p=@(t) [7*cos(t);4*sin(t)];%one curve p(t)
dp=@(t) [-7*sin(t);4*cos(t)];%p'(t)
q=@(s) [cos(s)-2;2*sin(s)-1];%another curve q(s)
dq=@(s) [-sin(s);2*cos(s)];%q'(t)

r=@(x) p(x(1))-q(x(2));%vector conecting p(t) and q(t)
dr=@(x) [dp(x(1)),-dq(x(2))];%Jacobian of r

F=@(x) r(x)'*r(x);%the distance (squared) between the two points
gradF=@(x) 2*dr(x)'*r(x);
x0=[3.5;2.7];%initial point
n=200;
X=gradientmethod(gradF,0.01,x0,n);
figure(1)
clf
hold on

picture(p,q,x0)
for i=100:100
    picture(p,q,X(:,i))
end
axis equal
sqrt(F(x0))

figure(2)
clf
hold on
graphF(F)
plot(X(1,:),X(2,:),'rx')