SOS Field of View

The field of view (FOV) needs to be specified in SOS for non-standard projector layouts.

Distance Measured in inches from the projector lens to the center of the Sphere. Minimum value: 36.55.

Field of View --

The field of view is not used for pre-rendered data, but is used for the dynamically rendered data, so a correct value will help align the two as well as possible. If the field of view is incorrect, the dynamically rendered data may still look ok, since alignment is done with a dynamic grid, but the pre-rendered data will all be off by some amount. The pre-rendered data will never be perfect for a non- standard projector layout, since we don’t adjust perspective calculations, but the proper field of view will get it as close as possible.

The “classic” SOS field of view is 18.72°.

When adjusting the field of view ($\theta$) to compensate for differing projector to sphere center distances ($d$), we strive for a constant height ($h$) to be illuminated by the projector at the sphere center. This height is a few inches taller than strictly needed to illuminate a sphere of a given radius ($r$), to allow for some mechanical shift in the projector positioning, which we can then compensate for in software. It turns out that

$$h=2\times d\times \sin \left(\frac{\theta }{2}\right)$$

Given the classic field of view ($\theta$) of 18.72°, and a distance ($d$) of 6.61 sphere radii ($r$):

$$h=2.15\times r$$

The radius of the current sphere is 34 inches, $r=\mathrm{34"}$, so $h=\mathrm{73.1"}$. If we treat $h$ as a constant, we can calculate the field of view ($\theta$) for any distance ($d$).

$$\theta =2\times \arcsin \left(\frac{h}{2\times d}\right)$$

If $d$ is measured in sphere radii, $h=2.15$. If $d$ is in inches, then $h=73.1$.

• More information about configuring SOS can be found in the Operations and Systems Administration Manual
• Field of View Calculator (Microsoft Excel)