Conversion of Toroidal Coordinates to Cartesian Coordinates
 

Dear Fellows,

I am working on fluid flow in curved pipes in which the flow is mainly represented by toroidal coordinates. I am working to convert equations from cartesian to toroidal coordinates. I came across the conversion from cartesian to toroidal coordinates as follows:

x= (R-r*CosB)CosA
y= (R-r*CosB)SinA
z= r*SinB

where R and r are Major and minor radius. and A, B are the angles varies from 0 to 2*pi.

Now I want to know the inverse relation from toroidal to cartesian. which is

r = sqrt( (R-sqrt(x^2+y^2))^2+ z^2)

but i dont know the relation for A and B. Can anybody please help me with this.

Thanks in advance.

Regards,