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I am laughing at myself ignorant on this. Google didn't produce an obvious answer. Could someone explain what orthogonal map and isometric map are, and how they are different?

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It is probably worth noting that maps are neither orthogonal nor isometric. What you are really asking about are projections. – Williham Totland Jan 12 '12 at 8:30
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@WillihamTotland Technically, yes. But the terms orthogonal map and isometric map are also sometimes used in the context of 2D tile based games to describe the game's point of view. For instance, this tool uses that designation. It's good to be aware of these alternative terminologies. – David Gouveia Jan 12 '12 at 19:49
    
@DavidGouveia: Thing is; the underlying map is still the same. Calling a map isometric or orthogonal is wrong; and doesn't even make any sense. – Williham Totland Jan 12 '12 at 22:16
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@WillihamTotland /shrugs/ Semantics.. I wasn't the one who made that up. It's just a common terminology, and simple to understand. You're absolute right that the underlying map does not change. But the way the map is rendered does, which I guess is what this is referring to, even if the wording does not make sense from a technical point of view. – David Gouveia Jan 12 '12 at 22:24
up vote 52 down vote accepted

I made a picture to sum it up. Basically, the difference between both types of maps has mostly to do with the angle formed between each axis which results in one appearing to be seen from a topdown point of view, while the other appears to be seen from an angle:

enter image description here

It is also worth noticing the visual difference between an isometric projection and perspective projection which is what almost every 3D game uses.

enter image description here

Notice how lines are drawn parallel to each other when using an isometric projection, while when using a perspective projection, lines converge towards one (or more) vanishing points.

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Wow. Awesome answer! Thanks so much. – Tae-Sung Shin Jan 12 '12 at 6:20
    
I feel this answer is misleading. Isometric does foreshorten the coordinates, the difference is that isometric is equally foreshortened along each axis. Also, orthographic specifically means each ray is perpendicular to the projection plane, not the projected axes. – Pubby Jan 12 '12 at 20:20
    
@Pubby I guess you're right. I'm not an artist so I've never been formally educated in the field of graphical projections beyond what is typically used in computer games. I would like to note though that the original question made no mention of graphical projections, and in my interpretation, asked simply for the difference between an orthogonal map and an isometric map - an informal concept sometimes used in 2D tile based games. Therefore I may also argue that your answer, although informative, does not answer the question. – David Gouveia Jan 12 '12 at 21:00
    
@Pubby So instead, I've decided to take the route of making my answer less formal. Does it still contain any misleading information? – David Gouveia Jan 12 '12 at 21:00
    
wow ! illustration using images - clarify all things at once. Perfect. I respect you @DavidGouveia ! Thx for such great illustration.\ – Sagar R. Kothari Jun 3 '12 at 14:45

From what I understand, an orthogonal tile map is more of a top-down style (such as this), although they can appear to have some tilt (that is, showing more front, back, side, etc). Orthogonal tiles will appear rectangular. In isometric tile maps, you view the tiles at a 45-degree angle; as a result, the tiles are generally diamond shaped (as seen here). Also see this Wikipedia article on isometric projection in games.

Sorry that I can't explain it any more formally!

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Good explanation! Thanks :) I like the way u should tiles. They cleared my concept. – Lara Dec 24 '13 at 13:17

An orthographic projection is one where the projection rays are perpendicular to the projection plane.

These are examples of orthographic projections, specifically axonometric. The first is perspective.

An isometric projection is a type of axonometric projection (and thus a type of orthographic) with 120 degrees between each projected coordinate axis.

Note that orthographic is sometimes used for instances where the plane of the object is parallel to the projection plane, such as a top-down map, however this is only a small case of what it encompasses.

Orthographic projections are a type of parallel projection, which is not shown in the diagram.

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I don't have time to type up a good answer, but I wanted to throw in that the difference between orthogonal and isometric maps goes beyond visual perspective in games. Maps are not just images or views in games, but have many things which happen within them and these things work differently between the two map types. Many of these differences are not seen by the user. For example, an algorithm used to determine trajectory of an arrow being shot by a player can be different between the two map types. The differences in the sprite of the arrow/shot can be considered a matter of visual prospective, but the math differs as well and is outside of the players view/perspective. While this may not answer "the" difference between the two, it describes one of many ways that the two are different outside of visual perspective.

It's also worth noting that maps in games often use many levels and groups of objects to create a specific view. How objects interact between these different layers and groups is different in the two maps as well (such as collision detection) and is typically easier when orthogonal.

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Considering that this question is from 2012, you don't need to hurry. You have all the time in the world to write a good answer. Also, the problems you mentioned can be easily circumvented by separating the game logic from the rendering. You can easily calculate all game mechanics orthogonally and only do the visualisation in an isometric perspective. – Philipp Jan 25 at 14:33

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