function F = movingframe(r,t,a,b,x0,x1,y0,y1,z0,z1)

% movingframe plots the curve r(t) for t in [a,b] and, one at a time, 
% the frame T,N,B at 100 equally spaced times in the interval [a,b]. The    
% axis for each frame is the same, with x-limits x0,x1, y-limits y0,y1 and 
% z-limits z0,z1.  T is blue, N is green and B is red.

 

%  Make the components of the parametrized curve functions
rx = inline(vectorize(r(1)));
ry = inline(vectorize(r(2)));
rz = inline(vectorize(r(3)));

% Calculate the derivative of the parametrized curve
rp = diff(r);

% Calculate the step size
c = (b-a)/100;

% Make the vector of points at which the curve will be plotted.
S = a:0.01:b;

% Calculate the unit tangent vector
T = simplify(diff(r)/sqrt(diff(r)*transpose(diff(r))));

%  Calculate the binormal
B1 = cross(T,diff(T)); B = simplify(B1/sqrt(B1*transpose(B1)));

% Calculate the unit normal
N = simplify(cross(B,T));

% Make the components of the frame vectors functions
Tx = inline(vectorize(T(1)));
Ty = inline(vectorize(T(2)));
Tz = inline(vectorize(T(3)));
Nx = inline(vectorize(N(1)));
Ny = inline(vectorize(N(2)));
Nz = inline(vectorize(N(3)));
Bx = inline(vectorize(B(1)));
By = inline(vectorize(B(2)));
Bz = inline(vectorize(B(3)));


for k = 1:101
    clf
    plot3(rx(S),ry(S),rz(S),'k')
    hold on
    quiver3(rx(a+c*(k-1)),ry(a+c*(k-1)),rz(a+c*(k-1)),Tx(a+c*(k-1)),Ty(a+c*(k-1)),...
        Tz(a+c*(k-1)),'LineWidth',2','color','b');
    quiver3(rx(a+c*(k-1)),ry(a+c*(k-1)),rz(a+c*(k-1)),Nx(a+c*(k-1)),...
        Ny(a+c*(k-1)),Nz(a+c*(k-1)),'LineWidth',2','color','g');
    quiver3(rx(a+c*(k-1)),ry(a+c*(k-1)),rz(a+c*(k-1)),Bx(a+c*(k-1)),...
        By(a+c*(k-1)),Bz(a+c*(k-1)),'LineWidth',2','color','r');
    axis([x0 x1 y0 y1 z0 z1])
    axis square
 F(k) = getframe;
end