# Vergence, Version and Disparity¶

## VERGENCE ANGLE¶

Vg = L - R

where L is the angle of the left camera with respect to the homed optical axis (which is the cameras z-axis) as in the figure above; R is the angle of the right camera with respect to the homed optical axis.

## VERSION ANGLE¶

The version angle is the angle between the axis orthogonal to the baseline and passing through the baseline's midpoint and a line connecting this midpoint and the vergence point. The version angle satisfies the following nonlinear relation:

tan(Vs) = (tan(L) + tan(R)) / 2

However, the Firmware sends as version the following value:

Vs = (L + R) / 2

which holds for small angles (where tan(x)≈x), so that even though there is no lack of information since L and R angles can be accurately retrieved (see hereafter), the version Vs has physical meaning only for small values of Vs, L and R.

## CONVERTING [VERGENCE|VERSION] TO [DECOUPLED L|R]¶

Combining the above equations yields:

L = Vs + Vg/2

R = Vs - Vg/2

## DISPARITY¶

Disparity is defined as:

d = xl - xr

where xl is the left image normalized coordinate and xr is the right image normalized coordinate. Object closer to the cameras than the current point of fixation, will elicit a positive disparity value.