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