Projection

Stereographic Projection

MATLAB code to project an image on a sphere. testImage.png must be present in your current MATLAB directory. x,y,z are original coordinates,X,Y,Z are projected coordinates.

[x,y]=meshgrid(linspace(-pi,pi,200));

%formula for projection

X=(2*x)./(1+x.^2+y.^2);

Y=(2*y)./(1+x.^2+y.^2);

Z=(-1+x.^2+y.^2)./(1+x.^2+y.^2);

img=imread('testImage.png');

hold on

h=warp(X,Y,Z,img); %projected image

warp(x,y,-1*ones(size(x)),img); %default image

hold off

axis equal

set(gcf,'color',[1 1 1]);