How to graph a Piecewise function?

I need to graph a piecewise function in terms of theta for a Homework assignment.

I must first create a 100 element vector for the values of theta between 0 and 2*pi. After that I must use a loop and a conditional statement to plot the graph. Here is what I have so far:

Theta= 0:(2*pi)/100:2*pi;    %the vector lists 100 elements(0 < Theta < 2Pi)

   if (0 <= Theta) && (Theta <= pi/2)             
                                                %0<= Theta<= pi/2

                       Eq1= 6*(2*Theta - .5*sin(2*Theta))/pi

   elseif (pi/2 <= Theta) && (Theta <= 2*pi/3)    
                                                %pi/2 <= Theta <= 2*pi/3

                       Eq2= 6

   elseif (2*pi/3 <= Theta) && (Theta <= 4*pi/3)  
                                                %2*pi/3 <= Theta <= 4*pi/3

                       Eq3=7.5 - (1 - .5* cos(1.5* (Theta - (2*pi/3))))

   elseif (4*pi/3 <= Theta) && (Theta <= 3*pi/2)
                                                %4*pi/3 <= Theta <= 3*pi/2

                       Eq4= 3

   elseif (3*pi/2 <= Theta) && (Theta <= 7*pi/4)  
                                                %3*pi/2<=Theta<=7*pi/4

                       Eq5= 3 - 1.5*((Theta - 3*(pi/2))/(pi/4))^2

   elseif (7*pi/4 <= Theta) && (Theta <= 2*pi)
                                                %7*pi/4 <= Theta <= 2*pi

                       Eq6= 1.5*(1 - ((Theta - 7*(pi/4/(pi/4)))^2
end

figure

plot(Theta, Eq1, Theta,Eq2,Theta,Eq3,Theta,Eq4,Theta,Eq5)

Everything is coming out jacked up, or not coming up at all... Please help! I know that I should place a loop, but where would it go?

Answer 1

[Thorsten]

%Theta= 0:(2*pi)/100:2*pi; %the vector lists 100 elemants between 0 and 2Pi
% Actually these are 101 elements; 
% use
Theta = linspace(0, 2*pi, 100);

F = nan(size(Theta));

% logical indexing
ind = 0 <= Theta & Theta <= pi/2;
F(ind) = 6*(2*Theta(ind) - .5*sin(2*Theta(ind)))/pi;

% just one value, no ind variable necessary
F(pi/2 <= Theta & Theta  <= 2*pi/3) = 6;
ind = 2*pi/3 <= Theta & Theta <= 4*pi/3;
F(ind) = 7.5 - (1 - 0.5* cos(1.5* (Theta(ind) - (2*pi/3))));
F(4*pi/3 <= Theta & Theta <= 3*pi/2) = 3;
ind = 3*pi/2 <= Theta & Theta <= 7*pi/4;

% use .^ to work on the whole vector
F(ind) =  3 - 1.5*((Theta(ind) - 3*(pi/2))/(pi/4)).^2;
ind = 7*pi/4 <= Theta & Theta  <= 2*pi;

% some ) were missing, I added them at the end;
% PLEASE CHECK IF THIS IS THE RIGHT FUNCTION!!!
F(ind)  = 1.5*(1 - ((Theta(ind) - 7*(pi/4/(pi/4))))).^2;
plot(Theta, F)

[Walshaikhli]

The graph looks vaguely similar to what I am trying to plot, but its too sharp. Is there a function in Matlab that can "smooth" it. For example some sort of regression?

[Martin Vatshelle]

plotting the vertical lines between the pieces does not look good. Any simple way to break lines at the steps?

[Walter Roberson]

When you plot() or line(), any nan or inf or -inf will be interpreted as a request to stop drawing the line and resume when the coordinates are finite.

Answer 2

[Image Analyst]

This kind of construct does not work

if  0 <= Theta <= pi/2

You need to do it in two comparisons, like this

if  (0 <= Theta) && (Theta <= pi/2)

Each one of those things in the parentheses will product a true or false result. If you AND them together, you will get what you tried to do.

[John D'Errico]

Note that Theta is a vector. if statements will still fail to produce the proper result if they are applied to a vector.

You will need to loop over those elements, or use another scheme to determine the location of each point.

[Image Analyst]

Good point. I didn't notice that because of the bad formatting, which can be fixed after viewing this: http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup