%% The Twisted Cubic

%%
% Here are two methods to plot the twisted cubic, the parametric space 
% curve 
% 
% $$x(t)=t,\ y(t)=t^2,\ z(t)=t^3\,$$
% 
% where the parameter t goes from -2 to 2.

%%
% * Using *plot3*
%
%%
% The first method uses the *plot3* command, which is the 3 dimensional 
% analogue of *plot*.  The command *linspace(a,b,n)* generates
% a vector with n equally spaced points between a and b, including a and b.
% (The command *linspace(a,b)* is the same as *linspace(a,b,100)*.)

t=linspace(-2,2,500);
x=t; y=t.^2; z=t.^3;
plot3(x,y,z), grid
xlabel('x(t)=t')
ylabel('y(t)=t^2')
zlabel('z(t)=t^3')
title('twisted cubic (t,t^2,t^3)')

%%
% * Using *ezplot3*
%
%%
% The second method uses the *ezplot3* command, which is the 3 dimensional
% analogue of *ezplot*.

syms t
ezplot3(t,t^2,t^3,[-2,2])
xlabel('x(t)=t')
ylabel('y(t)=t^2')
zlabel('z(t)=t^3')
title('twisted cubic (t,t^2,t^3)')

%%
% * Using plot tools
%
%%
% In the Tools menu for the plot, you can find Rotate 3D.  If you 
% click on this you will be able to rotate the plot to see other views of
% it.  You can also click on the rotate button (just to the right of the 
% hand) on the toolbar of the plot to be able to rotate it.