# What is the difference between an orthographic and oblique projection?

They both seem to be a parallel projection. I know that the angles of axes of viewing differ based on the type of orthographic projection (eg, an isometric projection has equal angles for all the axes).

But what sets the oblique projection apart from the orthographical projection?

I found this image on Wikipedia and I don't see what sets the two oblique examples apart from the dimetric example.

• With axonometric (iso/di/trimetric), the axes are foreshortened based on their angle to the viewer. See the trimetric example: the 3-unit distance left of the door is longer than the 3-unit height to the eave. In oblique images, these scales are arbitrary, and often exaggerated to ensure two or more axes are in 1:1 scale - see how the bottom-right example shows a 1:1 front view AND a 1:1 representation of the length of the roof in a single view. As Josh Petrie notes this is done by tilting the projection plane, but I find it easier to think about in terms of its observable effect on the image. Feb 24 '15 at 19:41
• I think this should be an answer :) Feb 24 '15 at 20:17

They're both similar, in that they are both parallel projections (lines that are parallel in the source are parallel in the projection). In a parallel projection of (x, y, z) onto the xy plane becomes (x + az, y + bz, 0). When a and b are equal, the projection is orthographic; otherwise the projection is oblique.

Another way to look at it is that in an orthographic projection, the projector lines intersect the plane being projected on to at a perpendicular angle (thus, they are orthogonal, thus the name of the projection), whereas in an oblique projection those lines form oblique angles (non-right angles) with the projection plane.

I would comment on Josh's accepted answer, which is certainly correct, but you need 50 rep to do that and I just happened to see this on the "Hot Network Questions" sidebar. But I digress...

Coming from a background in geography, there's an easy example of orthogonal vs oblique projections in remote sensing data (like the aerial imagery you see on Google or Bing Maps). Note the rooflines most especially in the following images.

Orthagonal imagery is usually shot from a plane (or satellite) with a camera pointing directly out the bottom of the plane and looks directly down on the ground below. Thus, assuming the aircraft is flying level and the ground is flat, you can take Josh's statement about projector lines intersecting the plane perpendicularly and make the plane the ground and the projector source the camera.

Oblique projection imagery is captured at an angle and once properly georeferenced, can provide imagery that can be measured and is generally a bit more "natural" in appearance (in Bing Maps they call this "Bird's Eye"). Again, the projector lines (extending out from the camera) hit the plane at an oblique angle, thus it is an oblique projection.

I know this may not help you actually code a game, but hopefully the photos help give you a better sense of the math involved!

(Image sources: http://www.eagleview.com/Products/ImageSolutionsAnalytics/PictometryImagery.aspx - I don't have any affiliation with them, this page was just a good reference to pull examples from)

• Both the images you've shown are actually axonometric/orthographic projections. Although we'd commonly term the angle in the second one as an "oblique view," it's not an oblique projection, because the rays are still perpendicular to the image plane (to within the capabilities of the optics & image processing in play). The fact that the projection rays are not perpendicular to the ground plane is a different matter. Feb 24 '15 at 19:39
• Interesting! That definitely makes sense though. Always neat to learn something new! Feb 24 '15 at 20:38