%Helicoid
[u,v] = meshgrid(-2:.1:2,0:pi/10:2*pi);
x = sinh(u).*sin(v);
y = sinh(u).*cos(v);
z = v;
figure(1); clf;
surf(x,y,z);
title('Helicoid x = sinh(u)sin(v), y = cosh(u)sin(v), z = v');
xlabel('x');ylabel('y');zlabel('z');

[U,V] = meshgrid(-1:.2:1,0:pi/10:pi/2);
Nx = sech(U).*cos(V);
Ny = -sech(U).*sin(V);
Nz = -tanh(U);
X = sinh(U).*sin(V);
Y = sinh(U).*cos(V);
Z = V;
figure(2);clf;
surfl(x,y,z);hold on;
quiver3(X,Y,Z,Nx,Ny,Nz);hold off;
%view(70,15);
title('Helicoid with normal vectors over -1 < u < 1, 0 < v < \pi/2');
xlabel('x');ylabel('y');zlabel('z');

[u,v] = meshgrid(-1:.1:1,0:pi/10:pi/2);
G1= sech(u).*cos(v);
G2 = -sech(u).*sin(v);
G3 = -tanh(u);
figure(3);clf;
surfl(G1,G2,G3);
axis([-3,3,-3,3,-3,3]);hold on;
%view(70,15);
%view(-85,30);axis equal;
plot3(0,0,0,'*');hold off;
title('Gauss map of Helicoid over -1 < u < 1, 0 < v < \pi/2');
xlabel('x');ylabel('y');zlabel('z');
