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coordinate-systems.md

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Comprehensive list of all coordinate systems

Physical Coordinates

A coordinate in such a system describes positions in the 3D space of the game world and rendering scene.

Positions are stored in NE (northeast), SE (southeast) and UP (elevation).

Units for distances are terrain units (tu) and terrain elevation units (teu).

phys2/phys3

Physics coordinates in the game world.

Used in these systems:

  • Core engine
  • Gamestate
  • Game entity (unit/building/projectile/...) positions

Orthonormal 2D/3D (NE, SE)/(NE, SE, UP), in tu/teu Fixed-point integer with a 16-bit fractional part.

Origin is in the west corner of tile (0, 0) (at sea level), and the west corner of chunk (0, 0). Positive in NE, SE, UP directions.

A unit at (0.5, 0.5) is at the center of tile (0, 0), with on-tile offset (0.5, 0.5). A unit at (8, 8) is at the center of chunk (0, 0).

  • NE: north-east, in tu (terrain length unit)
  • SE: south-east, in tu (terrain length unit)
  • UP: guess what, in teu (terrain elevation unit)

scene2/scene3

Same as phys2/phys3 but for usage in the renderer. All phys2/phys3 passed to the renderer are eventually converted to scene2/scene3.

Used in these systems:

  • World renderer (sprite renderer)
  • Terrain renderer
  • Camera positioning

scene2/scene3 types can be converted to Eigen vectors that are used for rendering operations, e.g. creating uniforms, matrix transformations, vertex calculations, etc.

Eigen vectors are created from scene3 coordinates using this transformation:

Eigen(x, y, z) = (SE, UP / sqrt(8), -NE)

This will ensure that objects at coordinates are correctly displayed when using the camera (i.e. the north east of a coordinate will also be displayed in the north east when using the renderer camera).

UP is divided by sqrt(8) to mimic AoE2 terrain heights (from aspect ration calculations), This means that a coordinate elevation of 1 teu is displayed at height 1 / sqrt(8) in the 3D scene. The actual relation is pretty irrelevant though and could be adjusted with other values.

Eigen vectors created from scene2 coordinates have a fixed y value of 0.0f but are otherwise the same:

Eigen(x, y, z) = (SE, 0.0, -NE)

tile/tile3

Tile coordinates. Orthonormal 2D/3D (NE, SE)/(NE, SE, UP), integer, in tu/teu

Identical to phys2/phys3 systems, but uses integers

The center of a tile has phys coordinates (0.5, 0.5).

Used in these systems:

  • Terrain
  • Buildings

chunk

Chunk coordinates. Orthonormal 2D (NE, SE), integer, in 16tu/16teu

Similar to tile system, but describes chunks of 16x16 tiles

Used in these systems:

  • Chunks

Pixel Coordinates

Coordinates in these systems designate a position on the screen plane.

input

Coordinates used for input events. Orthonormal 2D (x, y), integer, in pixels

Origin is the top left corner of the viewport, positive in right and down directions

Used in these systems:

  • Input manager

viewport

Viewport coordinates. Used for rendering generic objects in the viewport. Orthonormal 2D (x, y), integer, in pixels

Origin is bottom left corner of viewport, positive in right and up directions

Used in these systems:

  • Debugging

camhud

Game camera coordinates. Orthonormal 2D (x, y), integer, in pixels

Origin is bottom left corner of viewport, positive in right and up directions

Used in these systems:

  • HUD drawing

term

Terminal character coordinates. Orthonormal 2D (x, y), integer, in characters

Origin is top left corner of console area, positive in right and down directions

Used in these systems:

  • Console drawing

camgame

Deprecated: replaced by scene2/scene3 and new camera system

Game camera coordinates. Orthonormal 2D (x, y), integer, in pixels

Origin is center of viewport, positive in right and up directions

Conversions

For rendering

Depending on whether objects are inside the game world, rendered as part of hud or the GUI, different conversion take place.

  • Object that are part of the game world are converted from phys to scene when passed to the renderer, and finally from scene to Eigen vectors when passed to OpenGL/Vulkan shaders
  • HUD objects for ingame objects (e.g. HP bars for units) are transformed from phys to camhud

For input processing

Again depending on whether inputs were aimed at an HUD object or an entity rendered by the game camera, they (i.e. mouse clicks) are transformed from input to phys or camhud.

Possible conversions between coordinate types

           scene2 <----> phys2 <--------> tile <--------> chunk
              |           |                |
              |           |                |
              |           |                |
input ***> scene3 <----> phys3 <--------> tile3
   |          |
   |          |
   ------> viewport <--> term
              |
              |
           camhud
  • Conversions from input to scene3 are realized with raycasting using the camera direction and position. As the calculation is done with floating point values, the result is subject to float rounding errors and therefore not precise.

Possible conversions to/from renderer types

scene2 ----> world space (Eigen::Vector2f)
   |
   |
scene3 ----> world space (Eigen::Vector3f)
   |
   |
viewport --> normalized device space (Eigen::Vector2f)

Translation details

The translations make use of current coordinate state (e.g. scroll position, stored in CoordManager) and additional infos to solve degrees of freedom (see below).

  • input -> viewport: just flip the y axis
  • camgame -> viewport: both are 'on-screen' coordinates, the difference is a linear offset of their (0, 0) point and the camera zoom
  • camhud -> viewport: linear offset of their (0, 0)
  • phys3 -> camgame: add the camera scroll position (given in phys3), then perform spatial transform
  • The other translations should be intuitive

Parameters

These parameters are needed to solve remaining degrees of freedom when translating a coordinate of one system to another.

  • chunk -> tile: needs tile-on-chunk coordinates
  • tile -> phys2: needs position-on-tile coordinates
  • phys2 -> phys3: needs UP component ()
  • scene2 -> scene3: needs UP component ()
  • tile -> tile3: needs UP component (elevation)
  • camgame -> phys3: needs UP component (elevation above terrain. reason: intersection between ray through camera and the terrain, e.g. for 'move here' command on a hill)