Which way is North on a map rotated 45 degrees?

[johnegracejr]

When looking at a map that has been rotated 45 degrees, which way is North?

I have tow theories: Reading left to right, North would be upper left (but that would only work for some languages). More likely, using geometry as a starting point, a circle is measure clockwise with 0 degrees pointing straight up and 45 degrees would be upper right. Any other thoughs?

If it's not too much trouble I would like to know the accepted answer and the background about "why" that's the answer.

Thanks in advance from a new member.

[Redrobes]

Hello John, and welcome to the guild. You pose an interesting question but I think I would need a bit more clarity before I could even attempt an answer.

First of all is the map rotated clockwise or anticlockwise. Second, was North straight up before the map was rotated. Third, are we rotating the map and the projection on it or are you rotating the border and keeping the projection stationary such that when you realign the map the projection has to be rotated with it.

At first stab at an answer though I would say the representation of North is whatever the grid or the compass says it is.

Can I ask a question in return... why are you asking about a map being rotated at all ? Is this some kind of conundrum or test or a split of opinion on the topic that needs resolving ?

[johnegracejr]

Unfortunately I don't know which way it was rotated or I would know the answer. Similarly if there was a legend (or a compass mark) I would also know. This question has been on my mind for years. It started with computer games, mostly rpgs, but has occured in a few real life work situations too. In about 75% of the cases the borders are rotated and the contents aren't but the other times everything is rotated.

Now that you've mentioned the borders being rotated I guess the most correct answer would be up is still North (should that be capitalized) but if that's the case why rotate the borders at all?

Appreciate you quick response and thoughtful questions, which I'll give some thought and reply again later. The latest example is an android phone game called Saga of Survival: Stormfall but I have literally asked myself this question hundreds of times.

[waldronate]

If the question is about tiled isometric-view video games (see https://en.wikipedia.org/wiki/Isometric_projection and https://en.wikipedia.org/wiki/Tile-based_video_game), then it's a less meaningful question because isometric games tend to have a huge number of simplifying assumptions built into them. First, the game typically doesn't have a "projection" as such, because the game system is based on a square grid and covers such a small and abstract area that spherical distortion never comes into play. The game designer will typically assign the notion of "north / south / east / west" to either "grid up / grid down / grid left / grid right" or "screen up / screen down / screen left / screen right" or some other variation on grid coordinates / screen coordinates (grid coordinates will often end up with north at 45 degrees up and right or 45 degrees up and left, while screen coordinates often go with north being up). Using one of the game grid axes as "north" simplifies discussion in terms of keypresses mapping to the cardinal directions. Using screen directions as "north" keeps the familiar concepts for the user.

The above information relates to the classic games that are grid-based and units can only occupy one grid space because the game's implementation is more or less "units must occupy one grid space because we have one byte of memory to store one grid space and it has to index into one of our 256 different sprites". More modern third-person-perspective games based on fully 3D engines allow rotation around the in-world "up" axis and may dispense with the grid (partially or entirely), but might keep the isometric diamond shape onscreen purely for nostalgia reasons.

One thing to note above is that I keep harping on the idea of in-game world space "grid space" as being distinct from "screen space". That's a really important distinction because the abstract notion of "North" on the displayed screen will be whatever is convenient for the game developer. If you start with a simple tile-based game, you are starting from a rectangular grid. Using rectangular tiles for display of a piece of the game world gets you a rectangular section of the screen. Using diamond-shaped isometric tiles of the exact same piece of the game world gets you a diamond-shaped section of the screen. Either of those raw displays can be clipped to an arbitrary boundary, but just keeping the simplest-possible display will get you specific shapes.

I hope that made some sense, anyhow.