File:TorusSystoleLoop.png

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This graphic was created in MATLAB using the following code:

%create u-v grid space
u=linspace(0,2*pi,120);
v=linspace(0,2*pi,120);
[u,v]=meshgrid(u,v);

R=0.5;                      %set large radius of torus
r=abs(cos(v/2))*0.2+0.05;   %set small radius to vary with angle

%parametrization
x=(R+r.*cos(u)).*cos(v);
y=(R+r.*cos(u)).*sin(v);
z=r.*sin(u);

H=surf(x,y,z);
hold on;			    %put a hold on this figure
set(H,'FaceColor',[0.25 0.25 0.75],'EdgeColor','none');
set(H,'SpecularColorReflectance', 0.2, 'DiffuseStrength', 0.8);
set(H,'AmbientStrength', 0.3,'FaceLighting','phong');
set(H,'SpecularExponent', 100);

daspect([1 1 1]);   %set ratio of x,y,z axes
axis tight;         %fit axes to figure
axis off;           %don't show axes
view(190, 40);      %set viewing angle
camlight (-50, 54); lighting phong; %add light source

%add another torus to show tightest place on the torus
R2=0.075;
r2=0.025;

x2=(R2+r2.*cos(u)).*cos(v)-0.5;
y2=r2.*sin(u);
z2=(R2+r2.*cos(u)).*sin(v);

H2=surf(x2,y2,z2);
set(H2,'FaceColor',[0.75 0.25 0.25],'EdgeColor','none');
set(H2,'SpecularColorReflectance', 0.2, 'DiffuseStrength', 0.8);
set(H2,'AmbientStrength', 0.5,'FaceLighting','phong');
set(H2,'SpecularExponent', 100);

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