Equations for arc interpolation

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

$DX = R \cdot \cos(a) X_i - R \cdot \sin(a)Y_i$

$DY = R \cdot \cos(a) Y_i + R \cdot \sin(a)X_i$

$R$ 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.