# action

## Parameters for action

Several years ago, Florian Raudies, Swapnaa Jayaraman and I published a paper where we simulated the optic flow that infants would experience in different head/body postures. We computed cyclopian (one-eyed) flow on the basis of this schematic: Here, the key parameters were the instantaneous translation $$(v_x{}, v_y{}, v_z{})$$ and rotation $$(\omega_{x}, \omega_y{}, \omega_z{})$$ of the planar retina. Coupled with the optic flow equation, $$\begin{pmatrix}\dot{x} \\ \dot{y}\end{pmatrix}=\frac{1}{z} \begin{pmatrix}-f & 0 & x\\ 0 & -f & y \end{pmatrix} \begin{pmatrix}{v_x{}}\\ {v_y{}} \\{v_z{}}\end{pmatrix}+ \frac{1}{f} \begin{pmatrix} xy & -(f^2+x^2) & fy\\ f^2+y^2 & -xy & -fy \end{pmatrix} \begin{pmatrix} \omega_{x}\\ \omega_{y}\\ \omega_{z} \end{pmatrix}$$