[edit] Matlab source code
% illustration of the trace operator
function main()
L=5; % box size
N=10; % number of points in a lot of places
lw=2; % width of lines
alpha=0.23; % transparency
blue=[0, 0, 1];
red =[1, 0, 0];
black=[0, 0, 0];
% the function whose surface we will plot
f=inline('10-(x.^2-y.^2)/8', 'x', 'y');
XX=linspace(-L, L, N);
YY=XX;
[X, Y]=meshgrid(XX, YY);
Z=f(X, Y);
% the surface of the side
XS = [XX, 0*XX+L invert_vector(XX), 0*XX-L];
YS = [0*XX-L, YY, 0*XX+L, invert_vector(YY)];
XS = [XS' XS']';
YS = [YS' YS']';
ZS = 0*XS;
ZS(2, :) = f(XS(2, :), YS(2, :));
% the contour of the bottom
XD=[-L, L, L, -L, -L];
YD=[-L, -L, L, L, -L];
ZD=XD*0;
% prepare figure 1 for plotting
figure(1); clf; hold on; axis equal; axis off;
phi = -68; theta = 28;
view (phi, theta);
% plot the function u
surf(X, Y, Z, 'FaceColor', red, 'EdgeColor','none', 'FaceAlpha', 0.95);
surf(XS, YS, ZS, 'FaceColor', blue, 'EdgeColor','none', 'FaceAlpha', alpha);
camlight headlight; lighting phong; % make nice lightning
% contour of the bottom and the sides
plot3(XD, YD, ZD, 'color', black, 'linewidth', lw);
for i=1:length(XD)
plot3([XD(i) XD(i)], [YD(i), YD(i)], [0, f(XD(i), YD(i))], 'color', black, 'linewidth', lw);
end
% prepare figure 2 for plotting
figure(2); clf; hold on; axis equal; axis off;
view (phi, theta);
% plot the sides
surf(XS, YS, ZS, 'FaceColor', blue, 'EdgeColor','none', 'FaceAlpha', alpha);
% contour of the bottom and the sides
plot3(XD, YD, ZD, 'color', black, 'linewidth', lw);
for i=1:length(XD)
plot3([XD(i) XD(i)], [YD(i), YD(i)], [0, f(XD(i), YD(i))], 'color', black, 'linewidth', lw);
end
% plot the restriction of u
plot3(XS(2, :), YS(2, :), ZS(2, :), 'linewidth', 2*lw, 'color', red);
camlight headlight; lighting phong; % make nice lightning
figure(1); print('-dpng', '-r200', 'Trace1.png') % save to file.
figure(2); print('-dpng', '-r200', 'Trace2.png') % save to file.
function Z = invert_vector(X)
N=length(X);
Z = X;
for i=1:N
Z(i)=X(N-i+1);
end
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