Points, tripoints, and coordinate systems

Axes

The game is three-dimensional, with the axes oriented as follows:

• The x-axis goes from left to right across the display (in non-isometric views).
• The y-axis goes from top to bottom of the display.
• The z-axis is vertical, with negative z pointing underground and positive z pointing to the sky.

Coordinate systems

CDDA uses a variety of coordinate systems for different purposes. These differ by scale and origin.

The most precise coordinates are map square (ms) coordinates. These refer to the tiles you see normally when playing the game.

Two origins for map square coordinates are common:

• Absolute coordinates, sometimes called global, which are a global system for the whole game, relative to a fixed origin.
• Local coordinates, which are relative to the corner of the current “reality bubble”, or map roughly centered on the avatar. In local map square coordinates, x and y values will both fall in the range [0, MAPSIZE_X).

The next scale is submap (sm) coordinates. One submap is 12x12 (SEEXxSEEY) map squares. Submaps are the scale at which chunks of the map are loaded or saved as they enter or leave the reality bubble.

Next comes overmap terrain (omt) coordinates. One overmap terrain is 2x2 submaps. Overmap terrains correspond to a single tile on the map view in-game, and are the scale of chunk of mapgen.

Largest are overmap (om) coordinates. One overmap is 180x180 (OMAPXxOMAPY) overmap terrains. Large-scale mapgen (e.g. city layout) happens one overmap at a time.

Lastly, these is a system called segment (seg) coordinates. These are only used in saving/loading submaps and you are unlikely to encounter them.

As well as absolute and local coordinates, sometimes we need to use coordinates relative so some larger scale. For example, when performing mapgen for a single overmap, we want to work with coordinates within that overmap. This will be an overmap terrain-scale point relative to the corner of its containing overmap, and so typically take x and y values in the range [0,180).

Vertical coordinates

Although x and y coordinates work at all these various scales, z coordinates are consistent across all contexts. They lie in the range [-OVERMAP_DEPTH,OVERMAP_HEIGHT].

Vehicle coordinates

Each vehicle has its own origin point, which will be at a particular part of the vehicle (e.g. it might be at the driver’s seat). The origin can move if the vehicle is damaged and all the vehicle parts at that location are destroyed.

Vehicles use two systems of coordinates relative to their origin:

• mount coordinates provide a location for vehicle parts that does not change as the vehicle moves. It is the map square of that part, relative to the vehicle origin, when the vehicle is facing due east.

• map square is the map square, relative to the origin, but accounting for the vehicle’s current facing.

Vehicle facing is implemented via a combination of rotations (by quarter turns) and shearing to interpolate between quarter turns. The logic to convert between vehicle mount and map square coordinates is complicated and handled by the vehicle::coord_translate() and vehicle::mount_to_tripoint() families of functions.

Currently, vehicle mount coordinates do not have a z-level component, but vehicle map square coordinates do. The z coordinate is relative to the vehicle origin.

Point types

To work with these coordinate systems we have a variety of types. These are defined in coordinates.h. For example, we have point_abs_ms for absolute map-square coordinates. The three parts of the type name are dimension _ origin _ scale.

• dimension is either point for two-dimensional or tripoint for three-dimensional.
• origin specifies what the value is relative to, and can be:
  • rel means relative to some arbitrary point. This is the result of subtracting two points with a common origin. It would be used for example to represent the offset between the avatar and a monster they are shooting at.
  • abs means global absolute coordinates.
  • sm means relative to a corner of a submap.
  • omt means relative to a corner of an overmap terrain.
  • om means relative to a corner of an overmap.
  • veh means relative to a vehicle origin.
• scale means the scale as discussed above.
  • ms for map square.
  • sm for submap.
  • omt for overmap terrain.
  • seg for segment.
  • om for overmap.
  • mnt for vehicle mount coordinates (only relevant for the veh origin).

Raw point types

As well as these types with origin and scale encoded into the type, there are simple raw point types called just point and tripoint. These can be used when no particular game scale is intended.

At time of writing we are still in the process of transitioning the codebase away from using these raw point types everywhere, so you are likely to see legacy code using them in places where the more type-safe points might seem appropriate.

New code should prefer to use the types which include their coordinate system where feasible.

Converting between point types

Changing scale

To change the scale of a point without changing its origin, use project_to. For example:

point_abs_ms pos_ms = get_avatar()->global_square_location().xy();
point_abs_omt pos_omt = project_to<coords::omt>( pos_ms );
assert( pos_omt == get_avatar()->global_omt_location().xy() );

The same function project_to can be used for scaling up or down. When converting to a coarser coordinate system precision is of course lost. If you care about the remainder then you must instead use project_remain.

project_remain allows you to convert to a coarser coordinate system and also capture the remainder relative to that coarser point. It returns a helper struct intended to be used with std::tie to capture the two parts of the result. For example, suppose you want to know which overmap the avatar is in, and which overmap terrain they are in within that overmap.

point_abs_omt abs_pos = get_avatar()->global_omt_location().xy();
point_abs_om overmap;
point_om_omt omt_within_overmap;
std::tie( overmap, omt_within_overmap ) = project_remain<coords::om>( abs_pos );

That makes sense for two-dimensional point types, but how does it handle tripoint? Recall that the z-coordinates do not scale along with the horizontal dimensions, so z values are unchanged by project_to and project_remain. However, for project_remain we don’t want to duplicate the z-coordinate in both parts of the result, so you must choose exactly one to be a tripoint. In the example above, z-coodinates do not have much meaning at the overmap scale, so you probably want the z-coordinate in omt_within_overmap. That can be done as follows:

tripoint_abs_omt abs_pos = get_avatar()->global_omt_location();
point_abs_om overmap;
tripoint_om_omt omt_within_overmap;
std::tie( overmap, omt_within_overmap ) = project_remain<coords::om>( abs_pos );

The last available operation for rescaling points is project_combine. This performs the opposite operation from project_remain. Given two points where the origin of the second matches the scale of the first, you can combine them into a single value. As you might expect from the above discussion, one of these two can be a tripoint, but not both.

tripoint_abs_omt abs_pos = get_avatar()->global_omt_location();
point_abs_om overmap;
tripoint_om_omt omt_within_overmap;
std::tie( overmap, omt_within_overmap ) = project_remain<coords::om>( abs_pos );
tripoint_abs_omt abs_pos_again = project_combine( overmap, omt_within_overmap );
assert( abs_pos == abs_pos_again );

Changing origin

project_remain and project_combine facilitate some changes of origin, but only those origins specifically related to rescaling. To convert to or from local or vehicle coordinates requires a specific map or vehicle object.

TODO: write some examples once this is implemented.

Point operations

We provide standard arithmetic operations as overloaded operators, but limit them to prevent bugs. For example, most point types cannot be multiplied by a constant, but ones with the rel origin can (it makes sense to say “half as far in the same direction”).

Similarly, you can’t generally add two points together, but you can when one of them has the rel origin, or if one of them is a raw point type.

For computing distances a variety of functions are available, depending on your requirements: square_dist, trig_dist, rl_dist, manhattan_dist. Other related utility functions include direction_from and line_to.

To iterate over nearby points of the same type you can use closest_points_first.