I am trying to find the center of a logarithmic spiral in the complex domain given very limited information. Consider $4$ points on the spiral called $p_1,p_2,p_3,p_4$. Assume that $p_1,p_2$ and $p_3$ are close to one another such that their unwrapped delta-angles are small $(\ll π)$. $p_4$ can be anywhere else on the curve without constraints (could be far away from $p_1,p_2,p_3$). I am given only $3$ complex numbers; $p_1-p_2$, $p_2-p_3$, and $p_4$. Is this enough information to calculate the center of the spiral?
Bob