = delaunay(x,y);
trimesh(tri,x,y,z)

>> x = rand(1,50);
y = rand(1,50);
z = peaks(6*x-3,6*x-3);
tri = delaunay(x,y);
trisurf(tri,x,y,z);
colormap copper

As you can see from the examples in this chapter, you have many options at your disposal to enhance or modify your graphics to suit your needs.