polar coord on polar plane

[arturv]

Hello people of math

I want to generate polar coordinates on polar plane. I have r₂ but don’t really know how to find θ₂ properly

Code:

// polar coordinates
r = sqrt( s*s + t*t );
th = atan( s, t );

a = 0.2  // r coordinate of new polar centre
b = 3.1  // theta coordinate of new polar centre

r2 = r*r-2*r*a*cos(th-b)+a*a; // calculating new r
th2 = atan( r - a, th - b ); // calculating new theta using cartesian equation

so I’m using cartesian equation to find th2 but obviously its not really correct. There is some bending in theta direction and other issues when crossing the centre etc..

Just wondering if anyone knows a proper equation

Thanks

[arturv]

actually, maybe I should ask this question in math section?

[DarkBeam]

actually, maybe I should ask this question in math section?

Maybe.

[arturv]

got it

  theta' = arctan([r sin(theta)-r0sin(theta0)]/[r cos(theta)-r0cos(theta0)])

or

  theta' = atan2(r sin(theta) - r0 sin(theta0), r cos(theta) - r0 cos(theta0))