function F = curvetan3(r,t,a,b,x0,x1,y0,y1,z0,z1,az,el)

% curvetan3 plots the space curve r(t) and, one at a time, 
% tangent vectors at 100 equally spaced times in the interval [a,b].  The
% plots are saved as frames with the name F for use with the command movie
% or movieview or some other MATLAB movie player.  The axis for each frame
% is the same, with x-limits x0,x1, ylimits y0,y1, and z limits z0,z1.  The
% optional arguments az and el change the view in all the frames from the
% default to view([az el])

if nargin < 11
    az = -37.5; el = 30;
end
rx = inline(vectorize(r(1)));
ry = inline(vectorize(r(2)));
rz = inline(vectorize(r(3)));
rp = diff(r);
c = (b-a)/100;
T = a:0.01:b;
for j = 1:100
    clf
    plot3(rx(T),ry(T),rz(T),'LineWidth',2)
    hold on
    quiver3(rx(a+j*c),ry(a+j*c),rz(a+j*c),...
        subs(rp(1),t,a+j*c),subs(rp(2),t,a+j*c),subs(rp(3),t,a+j*c),1,...
        'LineWidth',2)
    axis([x0 x1 y0 y1 z0 z1])
    view([az el])
    F(j) = getframe;
end