How to plot vectors exactly on the edge of another graph?

The best I've got is expressed by the following:

clear

[u,v] = meshgrid(-2:0.2:2);

f = u.^2+v.^2-1;

[du,dv] = gradient(f);

hold all

g = @(a,b) a.^2+b.^2-1;

fimplicit(g)

D1 = u.^2+v.^2 >1;
D2 = u.^2+v.^2 <1.5;

v(~D1) = NaN;
u(~D2) = NaN;

norm = norm(gradient(f));

quiver(u,v,du./norm,dv./norm,'Color','r')

axis equal

However, the vectors are close to the edge, but not right originating from there. I can't think a straight way around it.

Answer 1

[Matt J]

t=linspace(0,360,91); t(end)=0;

u=cosd(t); 
v=sind(t);

fimplicit(@(a,b) a.^2+b.^2-1);hold on
quiver(u,v,u,v,'Color','r'); hold off

axis equal

[Niklas Kurz]

Appreciated approch, using the outward second derivat of a circle parametrization.