Abstract
Problem: How do 2D game developers choose between different tile shapes, walking directions, and projection methods — and how do these decisions interact?
Approach: Tim Cain draws on his engineering education and professional experience shipping Fallout and Arcanum to walk through the tradeoffs between 8-direction (square) and 6-direction (hex) walking, isometric vs. diametric vs. trimetric projection, and the tiling implications of each choice.
Findings: Most games labeled "isometric" are actually diametric (two equal angles, one different). The choice of walking grid, projection angle, and tile shape are deeply interdependent — affecting distance calculations, sprite memory, reflection opportunities, and visual appeal. Trimetric projection (used in Fallout) produces a subtly more interesting look that players preferred without knowing why.
Key insight: Tile shape, walking direction count, and projection method form an interconnected system — optimizing one constrains the others, and the "best" combination depends on what your designers want, what your artists can produce, and what your programmers can efficiently calculate.
1. Walking: 8 Directions vs. 6 Directions
In classic sprite-based 2D games (80s–90s era), developers had to choose between eight-direction walking (square grid) and six-direction walking (hex grid). Modern hardware allows 16 or 32 rotations, but back then memory and processing power forced this binary choice.
1.1. Eight-Direction Walking (Squares)
Eight directions means the four cardinal directions (up, down, left, right) plus four diagonals. The advantage is smooth walking in all eight directions.
The downside is distance calculation. Cardinal movement is easy — one unit per tile. But diagonal movement between square centers is √2 ≈ 1.414 units, an irrational number that can never be a clean integer regardless of your unit system. This creates problems for distance-based game mechanics.
1.2. Six-Direction Walking (Hexes)
Hex grids offer only six directions with two fewer sprite rotations needed. Depending on hex orientation (flat-top vs. pointy-top), movement will zigzag either vertically or horizontally when trying to travel in the non-native axis.
Smoothing hex movement causes characters to clip through adjacent hexes they weren't supposed to enter. However, the huge advantage is that distance is trivially easy to calculate — every direction is exactly one unit. This is why hexes are the standard for battle maps and strategy games.
2. Sprite Reflection: A Memory-Saving Trick
Since sprites must be stored for every walking direction, reflection (horizontal mirroring) can dramatically cut memory usage.
2.1. Reflection in 8-Direction Systems
With eight directions, you only need to store five unique sprite sets: up, down, right, upper-right diagonal, and lower-right diagonal. The left-facing and left-diagonal sprites are just mirror images. This saves nearly half the sprite memory.
2.2. Reflection in 6-Direction Systems
Hex reflection depends on orientation. Flat-top hexes require four unique sprites (reflect two). Pointy-top hexes need only three (reflect all three). Fallout used pointy-top hexes and could have reflected to save half its sprite memory but chose not to. Arcanum, which used eight directions, did use reflection.
2.3. Does Anyone Notice?
Tim reviewed years of game reviews and player feedback: nobody ever mentioned noticing sprite reflection. Only after developers revealed the technique did players claim they'd spotted it. It didn't affect sales or reviews — and the memory savings enabled more sprite variety and fewer frame-rate hitches from disk loading.
3. Projection Methods: Isometric, Diametric, and Trimetric
All 2D angled games use parallel projection (not perspective). In parallel projection, objects don't shrink with distance and parallel lines never converge. This is necessary because you want to load one sprite, one wall segment, one tile, and place it anywhere on screen without size adjustments.
3.1. Isometric (30/30)
True isometric has all three XYZ axes meeting at equal 120° angles, with both wall lines hitting the horizontal at 30°. Tim calls this "30/30" projection. Most games are not actually isometric despite the common label. At this angle, you can't see into buildings very well.
3.2. Diametric (45/45)
Diametric projection has two equal angles and one different. Most commonly the wall lines hit the horizontal at 45° — Tim's "45/45" projection. This is the most common choice because:
- You can see down into buildings much better
- Tiles have nice equal foreshortening on two axes
- Walls and tiles can be reflected (mirrored) around the vertical axis, saving memory
- It pairs naturally with 8-direction square walking
Arcanum used diametric projection. The left-going and right-going walls could be swapped via simple mirror operations.
3.3. Trimetric (60/30)
Trimetric has all three angles different. Fallout used this: 60° on the left, 30° on the right where walls meet the horizontal, creating top-corner angles of 90°/120°/150°.
Why trimetric? It works beautifully with hex walking. The 60/30 angles align with hex geometry, giving a rise/run ratio where going over one unit goes up exactly ½ — trivially fast to calculate via bit shifting even on old hardware.
The tradeoff: you cannot reflect walls because the two wall angles are different, requiring unique art for each direction.
3.4. The Fallout Visual Appeal Mystery
Tim notes that for years, players preferred Fallout's visual look over games like Baldur's Gate but couldn't articulate why. They attributed it to art style, lighting, or color palette. Tim believes trimetric projection itself is visually more interesting to the human eye than diametric — the asymmetry creates more visual variety, partly because less reflection means more unique art assets on screen.
4. Putting It All Together
The three decisions — walking directions, projection method, and tile shape — form an interdependent system:
- 8-direction walking + diametric (45/45) projection: The most common combination. Easy reflection, smooth walking, but diagonal distance is √2.
- 6-direction walking + trimetric (60/30) projection: What Fallout used. Clean distance math, visually distinctive, but no wall reflection and more art needed.
- Isometric (30/30): Rarely used in practice due to poor building visibility.
The "right" choice depends on three stakeholders: what designers want the game to feel like, what artists are comfortable producing, and what programmers can efficiently implement. Most teams default to diametric because it's the easiest to conceive, code, and create art for — with the only real downside being diagonal distance calculations that many developers simply accept.
5. References
- Tim Cain. YouTube video. https://www.youtube.com/watch?v=o4QcRQ5ucBk