Visualization

The figure is produced through linking the points. Therefore, in order to produce the figure, we first need to grap the axis of each point. In MATLAB, we can produce figures with two or three dimensions.

Plot with two dimensions

In Matlab, we use plot, ezplot and fplot function to produce two dimensional plot.

plot

Produce the figure for using red line and produce the figure for using green dash line.

x = linspace(0, 2 * pi, 30);
      y = sin(x);
      z = cos(x);
      plot(x, y, 'r', x, z, 'g--')

ezplot

Produce the figure for with interval of [0, pi] using ezplot

ezplot('sin(x)', [0, pi])

ezplot can also be used to produce figure for parametric equation and implicit function. For example, produce figure for parametric equation and with the interval of

ezplot('cos(t)^3', 'sin(t)^3', [0, 2*pi])

Produce figure for implicit function with the interval of and

ezplot('exp(x)-sin(x*y)', [-3, -1.5, 1, 3])

fplot

fplot('fun', lims) can be used to draw the figure in the interval lims=[xmin, xmax]. fun must be the name of the m file. fplot can not be used to produce figures for parametric equation and implicit function, but it can do multiple plotting.

Produce a figure for with the interval of .

Open a new Matlab script fun.m and type the following;

function Y = fun(x)
      Y = exp(2 * x) - sin(2 * x)
      end

flot('fun', [1, 3])

Plot with three dimensions

plot3(X, Y, Z), surf(X, Y, Z) and Mesh(X, Y, Z) create a three-dimensional surface plot. The difference among them is: plot3(X, Y, Z) is a line plot; the figure produced by surf(X, Y, Z) has solid edge colors and solid face colors and the figure produced by surf(X, Y, Z) has solid edge colors and no face colors.

plot3(x, y, z, s)

Produce the figure for the parametric equation x=sin(t), y=cos(t) and z=t with interval [0, 10*pi].

t = 0: pi/50 : 10*pi;
      plot3(sin(t), cos(t), t)
      rotate3d

surf(x, y, z)

Produce figure for within the interval of and .

x = -3: 0.1 :3;
      y = 1: 0.1 :5;
      [X, Y] = meshgrid(x, y) % Produce a matrix for x and y
      
      Z = (X + Y).^2
      surf(X, Y, Z)
      shading flat
      

Mesh(x, y, z)

x = -3: 0.1 :3;
      y = 1: 0.1 :5;
      [X, Y] = meshgrid(x, y) % Produce a matrix for x and y
      
      Z = (X + Y).^2
      mesh(X, Y, Z)
      

Plot processing

Notations and control of axis

After producing the figure, you may need to note the figure.

To control the axis, we can use the following commands

Axis(xmin xmax ymin ymax zmin zmax) % set the minium and maxium value for x, y and z axis
      Axis auto % set the value of axis as default
      
      Here is an example to control the axis for the plot of cos(1/x):
      
      ```matlab
      x = linspace(0.0001, 0.01, 1000)
      y = cos(1 ./ x)
      plot(x, y)
      axis([0.005 0.01, -1 1])

Combine figures

We sometimes need to combien different figures together. To do this, we use commands hold on and hold off. hold on retains plots in the current axes so that new plots added to the axes do not delete existing plots. hold off sets the hold state to off so that new plots added to the axes clear existing plots and reset all axes properties.

x = linspace(-pi,pi);
      y1 = sin(x);
      plot(x,y1)
      
      hold on;
      y2 = cos(x);
      plot(x,y2)
      hold off
      
      y3 = sin(2*x);
      plot(x,y3)

The style of line and color

We can also change the line into different styles and colors.

The stype of line

The color of line

The style of dot

Grid, box and legend

grid is for displaying or hiding axes grid lines. box is for displaying or hiding axes outline. legend is for adding legend to axes.

grid on 
      % displays the major grid lines for the current axes or chart
      
      grid off
      % removes all grid lines from the current axes or chart
      
      box on
      % displays the box outline around the current axes by setting their Box property to 'on'
      
      box off
      % removes the box outline around the current axes by setting their Box property to 'off'
      
      legend('string1', 'string2',...)

Here is an example to show how the legend can be added to the plot of two functions.

x = linspace(-pi, pi, 20)
      plot(x, cos(x), 'rd', x, sin(x), '-.b')
      legend('cos^2(x)', 'asin(x)')

Subfigures

subplot(m,n,p) divides the current figure into an m-by-n grid and creates axes in the position specified by p. MATLAB® numbers subplot positions by row. The first subplot is the first column of the first row, the second subplot is the second column of the first row, and so on. If axes exist in the specified position, then this command makes the axes the current axes.

Here is an example to show how four ovals can be produced in one figure.

      t = 0:2*pi/99:2*pi;
      x=1.15*cos(t); y=3.25*sin(t);
      subplot(2,2,1); plot(x, y);
      axis off
      title('axis off');
      subplot(2,2,2); plot(x,y);
      axis image;
      title('axis image');
      subplot(2,2,3); plot(x,y);
      axis equal;
      title('axis Equal');
      subplot(2,2,4); plot(x,y);
      axis square;
      title('axis Square');
      

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