Thank you!

This sentence ‘exp(-(x^2-2*sigma*x*y+y^2)/2/(1-sigma^2))/2/pi/sqrt(1-sigma^2)’

is puzzling for me! 

If we don't know these data is obtained from the normal distrbution,

we only have these data,how can I do?

I found a package 'rgl' which is used for 3D ,


#**********************alpha正态污染图***************************** 
alpha=0.1;sigma=5;
fn=function(x,y){(1-alpha)/(2*pi)*exp(-(x^2+y^2)/2)+
alpha/(2*pi*sigma)*exp(-(x^2+y^2)/(2*sigma))  }

x<-seq(-2,2,len=17);y<-seq(-2,2,len=17);
z<-outer(x,y,fn);
color<-rainbow(41)[1+round(10*outer(x,y,fn))]  ;
library(rgl)         #rgl为专门画3D图的包 
persp3d(x,y,z,color=color,smooth=FALSE)
surface3d(x,y,z+0.01,front="lines",back="culled")
#******************使图像自动旋转**********************************
M <- par3d("userMatrix")
play3d( par3dinterp( userMatrix=list(M,
                                     rotate3d(M, pi/2, 1, 0, 0),
                                     rotate3d(M, pi/2, 0, 1, 0) ) ),
        duration=4 )
movie3d( spin3d(), duration=5 )
#******************************************************************

Please check for me ,if you can draw a little time!

Thank you very much!