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Parabola's mapping on the complex sphere

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parabola,mapping,complex sphere

FuQiuMianPaoWuXian.m
%The program is inspired by the topics in  
%Tristan Needham's book Visual Complex Analysis
%


%begin to plot the complex sphere
u=0:0.1:pi;
v=0:0.1:2*pi+0.1;
[U,V]=meshgrid(u,v);
X=2*sin(U).*cos(V);
Y=2*sin(U).*sin(V);
Z=2*cos(U)+2;
mesh(X,Y,Z);
hold on
axis equal

%begin to plot the graph on the complex plane
x=-20:0.1:20;
y=exp(x);
z=zeros(length(x));
plot3(x,y,z,'r.','markersize',6);
hold on

%begin to plot the project of the graph on the complex plane to the complex graph
A=x;
B=y;
X=16*A./(A.^2+B.^2+16);
Y=16*B./(A.^2+B.^2+16);
Z=4*(A.^2+B.^2)./(A.^2+B.^2+16);
plot3(X,Y,Z,'k.','markersize',5);
colormap(bone);
xlabel('X');
ylabel('Y');
zlabel('Z');
axis([-4 4 -4 4 0 3]);

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