V = [1 0 0;
     0 1 0;
     0 0 1;
     1 1 1];

F = [1 2 3;
     1 3 4;
     1 2 4];

figure(1); clf;
trisurf(F, V(:,1), V(:,2), V(:,3))
axis equal
xlabel('x'); ylabel('y')'; zlabel('z');
hold on


a = V(3,:) - V(1,:);
b = V(4,:) - V(1,:);
c = V(2,:) - V(1,:);

n = cross(b, a);
n  = n / norm(n);

lw = 'linewidth'; ms = 'markersize';
q = V(1,:) + 1/3*a + 1/3*b;  % pt on plane
p = q + 1/3*n;
plot3([q(1) p(1)], [q(2) p(2)], [q(3) p(3)], 'r-', lw, 4)
plot3(p(1), p(2), p(3), 'r^', lw, 6, ms, 11)


n = cross(c, a);
n = -n / norm(n);

q = V(1,:) + 1/3*c + 1/3*a;  % pt on plane
p = q + 1/3*n;
plot3([q(1) p(1)], [q(2) p(2)], [q(3) p(3)], 'g-', lw, 4)
plot3(p(1), p(2), p(3), 'g^', lw, 4, ms, 11)


view([110, 20])

alpha(0.5)
