% A MATLAB guide to graph functions and curves from a data set.

clear;

% Grahing functions previously defined in a file named "f.m" 
% and "f2.m" both located in the same directory where this main 
% file is located. The approach is to obtain a set of points in the plane
% (x,y) by evaluating the function at the given set of points x.

% Interval [A,B], where the functions are going to be graphed.
A=-5;
B=5;
% Number of points to be used in the plot command to 
% obtain the graphs.
N=100;
% Step size. Distance between points in x-axis for a uniform
% partition of the interval [A,B].
step=(B-A)/(N-1);
% Uniform partition of the inteval [A,B] with stepsize step.
% It creates a row vector (x(1),....x(n)) of N components.
x = A:step:B;
% With the next command we will create a Row vector "y" whose 
% components are y(i)=f(x(i)) 
y = f1(x);
% Once the two vectors x and y have been created the command plot
% will make a graph in the x-y plane using these N (x(i),y(i)) 
% points by joining them with straight segment between 
% consecutive points.
plot(x,y);

% There is an easier way to create a graph once the function has been
% defined without creating vectors x and y. We only need to specify the
% ends of the interval where the function is going to be graphed. MATLAB
% will use a default number of points to construct the graph.
% We will use a separate coordinate plane for this graph by defining it
% just before writing the ezplot command.
figure;
ezplot('f1',-5,5);

% Now, we want to plot the two graphs of f(x) and f2(x) in the 
% same coordinate plane.
% First we will create a new coordinate plane.
figure;
% Then, we generate the z vector containing the values of z(i)=f2(x(i)).
z=f2(x);
% Now we use the command plot with some more parameters.
plot(x,y,x,z);

% We can especify the colors of the graphs
figure;
plot(x,y,'r',x,z,'b');

% We can draw the graphs using noncontinuous curves, just ploting the
% points where the functions have been evaluated.
figure;
plot(x,y,'--',x,z,'*');

% Now, we will draw a curve passing through the points defined
% by (x,y) and at the same time mark the points in the graph 
figure;
x=[1,3,5,6,7,9,10];
y=[5;-10;9;-1;-3;4;8];
plot(x,y,x,y,'*');

% Now some fun this is how I create an animated plot. 
% I start with 10 interpolation points and increase them to 100 by adding
% one point per iteration. If we do not create a new coordinate plane using
% the "figure" command the graphs will be superimposed and this is how the
% animation results. You can graduate the speed of the animation by
% increasing or decreasing the number inside the "pause( )" command
%           OK HAVE FUN!!!!!
N=10;
Nmax=100;
for NN=N:Nmax
    step=(B-A)/(NN-1);
    x=A:step:B;
    y=f1(x);
    plot(x,y,x,y,'*');
    pause(0.001);
end

% Here we will show how to draw curves by pieces in the same graph.
% It is useful for Bezier curves construction.

% Consider the vectors x1, y1, x2, y2.

x1=[1,3,4,8,10];
y1=[-2;4;9;3;-6];
x2=[10,12,13,14,15];
y2=[-6;3;5;2;7];

%Here we we will create a graph where a first piece is obtained 
% then a "hold on" command is given, and then a second portion
% in another part of the domain is graphed.
% 'g-' means use a green continuous line to joint neighbor points.
% 'm-' same for magenta color.
% '*' means mark the point (x1,y1) with a star in the plane.
figure;
plot(x1,y1,'g-');
hold on;
plot(x1,y1,'*');
hold on;
plot(x2,y2,'m-',x2,y2,'*');