I have the equations for arc interpolation when the origin is the center of the arc:

$DX = R \cdot \cos(a) X_i - R \cdot \sin(a)Y_i$
$DY = R \cdot \cos(a) Y_i + R \cdot \sin(a)X_i$
$R$ is the radius of the arc. The arc is divided into $N$ segments a.
The question is how to get the equations for the arc interpolation when the origin is not the center of the arc.
Thank you.