% illustration of a sphere with three handles
N = 100; % make 100 or so for good picture
S = 6.0; % sphere radius
r = 1.2; % torus cross section radius
R = 2.8; % torus big radius
Shift = 6.0; % shift torus away from origin
L = max(S, 2*r+R+Shift);
L = max(Shift + 2*r+R, S);
X = linspace(-L, L, N);
Y = linspace(-L, L, N);
Z = linspace(-L, L, N);
theta = pi/2.2; % angle between handles, measured from sphere center
W = zeros(N, N, N) + 100;
Mat = [cos(theta) -sin(theta);
sin(theta) cos(theta)];
for i=1:N
i
for j=1:N
for k=1:N
x = X(i);
y = Y(j);
z = Z(k);
W(i, j, k) = x^2+y^2+z^2-S^2; % sphere
for q=0:2 % tori
V = Mat*([x, y]');
x = V(1); y = V(2);
W(i, j, k) = min(W(i, j, k), ...
(sqrt((x-Shift)^2+y^2)-R)^2 + z^2-r^2);
end
end
end
end
if 1==1
% smooth a bit the places where the tori meet
XM = -2:60/N:2;
sigma = 1.5;
SM = exp(-XM.^2/sigma^2);
SM = SM/sum(SM);
W = filter(SM, [1], W, [], 1);
W = filter(SM, [1], W, [], 2);
W = filter(SM, [1], W, [], 3);
end
figure(1); clf; hold on;
axis equal; axis off;
light_green=[184, 224, 98]/256; % light green
H = patch(isosurface(X, Y, Z, W, 0));
isonormals(X, Y, Z, W, H);
mycolor = light_green;
%set(H, 'FaceColor', light_green, 'EdgeColor','none', 'FaceAlpha', 1);
%set(H, 'SpecularColorReflectance', 0.9, 'DiffuseStrength', 0.8);
%set(H, 'FaceLighting', 'phong', 'AmbientStrength', 0.35);
%set(H, 'SpecularExponent', 8, 'SpecularStrength', 0.2);
set(H, 'FaceColor', mycolor, 'EdgeColor','none', 'FaceAlpha', 1);
set(H, 'SpecularColorReflectance', 0.1, 'DiffuseStrength', 0.8);
set(H, 'FaceLighting', 'phong', 'AmbientStrength', 0.3);
set(H, 'SpecularExponent', 108);
daspect([1 1 1]);
axis tight;
colormap(prism(28))
view(-50, -54);
camlight headlight;
lighting phong;
%
print('-dpng', '-zbuffer', '-r400', sprintf('Sphere_with_three_handles%d.png', N));