GM Cwethan wrote:
While they certainly can be, I'm not sure I agree that light sources are by default attached to intersections, do you have a source?
Dancing lights "Depending on the version selected, you create up to four lights that resemble lanterns or torches (and cast that amount of light)"
Torch A torch burns for 1 hour, shedding normal light in a 20-foot radius and increasing the light level by one step for an additional 20 feet beyond that area (darkness becomes dim light and dim light becomes normal light).
20-foot radius.
Nearly all area of effects that reference a 'radius' come down to some version of one of the templates in the last link, and all of those radii templates originate from an intersection. In this way a character holding a torch can switch their torch from corner to corner of their space to shed slightly more or less light in the areas around them. Spells work in a similar fashion. "The point of origin of a spell is always a grid intersection."* Think of fireball or grease.
Most folks using dancing lights go with torches, or hooded lantern-like light, to keep things simple on the map and illuminate all directions at once--a radius (or, in the case of four lights, multiple overlapping radii) of effect.
There is though a case for allowing bullseye lantern-like light which would project cones from a single square, but that would only be in one particular direction, and not be quite as helpful in this instance. I have never actually seen this use in a game, but the vagueness of the term 'lantern' in the entry for dancing lights might technically allow for it.
Your honor, I rest my case. ;)
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* Taken from the same page as the last link listed above.