This looks like a great thread for some clarification and clean-up of our language. Consistent language is vital to avoiding confusion.
The theory behind the Dec-arc approach is that it concentrates the data used to model along the natural arc in declination that the object appears to trace across the sky.
The Dec-arc approach suffers the same naming pitfall as the all-sky approach. The biggest offender is the word *model*.
A model is a predictive set of algorithms that take existing real data, and apply that data to predict future outcomes. Numerous algorithms are employed to optimize results.
To acquire that data, we employ a technique we call *mapping*. The better the data we map, the better the predictive value.
We, as users, never see the model. We don't create the model. We do, however, collect the data that the model will employ, and we do this by *mapping* points in the sky.
APPM stands for Astro-Physics Point Mapper. APPM is simply the data collector for APCC. APPM allows you to strategize your data collection to best serve your individual needs.
Our observing and imaging goals determine the best approach to mapping and using the data.
Are you worried about pointing? Create an all-sky mapping in APPM and then go ahead and bounce from target to target.
Are you tracking just one or two objects over the course of a night? Then use APPM to map the relevant individual arcs in declination that you will be following as you track.
All we do is to map. What APCC does is to take our mapped data and build a model.
