Unroll the surface of an Oloid

Hi,

I want to unroll or unwrap the surface of an oloid.

I've got:

[v,t] = meshgrid(linspace(0,1,g),linspace(-120*pi/180,120*pi/180,s));
x  = 1*cos(t)-v.*((1+cos(t)+cos(t).*cos(t))./(1+cos(t)));
y  = sin(t)-v.*sin(t);
z = v.*(sqrt(1+2*cos(t))./(1+cos(t)));
X = [x,x];
Y = [y,y];
Z = [z,-z];

with s =2000 and g = 10 i get for X, Y and Z each a 2000x20 matrix.

I already calculated the the principal curvatures, surface and volume, but i have absolutly no idea how to unroll the surface in an 2d plot.

Answer 1

[Tanmay Das]

Hi,

Contourf projects the 3D plot into a 2D contour plot. You just need to add this line at the end of your code:

contourf(X,Y,Z);