How to Compute r in Stereographic Projection from R^4 to R^3?

[whattttt]

I am computing a stereographic projection in R^4 and i think i am correct in setting
x=rcos(x)sin(y)
y=rsin(x)sin(y)
z=rcos(y)
but can't see how to compute r as I do not know to visualise it graphically as was possible in R^3, any help would be greatly appreciated

 

[Tinyboss]

That doesn't look like stereographic projection to me...do you mean spherical?

 

[whattttt]

No. In a previous example it was in R^3 and polar coordinates were used with x=rcosx and y=rsinx and r was computed from the diagram and equaled something like 2tan(pi-theta) which could be computed from the diagram by projection onto the x-axis but I'm not sure if such a formula exists in R^4

 

[lavinia]

I am computing a stereographic projection in R^4 and i think i am correct in setting
x=rcos(x)sin(y)
y=rsin(x)sin(y)
z=rcos(y)
but can't see how to compute r as I do not know to visualize it graphically as was possible in R^3, any help would be greatly appreciated

Stereographic projection is the same in all dimensions. Draw straight lines from the north pole through the points of the sphere and calculate the intersection of these lines with the hyperplane that is perpendicular to the direction of the north pole. You do not need polar coordinates for this.