function F = curvetan(r,t,a,b,x0,x1,y0,y1)

% curvetan plots the curve r(t) for t in [a,b] 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.
% 

rx = inline(vectorize(r(1)));
ry = inline(vectorize(r(2)));
rp = diff(r);
c = (b-a)/100;
T = a:0.01:b;
for j = 1:100 
    clf
    plot(rx(T),ry(T),'LineWidth',2)
    hold on
    quiver(rx(a+j*c),ry(a+j*c),...
        subs(rp(1),t,a+j*c),subs(rp(2),t,a+j*c),1,'LineWidth',2)
    axis([x0 x1 y0 y1])
    F(j) = getframe;
end