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Fov and los
Below are the required properties of the FOV algorithm. Most of them taken from this discussion.
- symmetry (everything you see can see you, and vice versa)
- digital lines (there is a digital line from actor to his every visible tile going exclusively through visually reachable tiles)
- efficiency (we have to allow battles involving many units)
- expansive wall display (you can see all of a room's walls while standing anywhere inside of it)
- retreating is safe (if you keep retreating into a corridor, once you are hidden from an immovable monster's sight, you stay hidden; this applies for arbitrarily twisted corridors of width 1 (probably enough to consider digital lines); with symmetry, this implies that retreating doesn't improve your sight, either)
- no blind corners (moving diagonally around a corner does not place you in melee range of a previous non-visible tile)
- permissive way of determining if a tile is seen, resulting in few shadows for areas with lots of randomly scattered pillars; otherwise exploring such areas is tedious
- realistic physical interpretation of walls, so that visible implies reachable by walking, if no translucent obstructions. (Note however that digital lines are not the only curves with minimal distance in the chessboard metric between two points, so there is not a perfect match between the movement metric and the FOV metric. But at least digital lines are a subset of shortest lines and their length counted as the number of tiles is equal to the movement distance between their start and end. If the Angband metric (longer axis plus half of the shorter axis) or Euclidean metric is used, the discrepancy is much wider, resulting in complex game mechanics, so that, e.g., melee characters prefer to approach their foes diagonally and ranged characters prefer vertical and horizontal lines.)
The 'realistic shadows' properties from the Roguebasin discussion are disregarded on the principle of gameplay over realism. The properties are even less important in games with no passwall monsters and a very small real world tile size (e.g., 1m by 1m), where we can realistically expect that heroes peek around the flimsy single pillars, room entrances, etc. If the engine is used for other kinds of games, we'd have to reconsider the trade-offs.
Property 5 is only satisfied by algorithms that, to tell if a tile is visible from another, analyze visibility between continuous sections of each of the two tiles, not a small set of points in one of the tiles. Such algorithms are beam casting (e.g, parallel beams starting from diagonals of a tile), Digital FOV (DFOV, visibility from a cross dividing a tile into 4 squares) and Precise Permissive FOV (PFOV, visibility from an 'X' dividing a tile into 4 triangles). Beam casting is usually either costly or has artifacts. Digital FOV and Permissive FOV easily satisfy 4 and 6, which are not so natural for many other algorithms. Digital FOV satisfies 8 (walls are beveled and pillars are diamonds) and is more permissive than Permissive FOV, but the latter is reported by people to be much more efficient, at least in current implementations, and permissive lines are more visually straight than digital lines.
PFOV is clean-room implemented at https://github.com/AllureOfTheStars/Allure/blob/last_standalone/src/FOV/Permissive.hs, according to the description in Precise Permissive FOV. Its general structure is modeled after recursive shadow casting and so it avoids inspecting tiles behind obstacles, which should make it much faster than a straightforward implementation on maps with long corridors. It is transformed into Digital FOV, at https://github.com/AllureOfTheStars/Allure/blob/last_standalone/src/FOV/Digital.hs, as described in Digital field of view implementation. The DFOV implementations turns out to be much simpler and somewhat faster than PFOV implementation. It's faster especially for conventional dungeons, because it needs half as many sweeps for rectangular rooms with the hero in the middle. OTOH, it makes a bit more tiles visible, so the algorithm is run for more tiles and refreshing them all is more costly.
The required properties of the LOS algorithm:
- symmetry (including the line to target, which should be the same as line from target)
- digital lines
- can be hit = is visible and directly targetable (no trick shots required)
- retreating is safe
By setting visible = targetable (that's the choice for this game) and the properties of FOV, we get properties 3, 4. By drawing lines to target with Bresenham's line algorithm, swerving one tile, whenever required, we get 1 and 2. Note that the distance a projectile covers is calculated using the chessboard metric, but the trajectory is determined by a (quasi?)metric induced by digital lines. This is a discrepancy, but much less pronounced than if the FOV radius and LOS distance was calculated with the Angband or Euclidean metric.
The matter gets complicated when we have tiles that are clear, but not walkable (glass blocks), walkable, but not clear (curtains), clear, but not lit, etc. We've made a design decision that the only information the player gets is the total set of visible (not visually reachable) tiles --- the sum for all his party actors. This is KISS and cheap computationally and UI-wise. So, if many actors are within sight radius of a visible target tile, the player can't tell which of the actors actually sees it (only that at least one does). Consequently, if an actor is separated from a visible tile by an unexplored tile, the player can't tell if the actor can shoot at the tile (if the unexplored tile is glass or empty floor or perhaps solid wall). The player needs to experiment in that case. This also leads to interesting trade-offs in path-finding through unexplored regions, both by AI and by human players.