%% Movies of the TNB frame along a curve

%%
% In these movies, *T* is blue, *N* is green and *B* is red.

%% A warning
% To get the frame to look like an orthonormal frame, you must have
% intervals of approximately equal length along the axes.  

%% A helix
% The file *helixframe.mat* was created with the commands

syms t
r = [3*cos(t),3*sin(t),t]
helixframe = movingframe(r,t,0,4*pi,-6,6,-6,6,0,4*pi)
save('helixframe','helixframe')

%%
% You can view the movie without executing these commands by giving the
% commands

load('helixframe')
mplay(helixframe)

%% A warning
% To get the frame to look like an orthonormal frame, you must have
% intervals of approximately equal length along the axes.

%% Twisted cubic
% The file *twistedcubicrame.mat* was created with the commands

syms t
r = [t,t^2,t^3]
twistedcubicframe = movingframe(r,t,-1,1,-2,2,-2,2,-2,2)
save('twistedcubicframe','twistedcubicframe')

%%
% You can view the movie without executing these commands by giving the
% commands

load('twistedcubicframe')
mplay(twistedcubicframe)